INTEGRATION OF THE REGRESSION- BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION- ASSIGNMENT TRANSPORTATION MODEL

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1 Unversty of Kentucky UKnowledge Unversty of Kentucky Doctoral Dssertatons Graduate School 2010 INTEGRATION OF THE REGRESSION- BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION- ASSIGNMENT TRANSPORTATION MODEL Mewu An Unversty of Kentucky, Clck here to let us know how access to ths document benefts you. Recommended Ctaton An, Mewu, "INTEGRATION OF THE REGRESSION-BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION-ASSIGNMENT TRANSPORTATION MODEL" (2010). Unversty of Kentucky Doctoral Dssertatons Ths Dssertaton s brought to you for free and open access by the Graduate School at UKnowledge. It has been accepted for ncluson n Unversty of Kentucky Doctoral Dssertatons by an authorzed admnstrator of UKnowledge. For more nformaton, please contact UKnowledge@lsv.uky.edu.

2 ABSTRACT OF DISSERTATION Mewu An The Graduate School Unversty of Kentucky 2009

3 INTEGRATION OF THE REGRESSION-BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION-ASSIGNMENT TRANSPORTATION MODEL ABSTRACT OF DISSERTATION A dssertaton submtted n partal fulfllment of the requrements for the degree of Doctor of Phlosophy n the College of Engneerng at the Unversty of Kentucky By Mewu An Lexngton, Kentucky Co-Drector: Dr. Me Chen, Professor of Cvl Engneerng and Dr. Nck Stamatads, Professor of Cvl Engneerng Lexngton, Kentucky 2009 Copyrght Mewu An 2009

4 ABSTRACT OF DISSERTATION INTEGRATION OF THE REGRESSION-BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION-ASSIGNMENT TRANSPORTATION MODEL Regonal growth caused the emergence of traffc congeston and polluton n the past few decades, whch have started to affect small urban areas. These problems are not only related to transportaton system desgn but also to land use plannng. There has been growng recognton that the relatonshp between land use and transportaton needs to be understood and analyzed n a consstent and systematc way. Integrated urban models have recently been ntroduced and mplemented n several metropoltan areas to systematcally examne the relatonshp between land use and transportaton. The general consensus n the feld of ntegrated urban models s that each model has ts own lmtatons and assumptons because they are each desgned for dfferent applcaton purposes. Ths dssertaton proposes a new type of methodology to ntegrate the regresson-based land use model and the combned trp dstrbuton-assgnment transportaton model that can be appled to both metropoltan areas and small urban areas. The proposed ntegrated land use and transportaton model framework has three components: the regresson-based land use model, the combned trp dstrbutonassgnment transportaton model, and the nteracton between these two models. The combned trp dstrbuton-assgnment model framework provdes the platform to smultaneously ntegrate the transportaton model wth the land use model. The land use model s developed usng an easy-to-mplement method n terms of correlaton and regresson analyss. The nteracton between the land use model and the transportaton model s examned by two model frameworks: feedback model framework and smultaneous model framework. The feedback model framework solves the land use model and the transportaton model teratvely. The smultaneous model framework brngs the land use model and the transportaton models nto one optmzaton program after ntroducng the used path set. Both the feedback model and the smultaneous model can be solved to estmate lnk flow, orgn-destnaton (OD) trps, and household dstrbuton wth the results satsfyng network equlbrum condtons.

5 The proposed ntegrated model framework has an affordable and easy-tomplement land use model; t can be performed n small urban areas wth lmted resources. The model applcatons show that usng the proposed ntegrated model framework can help decson-makers and planners n preparng for the future of ther communtes. KEYWORDS: Integrated Land Use and Transportaton Model, Travel Demand Model, Combned Trp Dstrbuton and Traffc Assgnment, User Equlbrum, Entropy Mewu An

6 INTEGRATION OF THE REGRESSION-BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION-ASSIGNMENT TRANSPORTATION MODEL By Mewu An Dr. Me Chen Co-Drector of Dssertaton Dr. Nck Stamatads Co-Drector of Dssertaton Dr. Kamyar C. Mahboub Drector of Graduate Studes

7 RULES FOR THE USE OF DISSERTATIONS Unpublshed dssertatons submtted for the Doctor's degree and deposted n the Unversty of Kentucky Lbrary are as a rule open for nspecton, but are to be used only wth due regard to the rghts of the authors. Bblographcal references may be noted, but quotatons or summares of parts may be publshed only wth the permsson of the author, and wth the usual scholarly acknowledgments. Extensve copyng or publcaton of the dssertaton n whole or n part also requres the consent of the Dean of the Graduate School of the Unversty of Kentucky. A lbrary that borrows ths dssertaton for use by ts patrons s expected to secure the sgnature of each user. Name Date

8 DISSERTATION Mewu An The Graduate School Unversty of Kentucky 2009

9 INTEGRATION OF THE REGRESSION-BASED LAND USE MODEL AND THE COMBINED TRIP DISTRIBUTION-ASSIGNMENT TRANSPORTATION MODEL DISSERTATION A dssertaton submtted n partal fulfllment of the requrements for the degree of Doctor of Phlosophy n the College of Engneerng at the Unversty of Kentucky By Mewu An Lexngton, Kentucky Co-Drector: Dr. Me Chen, Professor of Cvl Engneerng and Dr. Nck Stamatads, Professor of Cvl Engneerng Lexngton, Kentucky 2009 Copyrght Mewu An 2009

10 For my well-beloved famly

11 ACKNOWLEDGMENTS I would lke to acknowledge and thank my advsor, Dr.Me Chen who offered ths great opportunty for me to complete ths dssertaton. Ths research would never have been accomplshed wthout your contnual gudance, support, nspraton n tme of doubt and trbulaton. Your nsghtful and sgnfcant challenges have been playng an extremely mportant role n mprovng ths study throughout many starts and stops along the way. I would lke to express my sncere grattude to Dr. Nck Stamatads for servng co-drector of my dssertaton. Your thoughtful support and advce have greatly mproved the qualty of ths dssertaton. Your genal frendshp and encouragement are always helpful n sustanng me through the dssertaton procedure. I truly apprecate Dr.Carl Lee, who s wllng to gve up precous tme to help mprovng math formulaton for ths dssertaton. Your valuable suggeston and dscusson s ndspensable n developng ths dssertaton. Thanks for provdng me wth math knowledge as well as nspraton and encouragement. I greatly apprecate Dr. Jerry G. Rose for servng as my commttee member. Both your nsghtful advce, comments and your encouragement, support are essental to makng sold progress on ths dssertaton. My specal thanks go to Dr.Ted Grossardt and John Rpy (Kentucky Transportaton Center), Davd Hamlton and Kong Ee (Kentucky Transportaton Cabnet), Ncole Lefever (Woodford County Plannng Commsson) for your generous sharng of your data resource, techncal assstance, encouragement and expertse. I must earnestly be grateful to my parents and my frends whose love and support made ths work possble. Although my parents n Chna are thousands of mles away from me, ther endless hours of chld care, unrelentng optmsm made t possble for me to pursue ths study at ease. Above all I want to thank my wfe Fengxa Wang and my son Fredy An who are always brngng me the love, laughter, encouragement and nspraton whch stmulates me to complete my goals and accomplsh ths work n greater perspectve.

12 TABLE OF CONTENTS ACKNOWLEDGMENTS... TABLE OF CONTENTS... v LIST OF TABLES... v LIST OF FIGURES... x CHAPTER 1 INTRODUCTION BACKGROUND Problem Statement Why Integrated Land Use and Transportaton Model INTEGRATED LAND USE AND TRANSPORTATION MODEL Connecton between Land Use and Transportaton Integrated Land Use and Transportaton Model RESEARCH OBJECTIVES AND CONTRIBUTION RESEARCH APPROACHES ORGANIZATION OF THIS DISSERTATION... 8 CHAPTER 2 LITERATURE REVIEW INTRODUCTION GRAVITY-BASED INTEGRATED URBAN MODELS Lowry Model Integrated Transportaton-Land Use Package Other Gravty-Based Models INPUT-OUTPUT-BASED MODEL Input-Output Framework MEPLAN Model v

13 2.3.3 Other Input-Output Based Models DISCRETE RESPONSE SIMULATION MODEL Dscrete Choce Model Bd-Rent Model LIMITATIONS OF EXISTING MODELS CHAPTER 3 DATA COLLECTION AND PREPARATION DATA COLLECTION Land Use Data Descrpton Transportaton Network Data TRANSPORTATION SYSTEM DATA CHAPTER 4 TRANSPORTATION MODEL DEVELOPMENT COMBINED TRIP DISTRIBUTION-ASSIGNMENT MODEL Model Formulaton User Equlbrum Condtons and Trp Dstrbuton Functon Model Soluton Model Calbraton Trp Generaton Model Calbraton Trp Dstrbuton Model Calbraton MODEL TEST Algorthm Model Test CHAPTER 5 LAND USE MODEL DEVELOPMENT MOTIVATION VARIABLE SPECIFICATION v

14 5.2.1 Land Use Structure Varables Transportaton Measures CORRELATION ANALYSIS Household Densty Correlaton Analyss Employment Densty Correlaton Analyss REGRESSION MODELING ANALYSIS Statstcal Technques Household Densty Model Development Employment Densty Model Development CHAPTER 6 THE INTERACTION OVERVIEW FEEDBACK MODEL CONFIGURATION Formulaton Numercal Example Future Model Applcaton SIMULTANEOUS MODEL CONFIGURATION Smultaneous Model Framework Smultaneous Model Soluton Future Model Applcaton MODEL COMPARISON Model Structure Comparson Model Output Comparson INTEGRATED MODEL CAPABILITY CHAPTER 7 CONCLUSIONS AND FUTURE RESEARCH v

15 7.1 CONCLUSIONS RECOMMENDATIONS FOR FUTURE RESEARCH APPENDIX Appendx 2-A1: ITLUP Land Use Model Equatons Appendx 2-A2: Quas-Gravty Model Equatons Appendx 2-B: MEPLAN Model Equatons Appendx 2-C: Locaton Choce Model Equaton n fve-stage Urban Model Appendx 3-A: Tradtonal Four-Step Travel Demand Model Development Trp Generaton External Trp Estmaton Trp Balancng Trp Dstrbuton Traffc Assgnment Model Calbraton Appendx 3-B: Comparson between Assgned and Observed Volumes Appendx 5-A: Household Dstrbuton Results from the ITLUP model Appendx 5-B: Numercal Value of Varables REFERENCES VITA v

16 LIST OF TABLES Table 3.1 Functonal System Mleage Table 3.2 Estmated OD Trp Table Table 3.3 Estmated OD Travel Tme Table 4.1 Trp Generaton, Household, and Employment n Each Zone Table 4.2 Trp Generaton Regresson Model Statstcs Table 4.3 Selected Lnk Attrbutes and Assgned Flow Table 5.1 Varable Descrpton Table 5.2 Correlaton Coeffcents for Household/Employment Densty Table 5.3 Household Densty Model Statstcs Table 5.4 Employment Densty Model Statstcs Table 5.5 Employment Densty Hstory Model Statstcs Table 6.1 Selected Feedback Model Output Table 6.2 Selected Smultaneous Model Output Table 6.3 Comparsons between Selected Feedback and Smultaneous Model Outputs v

17 LIST OF FIGURES Fgure 1.1 Accessblty Lnks Land Use and Transportaton... 4 Fgure 2.1 ITLUP Iteratve Model Structure Fgure 3.1 Woodford County TAZ Confguraton Fgure 3.2 Woodford County Roadway Network by Functonal Classfcaton Fgure 4.1 Relatonshp between Trp Generaton and Household Fgure 4.2 Relatonshp between Trp Generaton and Employment Fgure 4.3 Comparson between Observed and Estmated Trp Generaton Fgure 4.4 V/C Rato Frequency Dstrbuton Fgure 5.1 Commutng Patterns of the Study Area Fgure 5.2a Scatter Plot between Household Densty and Land Use Structure Varables Fgure 5.2b Scatter Plot between Household Densty and Transportaton Measure Fgure 5.3a Scatter Plot between Employment Densty and Land Use Structure Varables Fgure 5.3b Scatter Plot between Employment Densty and Transportaton Measure 72 Fgure 5.4 Comparson between Observed and Estmated Household Densty Fgure 5.5 Comparson between Observed and Estmated Employment Densty Fgure 6.1 Feedback Model Confguraton Fgure 6.2 Frequency Dstrbuton of V/C Rato from Feedback Model Fgure 6.3 Development Area Fgure 6.4 Comparsons of V/C Rato Frequency Dstrbuton between the Base Year and the Future Fgure 6.5 Smultaneous Model Confguraton Fgure 6.6 V/C Rato Frequency Dstrbuton from Smultaneous Model Output x

18 Fgure 6.7 Future Household Dstrbuton From Smultaneous Model Fgure 6.8 Comparsons of V/C Rato Frequency Dstrbuton between Feedback and Smultaneous Model Fgure 6.9 Comparsons of Household Dstrbuton between Feedback and Smultaneous Model x

19 CHAPTER 1 INTRODUCTION 1.1 BACKGROUND Problem Statement The emergence of explct transportaton problems such as congeston and polluton has caused ncreasng governmental and publc concerns about urban development. These problems are not only caused by transportaton system desgn, but also relate to land use plannng (urban sprawl) to some degree. There has been growng recognton that the relatonshp between land use and transportaton needs to be understood n a consstent and systematc way (Mller, 2004). Land use has been nteractng wth transportaton systems durng the course of urban development. For example, a new urban road wll encourage the development of adacent land. As the land s developed, travel demand wll ncrease, leadng to the congeston on ths new road. As the traffc ncreases, the road need to be mproved or a new road wll have to be bult. The new hghway wll then encourage addtonal land development, and the cycle contnues. Consderng envronmental and fnancal constrants, t s mplausble to buld our way out of congeston by contnung new hghway constructon. Ths cycle has resulted n reshapng polcy for metropoltan plannng (Downs, 1992). The nteracton between land use and transportaton needs to be better understood as we strve to resolve urban problems and work toward sustanable development. Recognzng the nteracton between transportaton systems and land use development, legslators have attempted to coordnate transportaton and land use plans. Recent legslaton ncludes the Inter-modal Surface Transportaton Effcency Act of 1991 (ISTEA), the Transportaton Equty Act for the 21st Century (TEA 21), and Safe, Accountable, Flexble, Effcent Transportaton Equty Act: a Legacy for Users 1

20 (SAFETEA-LU). ISTEA mandates that Metropoltan Plannng Organzatons (MPOs) ntegrate land use and transportaton plannng as stated n secton 134: In developng transportaton plannng plans and programs pursuant to ths secton, each metropoltan plannng organzaton shall, at a mnmum consder the followng The lkely effect of transportaton polcy decsons on land use and development and the consstency of transportaton plans and programs wth the provson of all applcable short- and long-term land use and development plans Although these laws explctly requre the coordnaton between land use plans and transportaton plans, none of them specfy the methods to be used to acheve ths ntegraton. In general, land use plans are developed by local government; regonal land use plans are rare, and only a few states have establshed statewde frameworks for land use plannng (Parsons Brnckerhoff, 1998). However, transportaton plans are developed by state Departments of Transportaton (DOT), MPOs and transt agences wth sgnfcant fundng support and regulaton from the federal government. Snce dfferent organzatons make publc decsons on land use plannng and transportaton plannng, coordnaton s dffcult. Even n the same ursdcton such as cty governments, land use and transportaton are often handled by dfferent departments, wth engneers responsble for transportaton decsons and planners responsble for land use plannng. As a result, land use planners, transportaton engneers, and decson makers could have dfferent or even conflctng goals and obectves (Parsons Brnckerhoff, 1998). Not only are land use plans and transportaton plans developed by separate organzatons, but these plans are mplemented by dfferent sectors. In the Unted States, transportaton nfrastructure nvestment and constructon are made by multple levels of governments, ncludng federal, state and local. Local government s responsble for mantanng local roads and new local roads are usually constructed by land developers through contrbuton or mpact fees. Federal and state governments are manly n charge of mantanng, rehabltatng and constructng federal and state hghway networks n order to accomplsh state or regonal goals. In contrast, most land use development and nvestment s made by ndvduals and frms wthn the context of local land-use plans. 2

21 Governments have lmted control on land-use development, snce land owners are permtted to develop ther property to ts hghest use. Governments only ntervene when development causes damage to protected speces or s ncompatble wth land use plans (Parsons Brnckerhoff, 1998) Why Integrated Land Use and Transportaton Model In response to both federal legslaton and ncreasng concerns regardng transportaton system problems, the ntegrated land use and transportaton (urban) model has been proposed as a tool to strengthen the coordnaton between land use plans and transportaton plans at dfferent level of governments. An ntegrated model can also be used to nvestgate the nterrelatonshp between land use and transportaton n a systematc way. Decson makers are able to use model outputs to assess the mpact of land use development on transportaton systems, and the mpact of transportaton polces on land use development. Publc polces can be developed that nclude transportaton demand management, congeston prcng, parkng prcng and management, and etc. Thus, the ntegrated model can play an mportant role n shapng the long-term future of a communty. 1.2 INTEGRATED LAND USE AND TRANSPORTATION MODEL Connecton between Land Use and Transportaton Land use can be defned as the way n whch land s used; t not only ncludes the buldngs on the land such as houses, factores, offces, stores, etc., but also ncludes the actvtes occurrng n these buldngs such as workng, shoppng, educaton, etc. (Mller, 2004). The partcpaton of out-of-house actvtes such as workng and shoppng gves rse to the need for travel on transportaton networks. For example, movement of people 3

22 from home to workplace and goods from one factory to another for producton cannot be acheved wthout the support of transportaton systems. It s ncreasngly recognzed that there s a sgnfcant nteractve relatonshp between land use and transportaton. Transportaton demand s engendered from land use development; but also transportaton systems have an mportant mpact on land use development by provdng accessblty. Land-use development confguraton s hghly related to transportaton system desgn, and vce versa. For example, f a transportaton system s bult dfferently, people wll use t dfferently, and they wll spatally organze themselves dfferently. Conversely, f a cty s bult dfferently, transportaton systems and needs wll be dfferent (Mller et al, 1999). Accessblty s the nexus between land use and transportaton systems. The nteracton between land use and transportaton can be measured by accessblty, whch reflects both attractveness and ease of reachng destnatons (Handy, 1993). The accessblty can be defned as a functon of land use development (urban actvty) dstrbuton and transportaton system confguraton. The pattern of land-use development has a sgnfcant mpact on accessblty snce t determnes the dstrbuton of attractveness n terms of urban actvtes. The structure and capacty of the transportaton system affects accessblty as sgnfcantly as land-use pattern snce t determnes the ease of reachng urban actvtes. For example, decreasng transportaton cost n terms of money or tme between any two places wll result n ncreasng nteracton between them. The relatonshp between land use and transportaton can be llustrated n Fgure 1.1 (Parsons Brnckerhoff, 1998). Fgure 1.1 Accessblty Lnks Land Use and Transportaton 4

23 1.2.2 Integrated Land Use and Transportaton Model A model s a pattern or representaton desgned to smulate the structure or workng of an obect. In the context of an urban actvty system, a model conssts of mathematc equatons that can be used to smulate human actvtes such as demographc dstrbuton and travel patterns (Mller et al, 1999). As a consequence, land use models are desgned to scentfcally smulate demographc and economc dstrbuton n urban or regonal areas. In ths dssertaton, land use models focus on the estmaton of the household, employment dstrbuton. The output of land use models wll provde key nputs for travel demand models. A transportaton model s prmarly devsed to forecast the spatal movement of people and goods and convert these movements nto traffc volume over a transportaton system. Hstorcally, land use models and transportaton models are developed separately and appled n urban and transportaton plannng. The nnate and ndspensable connecton between land use and transportaton systems brngs about the demand to comprehensvely unte transportaton models and land use models. An ntegrated model s desgned to capture the nterrelatonshp between land use and transportaton as much as possble (Mller, 2004). Therefore, creatng an ntegrated model ncludes not only developng land use and transportaton models but also nvestgatng the nteractons between them. 1.3 RESEARCH OBJECTIVES AND CONTRIBUTION There have been substantal research developments n the feld of ntegrated urban modelng. Several operatonal ntegrated urban models have been developed and appled to some metropoltan areas, whch wll be dscussed n Chapter 2. However, each model has ts own lmtatons because of dfferent applcaton purposes. For example, exstng ntegrated urban models cannot be appled to small urban areas snce they target large metropoltan areas. 5

24 Ths dssertaton ams to develop a new type of ntegrated land use and transportaton model framework that can be used on both small urban areas and large metropoltan areas. Ths new ntegrated model framework s composed of a regressonbased land use model, a combned trp dstrbuton-assgnment transportaton model, and the nteracton between these two models. The new model ntegrates the regressonbased land use model and the combned trp dstrbuton-assgnment transportaton model. Ths model framework s capable of estmatng urban actvty dstrbuton and traffc flow dstrbuton n a consstent and comprehensve way. Compared to exstng ntegrated models, ths model framework possesses several clear-cut advantages. Ths framework presents the frst nstance of ntegraton of the regresson-based land use model and the combned trp dstrbuton-assgnment transportaton model. It s desgned to be compatble wth modern transportaton modelng and to be affordable to mplement not only by metropoltan areas wth adequate resources but also by small urban areas wth lmted resources. The combned trp dstrbuton-assgnment model wll serve as the transportaton model n ths framework, whch has rarely been examned n exstng ntegrated model frameworks. Exstng ntegrated models mostly adopt a tradtonal four-step travel demand model as the transportaton model. Ths dssertaton wll contrbute to explorng the combned trp dstrbuton-assgnment transportaton model wthn the context of an ntegrated model framework, ncludng formulaton, calbraton, and applcaton. The land use model s developed usng an easy-to-mplement method n terms of correlaton and regresson analyss. Ths easy-to-mplement method has not been seen n the current lterature of land use models. Ths land use model can be reasonably acheved wth a lmted budget and wth lmted professonal crew n small urban areas. In contrast, exstng land use models requre extensve data and a large budget, whch typcal small urban areas cannot afford. The nteracton between land use and transportaton models wll be nvestgated by two methods n ths framework. One s to buld a feedback loop between these two models through ntermedate varables of accessblty; the other s to formulate the land use model and the transportaton model as a unted optmzaton program after 6

25 ntroducng the used path set. Under the method, the land use model and the transportaton model can be smultaneously solved. In the second method, household and employment dstrbuton, as well as traffc flow over the network are regarded as endogenously-determned varables and can be smultaneously estmated. Ths method utlzes the used path set to smultaneously formulate/solve the land use model and the transportaton model, whch has not been seen n the exstng ntegrated models. 1.4 RESEARCH APPROACHES The proposed new type of ntegrated model framework conssts of three components: a transportaton model, a land use model, and the nteracton between these two models. After gatherng necessary transportaton data such as soco-economc data and roadway characterstcs, orgn-destnaton (OD) trp tables, and land use data such as the area of each type of land use from multple data sources, t starts to develop the proposed model framework. The combned trp dstrbuton-assgnment model s formulated based on entropy concepts and calbrated by base year data. The gravty model form s bult n ths transportaton model for trp dstrbuton. The output of trp assgnment s able to satsfy the condtons of user equlbrum (or network equlbrum), whch wll be dscussed n detal n Chapter 4. Ths transportaton model can help dentfy the defcency n transportaton networks usng the measure of operatonal level of servce and systemwde measures of effectveness over tme throughout the study area. It can also generate transportaton performance measures for each analyss zone n terms of accessblty, whch are crtcal nputs to the land use model. The land use model s then establshed after developng two categores of factors assocated wth land use structure and transportaton measures. The factors wth statstcally sgnfcant nfluence on the urban actvty dstrbuton are dentfed through correlaton analyss. The approprate model forms are developed by combnng some of these factors, whch provde better explanaton and estmaton for urban actvty dstrbuton. These models can help n understandng not only the mpact of certan 7

26 transportaton measures on urban actvty dstrbuton, but also the mpacts of neghborhood desgn such as zone characterstcs on urban actvty dstrbuton. More mportantly, the output of the land use models n terms of household and employment dstrbuton wll serve as a maor nput to the transportaton model. The nteracton between these two models s then nvestgated usng two soluton procedures. These two soluton procedures are able to produce the consstency between the land use model output and the transportaton model output. The consstency s such a condton that the transportaton model outputs as nput to the land use model wll be able to produce the same land use model outputs as those ntally put nto the transportaton model, and vce versa. These two soluton procedures are formulated by two types of model frameworks respectvely. The frst s a feedback loop confguraton between the land use model and the transportaton model through the ntermedate varables of accessblty. The teraton between the land use and the transportaton model contnues untl pre-defned convergence crtera are reached (dscussed n Chapter 6). The second s the smultaneous model framework, whch formulates the land use model and the transportaton model together as an optmzaton program after ntroducng the used path set. Therefore, the land use model and the transportaton model can be solved at the same tme nstead of the teratons between these two models n the feedback loop confguraton. 1.5 ORGANIZATION OF THIS DISSERTATION Ths dssertaton s dvded nto seven chapters. Chapter 1 dscusses the background, problem statement, research obectve and methodology, and dssertaton organzaton. The lterature revew of ntegrated land use and transportaton models based on dfferent theory s provded n Chapter 2. Chapter 3 ntroduces the procedure to prepare the data for developng the new type of ntegrated land use and transportaton model. Chapter 4 dscusses the formulaton and calbraton of the combned trp dstrbuton-assgnment transportaton model. Chapter 5 descrbes the correlaton and 8

27 regresson analyss for developng the regresson-based land use model. Chapter 6 dscusses the nteracton between the land use and transportaton models usng a feedback loop model framework and a smultaneous model framework. Conclusons and recommendatons for future research are presented n Chapter 7. 9

28 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION An urban system can be dvded nto several subsystems such as transportaton network, travel, goods transport, land use, employment, populaton, housng, workplace, and envronment (Wegener, 1994). An urban model smulates the structure or functon of one subsystem n an urban system. An ntegrated urban model smulates two or more subsystems. Before 1960, ntegrated urban models dd not truly exst. After 1960, demand for preparng hghway mpact statements and government concern about urban problems such as envronment and energy greatly stmulated the development of ntegrated urban models. A few ntegrated urban models have been developed, whch are desgned to model land use and transportaton subsystems and other subsystems as well. Several comprehensve studes about these ntegrated urban models have been conducted by researchers for dfferent purposes. Wegener (1994) revewed the state-of-the-art of ntegrated urban models accordng to subsystem modeled, model structure, and theory. The Oak Rdge Natonal Laboratory compled a report that dscussed the ablty of current ntegrated models to develop vehcle travel reducton strateges assocated wth energy concerns (Southworth, 1995). NCHRP (Natonal Cooperatve Hghway Research Program) report 423 summarzed the pros and cons of dfferent operatonal land use models assocated wth ts applcaton (Parsons, 1998). Hunt, et al (2005) dscussed sx ntegrated models that are regarded as operatonal, comprehensve and ntegrated. As dscussed n Chapter 1, ths dssertaton s devoted to developng a new type of ntegrated land use and transportaton model that models two subsystems n terms of land use and transportaton n the context of urban system. Therefore, a land use model and a transportaton model are two core components. The transportaton model smulates travel 10

29 behavor of trp-makers as well as traffc flow on physcal road networks. The land use model smulates the locaton choce of household and employer, whch leads to the dstrbuton of household and employment. The land use model can further be decomposed nto household dstrbuton and employment dstrbuton models n ths dssertaton. The household dstrbuton model s manly devsed to estmate the number of households located n each plannng zone. The employment dstrbuton model s prmarly used to forecast the number of employments aggregated n each plannng zone. When household and employer choose ther locaton, transportaton cost plays an mportant role n ther decson-makng. Consumer equlbrum theory s proposed to descrbe how a household choose ts resdental locaton (Alonso, 1964). It assumes that household ncome s equal to the summaton of house cost, transportaton cost, and all other expendtures. Transportaton cost s a general term; n real applcaton, t needs to be combned wth urban actvtes. For example, the household wth a fxed employment locaton consders commutng cost when searchng for a locaton to resde, whle an ndustry prefers to choose a locaton wth hgh access to suppler and customers. Accessblty as a functon of transportaton cost and urban actvty dstrbuton has been commonly used n modelng locaton choce. Accessblty s the rason d être of transportaton system, to provde the ablty for people and goods to be able to move effcently and effectvely from pont to pont n space n as unconstraned a fashon as possble (Mller, 2004). Ths chapter revews exstng ntegrated urban models n a comprehensve way. Based on model theory and model structure prmarly assocated wth land use models, exstng ntegrated urban models can fall nto one of three maor categores: gravty-based model, nput-output based models, and dscrete response smulaton models referrng to categores of land use models (Lemp et al, 2007). The representatve ntegrated urban models under each category are dscussed n detal. 11

30 2.2 GRAVITY-BASED INTEGRATED URBAN MODELS Gravty-based ntegrated urban models orgnate from the Lowry model, whch was developed for the cty of Pttsburgh (Lowry, 1964). The most wdely used successor to Lowy s model s ntegrated transportaton-land use package (ITLUP) Lowry Model The Lowy model estmates spatal dstrbuton of household and employment based on the concept of gravty. The orgnal Newton s law states that any two bodes attract one another wth a force that s proportonal to the product of ther masses and nversely proportonal to the square of the dstance between them. By takng the concept of dstance nto consderaton, the Lowy model assumes that the probablty of makng a trp s nversely proportonal to the travel tme (trp length) between orgn and destnaton. It ndcates that the longer the travel tme between two zones, the less lkely a person wll make a trp between them. Accordng to ths assumpton, the probablty for a worker to choose a resdental locaton s nversely proportonal to the travel tme between workng place and resdental locaton. The framework of the Lowry model can be brefly descrbed as follows. Employment s categorzed as basc and servce sectors. The magntude and locaton of basc employment are exogenously determned by macro, regonal factors such as land use plan and polcy. The workers n basc sectors generate dependent households accordng to a regonal actvty rato (the rato of total regonal households to total regonal employment). These households wll choose ther resdental locatons based on the model assumpton that probablty of choosng a resdental locaton s nversely proportonal to the travel tme between workplace and resdental locaton. These households wll be allocated nto each plannng zone after choosng ther locaton. Plannng zone s the geographc area dvdng the plannng regon nto relatvely small areas durng land use plannng. The households generated from basc employment demand servces to satsfy ther lvng needs. The number of servce ob created wll be estmated by household-to- 12

31 servce multplers n the regon. The employment dstrbuton model s then used to allocate these servce obs nto plannng zones based on the same model assumpton. Snce the Lowry model s almost the same as the land use models used n ITLUP, a detaled descrpton of model theory and structure s gven n secton Integrated Transportaton-Land Use Package ITLUP s the most wdely used ntegrated urban model currently used. It was developed under contract wth the U.S. Department of Transportaton (Putman, 1983). It was desgned to mprove long-range forecastng results by establshng the lnkage between land use and transportaton. Ths ntegrated urban model has been appled to nearly four dozen ctes n the Unted States and abroad for polcy analyss and plannng (Wegener, 1994). For example, t s used by the Md-Amerca Councl of Governments (Kansas Cty) and the Puget Sound Councl of Governments (Seattle), and n Dallas-Fort Worth, Detrot, Houston, Los Angeles, Phoenx, and by the Florda DOT. ITLUP conssts of two maor model components: a land use model and a transportaton model. The land use model s composed of dsaggregate resdental allocaton model (DRAM) and employment allocaton model (EMPAL), whch were developed by Putman and colleagues (Putman, 1983, 1988; Putman, S. H. Assocates, 2001). The tradtonal fourstep travel demand model serves as the transportaton model. The feedback mechansm between DRAM/EMPAL and the transportaton model s bult to the ITLUP framework Land Use Model The logc behnd DRAM les n that the probablty for a worker to choose a zone as a resdental locaton s proportonal to ths zone s attractveness and accessblty. The number of workers n zone who are wllng to choose zone n whch to resde are determned by the rato of attractveness and accessblty of zone to all other zones attractveness and accessblty. Accessblty s a functon of congested travel tme between zones. The attractveness functon s expressed as the product of land area and 13

32 dstrbuton of dfferent levels of household ncome groups. The orgnal equaton of DRAM can be seen n Appendx 2-A1. The assumpton n EMPAL s that the probablty for a household to choose a zone n whch to work s proportonal to ths zone s attractveness and accessblty. EMPAL allocates employment across each plannng zone not only based on attractveness and accessblty but also on the number of obs n the prevous perod, snce employment dstrbuton has a strong hstorc trend. EMAPL allocates employment n the future (perod t+1) based on employment n base year (perod t), accessblty and attractveness n base year (perod t). Accessblty functon s a functon of congested travel tme between zones. Attractveness s a functon of land area and employment n the prevous perod. The orgnal EMAPL model equatons can be found n Appendx 2- A1. The DRAM and EMPAL equatons have undergone changes over tme assocated wth data avalablty and applcaton purposes (Putman, 1983, 1991, 1995; Cambrdge Systematcs, 2004). For example, Krshnamurthy and Kockelman (2003) used dfferent DRAM and EMPAL model forms to nvestgate the propagaton of uncertanty n ths ntegrated land use and transportaton model; peak travel tme and off-peak travel tme are utlzed n the accessblty functon Transportaton Model The tradtonal four-step travel demand model s mplemented n ITLUP; ths transportaton model can be mplemented usng dfferent professonal software package. It conssts of four sub-models for each step: trp generaton, trp dstrbuton, mode choce and traffc assgnment. Durng transportaton model development, a study area s dvded nto smaller geographc areas called traffc analyss zones (TAZs). TAZs represent orgns and destnatons of travel actvty. The trp generaton model ncludes trp producton and trp attracton; trp producton estmates the number of trps produced n each TAZ; trp attracton predcts the number of trps attracted to each TAZ. The model s generally 14

33 developed accordng to trp purpose, whch typcally ncludes home-based work (HBW: work trps that begn or end at home), home-based others (HBO: other home-based trps such as to shop or attend school that begn or end at home), non-home-based trps (NHB: trps that nether begn nor end at home). Trp dstrbuton s the second sub-model, whch estmates the number of trps between each two TAZs based on travel tme (cost) and trp generaton. Mode choce, the thrd sub-model, s used to predct the choces that ndvduals or groups make n selectng transportaton modes such as auto or transt to acheve ther travel purposes. Traffc assgnment s the fourth sub-model n the four-step transportaton model. It s the process of assgnng nterzonal trps to physcal roadway networks usng dfferent mathematc methodologes such as user equlbrum. Its output ncludes traffc flow, travel tme on each road segment, etc ITLUP Confguraton ITLUP can be a sequental procedure or an teratve procedure. In the sequental procedure, land use models (DRAM/EMPAL) estmate future household/employment dstrbuton usng base-year congested travel tme or future free-flow travel tme; future household/employment dstrbuton (output of land use models) s then added to the transportaton model to forecast future traffc flow. The sequental procedure does not put future congested travel tme (output of transportaton model) back nto land use models to re-estmate future household/employment dstrbuton (Putman, S. H. Assocates, 2001). Therefore, t lacks the consstency between land use model outputs and transportaton model outputs. The teratve procedure strengthens the consstency between land use model outputs and transportaton model outputs. The teratve procedure s shown n Fgure 2.1. The teratve procedure has a loop between land use model and transportaton model. In teratve procedure, after runnng the land use model and the transportaton model, future congested travel tme (outputs of the transportaton model) s then put back nto the land use model to re-estmate future household/employment dstrbuton, whch s then put 15

34 nto the transportaton model to re-forecast future traffc flow and travel tme. Iteraton between the land use model and the transportaton model contnues untl pre-defned crtera (lnk flow varaton) are reached between the two successve teratons, or untl the maxmum number of teratons has been reached (Putman, S. H. Assocates, 2001). It s worth notng that the sze of plannng zones n the land use model s not the same as the sze of TAZs n the transportaton model. A plannng zone s typcally composed of several TAZs. After DRAM/EMAPL estmates household/employment dstrbuton, these outputs have to be dsaggregated nto TAZs from larger plannng zones. Once the transportaton model generates the congested travel-tme matrx, t has to be aggregated or squeezed nto a larger spatal level of plannng zones from TAZs. Both the aggregatng and dsaggregatng process nevtably result n losng nformaton about accessblty, household and employment dstrbuton (Parsons Brnckerhoff, 1998). However, no study has been conducted to assess the errors produced n these aggregatng/dsaggregatng processes (Tayman, 1996). 16

35 Congested Travel tme n tme t or Free-flow travel tme n t+1 Household dstrbuton, employment dstrbuton, land use confguraton n t Regonal forecast of employment, household-employment actvty rato n t EMPAL Employment Dstrbuton n t+1 DRAM Household Dstrbuton n t+1 Update congested travel tme n t+1 Transportaton Model: Lnk flow congested travel tme n tme t+1 OD travel tme Lnk flow converge/congested travel tme YES STOP Fgure 2.1: ITLUP Iteratve Model Structure It can be seen that ITLUP can assess the mpact of changes n accessblty assocated wth transportaton proects on land use. However, EMPAL/DRAM models do not ncorporate land use polcy varables n attractveness functon such as resdental/ndustral land use (as shown n Appendx 2-A). Thus, they cannot be used to evaluate the mpact of land use polcy on household/employment dstrbuton (Parsons Brnckerhoff, 1998). Also, ITLUP s desgned for regonal plannng rather than local/small communty plannng. Ths model assumes that model area s a closed system, whch s sutable for a regon. In a closed system, 95 percent of obs are flled by the resdents from the model area, and 95 percent workers n the model area work n the 17

36 model area. Therefore, ITLUP cannot be appled on those open system areas such as the study area n ths dssertaton, n whch a sgnfcant number of obs are flled by workers from outsde the study area Other Gravty-Based Models Other gravty-based models are brefly ntroduced n ths secton snce they are only formulated by ther own authors and are not get used by other urban plannng agences. Myag (1989) followed the prncples of the Lowry model to develop an ntegrated urban model that combnes the resdental locaton choce model and the transportaton network equlbrum model. Mackett (1983) summarzed the propertes of the Leeds Integrated Land-Use Transport (LILT) model; the land use model s Lowybased. An nterestng ntegrated urban model s formulated by lnkng the Lowy-based land use model and the combned trp dstrbuton-assgnment transportaton model (Meng et al, 2000). In ths ntegrated model, only ourney-to-work trps are consdered; both the land use model and the combned trp dstrbuton-assgnment mode are only theoretcally formulated wthout dscusson of calbraton and mplementaton concerns. Assumed parameters were used to test ths framework. A quas-gravty-based model s developed by Boyce and colleagues for home-towork trp purpose trps (Boyce, 1978, 1980, 1986; Boyce et al 1978; Boyce et al, 1983; Boyce et al, 1988). The reason ts name s quas-gravty s that t has the same model assumpton/theory as the Lowy-based model but has a dfferent model formulaton. By renterpretng the home-to-work trp varable between each OD par, the tradtonal traffc assgnment model can be assocated wth household locaton choce. As for home-towork trps, orgns are related to resdental locaton and destnatons are assocated wth employment locaton. By addng entropy constrants nto the traffc assgnment model formulaton, ths ntegrated model s then theoretcally formulated. The household dstrbuton model emerges n the optmal condtons of ths ntegrated urban model, whch has the same model form as the DRAM n ITLUP. The orgnal equatons of quas-gravty model are lsted n Appendx 2-A2. 18

37 The entropy constrants n the traffc assgnment model were dscussed by Erlander and colleagues (Erlander, 1974, 1977, 1980, 1981; Erlander et al, 1979). The entropy s denoted by as S and S p ln p where p s defned as t / T s the number of trps from zone to ; and T s total tps n a model area. Erlander noted that entropy S could be explaned as a measure of the spread of dstrbuton of ourneys over the cells of trp matrx (Erlander 1977). Boyce and Southworth (1979) explaned ths term as a measure of the level of spatal nteracton among zones n a regon. The value of S for the home-to-work trp ndcates the level of nteracton between resdental zones and employment zones. ; t Hgh value of S mples that households n a resdental zone are workng n most of the employment zones. Low value of S ndcates that households n a resdental zone are workng n only a few employment zones. In the quas-gravty-based model, the congested travel tme s endogenously determned snce the transportaton model and household locaton model are smultaneously solved, whle the DRAM model takes congested travel tme from the output of the transportaton model as exogenously determned varables. smultaneous formulaton of the household locaton model and transportaton model provded the nspraton for developng the smultaneous model confguraton used to solve the proposed ntegrated model n ths dssertaton. The combned trp dstrbutonassgnment model provdes the feasble platform to smultaneously formulate the proposed land use and transportaton models. However, ths quas-gravty ntegrated urban model s only theoretcally formulated and not operatonal yet. Several areas need to be nvestgated before ths model can be put nto real applcaton, ncludng the method used to calbrate, how to consder trps wth purposes other than home to work, and dentfyng the physcal meanng of entropy constrants. The 19

38 2.3 INPUT-OUTPUT-BASED MODEL The nput-output-based ntegrated urban model s based on relatonshp among dfferent economc sectors. The relatonshp or nteracton between these economc sectors s used to forecast the dstrbuton of urban actvty, person trps and commodty flows Input-Output Framework The nput-output framework has been used for urban model development snce ts ntroducton by Leontef (1967). Ths framework formulates an urban system as a system of equatons usng dfferent economc sectors. Household and employment are dvded nto dfferent economc sectors based on ndustry classfcaton and household ncome. The nput-output framework s brefly descrbed below. There are n economc sectors n a regon: 1 n : each economc sector has to consume some products from other economc sectors, ncludng tself, n order to produce ts own product. Let m denote the number of unts from sector that s requred to produce one unt of sector. If producton level (or total product) of each economc sector n ths regon s known as sector that are used to produce P, then m P s equal to the number of unts from P. It s assumed that the total product of sector s consumed by all other sectors to meet ther producton levels. Therefore, the total product of sector s equal to the summaton of all consumpton by other sectors: m 1 P m P... m n P n P It s assumed that the economy of ths regon s n balance and that the total product of each economc sector wll be consumed by all other sectors. The economy of ths regon can be formulated as a lnear system to represent the relatonshp between dfferent economc sectors. 20

39 m m m n1 P m 1 P m 1 P m n2 P... m 1n P... m 2n P... m nn P P n P P n P P n 1 2 n Let m m A... mn m m m n m1 n m2n... m nn A s called the nput-output matrx or techncal coeffcent n the MEPLAN model (Hunt, 1994), whch ndcates the relatonshp between dfferent economc sectors. The MEPLAN model wll be dscussed n the next secton. A s the core of the nputoutput-based urban models. Then the lnear system above can be transformed nto: P1 P2 AP P, where P... P n Ths s the basc framework of the Leontef nput-output model. The followng secton wll ntroduce the MEPLAN model framework, whch s the most wdely used nput-output-based urban model MEPLAN Model The MEPLAN model framework has been n use for 25 years and s the second most wdely used ntegrated urban model (Wegener, 1994). It has been appled to more than a dozen urban regons, ncludng Greater London, the Unted Kngdom; Naples, Italy; and Sacramento, Calforna (Wegener, 1994; Hunt, 1994; Abraham and Hunt, 1999). Ths model was developed under the leadershp of Marcal Eschenque and s the property of Marcal Echenque and Partners (MEP) frm (Echenque et al, 1990). 21

40 The core feature of the MEPLAN model s the relatonshp/nteracton between dfferent economc sectors n a regon. The product of each sector n a zone wll be transported nto all zones for consumpton; ths generates economc nteractons among dfferent economc sectors n zones. Input-output framework and random utlty choce modelng are two maor components n ths model framework. Frst, the nput-output framework s utlzed to estmate the number of products of each sector whch wll be consumed n a zone n order to meet the producton level of each economc sector n ths zone. Ths estmaton s acheved by usng the techncal coeffcent. After the consumpton of each sector n a zone s obtaned, a random utlty choce model s developed to allocate ths consumpton nto all other zones for the purpose of producton. Two maor varables n ths utlty functon are transportaton cost and producton cost. A detaled descrpton of the orgnal MEPLAN equatons s shown n Appendx 2-B. The economc sectors can be categorzed based on ndustry classfcaton and household ncome. For example, n the Sacramento model, ndustres are dvded nto: agrculture, manufacturng, servce and offce, retal, health, educaton, government, prvate educaton, commercal transportaton, and wholesale; households are dvded nto low-ncome, md-ncome, and hgh-ncome households. The ndustres and households wll occupy lands at dfferent rates and prces. Household sectors provde the labor force to other ndustry sectors and also generate person trps. The nteractons among dfferent sectors n varous zones brng about freght flow and person-trp flow, whch generates the demand for transportaton. Freght flow and person-trp flow are dstrbuted across dfferent transportaton modes and are then assgned to the physcal transportaton network, whch produces transportaton costs between zones for each sector. Clay and Johnston (2006) dscussed the error and uncertanty propagaton n every step of the MEPLAN model. They concluded that commercal trp generaton rates have the most effect on model outputs after comparson wth other soco-economc nput. Zhao and Kockelman (2004) nvestgated the exstence and unqueness of nput-outputbased model soluton. The models were proved to have a unque soluton and to be solved wth convergence by fxed pont algorthm. 22

41 By ncorporatng dfferent ndustry and household factors, MEPLAN s able to evaluate a varety of land use polces (Abraham, et al, 1999). However, ths model requres a large amount of data such as producton costs and land use prces n each economc sector, whch are not normally collected by typcal urban areas and MPOs. The structure of MEPLAN focuses on the economc nteracton between dfferent economc factors; t s sutable for regonal or ntercty modelng rather than for the typcal urban area Other Input-Output Based Models Other nput-output-based urban models wll be brefly dscussed snce they ether have a smlar model framework as MEPLAN or they are only formulated by ther own authors wthout calbraton and applcaton n urban plannng. TRANUS s an ntegrated urban model based on nput-output framework (de la Barra et al, 1984; de la Barra, 1989). It s smlar to the MEPLAN model framework; both have the same structure n model framework and concept (Hunt et al, 2005). Most of the descrptons n MEPLAN apply to TRANUS. Another ntegrated urban model was developed by Km based on nput-output framework (Km, 1989 and 1990). Ths model ams to fnd general equlbrum between demand and supply assocated wth transportaton nfrastructures and actvty locatons n a strct economc sense. The model s formulated as a standard lnear programmng wth an obectve functon and four constrants. The obectve s to mnmze total cost, ncludng producton costs and transportaton costs under resource constrants and producton-consumpton equlbrum constrants. Resource constrants nclude: Export constrants: the producton of an economc sector should at least satsfy export needs of ths sector. Land constrants: all lands used by dfferent economc sectors and transportaton systems cannot exceed the amount of avalable land n the study regon. 23

42 Transportaton constrants: the transportaton supply (ncludng mode and capacty) should satsfy the needs of transportng freght flows and person-trp flows. Producton-consumpton equlbrum constrants use the nput-output framework s utlzed to descrbe the relatonshp among dfferent economc sectors n zones. In ths model, the transportaton network s converted nto unts of nput for carryng each economc sector, such as operatng cost per mle to move a unt of sector. Ths model requres extensve data sources that are not regularly gathered by a typcal urban area such as operatng cost per mle and export need. To date, the model has not been appled to any regon for the purpose of urban plannng or polcy analyss. Jun (1999) used the nput-output framework to develop an ntegrated metropoltan model, whch examnes the nterspatal relatonshp between the demographc-economc system and the transportaton system. However, ths model s only theoretcally formulated wth no dscusson of calbraton and mplementaton. 2.4 DISCRETE RESPONSE SIMULATION MODEL Ths category of urban models ams to smulate household and employment locaton choce. It manly takes nto consderaton transportaton measures generated from the transportaton model along wth other varables n modelng household and employment locaton choce. The most wdely used methodologes are dscrete choce theory and bd rent theory Dscrete Choce Model Dscrete choce theory (random utlty maxmzaton) can be utlzed to develop the locaton choce model (Mcfadden, 1974, 1978, 2001; Domencch and McFadden 1975). Ths approach s to estmate the choce between mutually exclusve alternatves on the bass of attrbutes of these alternatves. The attrbutes of these alternatves are descrbed by a utlty functon. When ths approach s appled n the context of urban 24

43 models, t s used to forecast whch zone among all zones n a cty wll be chosen by a household or employer to resde n. The most popular urban model based on dscrete choce theory s UrbanSm, whch was developed under the program of travel model mprovement program (TMIP) (Waddle, 2002; Waddle et al, 2007). In UrbanSm, a cty s dvded nto many grd cells so that households and employers can make locaton choces among these cells. The utlty functon s used to descrbe attrbutes of these grd cells assocated wth dfferent categores of varables. For example, n the employment locaton choce model, varables nclude real estate attrbutes, land use composton, land value n the mmedate neghborhood, land use mx, the number of obs n the neghborhood, and transportaton measures such as accessblty to labor and consumers (Waddle and Ulfarsson, 2003a). In the household locaton choce model, varables nclude house prce, development types, neghborhood employment, neghborhood land use mx, transportaton measures such as accessblty to obs and travel tme to central busness dstrct (CBD) (Waddle, et al. 2003b). Transportaton measures are generated from the transportaton model outputs. However, the transportaton model s usually not performed n the same tme frame as UrbanSm. For example, n the Wasatch Front Regonal Councl ntegrated urban model, UrbanSm s performed every year to estmate household and employment dstrbuton; the transportaton model (tradtonal four-step travel demand model) s only performed every fve years. Therefore, transportaton measures used n the UrbanSm are not updated untl the transportaton model s performed (Waddle et al, 2007). POLIS (Proectve Optmzaton Land Use Informaton System) s developed based on ths theory to allocate urban actvtes subect to plannng constrants such as land supply (Prastacos, 1986a, 1986b); CUF-I/CUF-II (Calforna Urban Future models) s also developed from ths theory to allocate new development nto grd cells (Lands and Zhang, 1998a, 1998b). 25

44 2.4.2 Bd-Rent Model The concept lyng the bd-rent urban model s that consumers (households and developers) choose ther locaton based on the lowest prce, and land owners want to sell ther land (locaton) for maxmum proft. Market equlbrum can be reached after balancng the nteracton between consumers and land owners. In the land bd-rent process, consumer surplus can be used to descrbe consumer behavor, whch s defned as the dfference between the prce that consumers are wllng to pay and the actual pad prce. Martnez (1991, 1992a, 1992b) developed a fve-stage urban model based on bdrent theory. In ths model, accessblty measures produced from the transportaton model are used to represent the transportaton characterstcs of specfc land lots. The wllngness to pay (WP) functon s utlzed to descrbe the attrbutes of land lots or zones. In ts household locaton choce model, varables the n WP functon consst of proporton of resdental land, accessblty measures, neghborhood characterstcs such as neghborhood land use mx, and land prce. In ts employment locaton choce model, varables n WP functon nclude proporton of ndustry land, employment accessblty measures, neghborhood employment, and land prce. Appendx 2-C shows the orgnal equatons of the household locaton choce model. Ths model uses transportaton measures produced from the transportaton model to estmate household/employment locaton choce. There s no feedback between ths urban model and the transportaton model. Other urban models based on the bd-rent concept nclude the RURBAN model developed by Myamoto and Ktazume (1989), and the b-level transport and resdental locaton model (Chang and Mackett, 2006). 2.5 LIMITATIONS OF EXISTING MODELS Integrated urban models have recently been ntroduced and mplemented n several metropoltan areas and regons for dfferent applcaton purposes. Snce these 26

45 models target large metropoltan areas, they lack the flexblty to be appled to small urban areas. For example, the most wdely used ntegrated model, ITLUP, assumes that the model area s a closed system,.e., there are no sgnfcant percentage of households who are employed outsde of the model area, and no sgnfcant percentage of obs are occuped by the workers from outsde of the model area (Putman, 1983, 1988; Putman, S. H. Assocates, 2001). But n some small urban areas such as the study area n ths dssertaton, a consderable number of households are employed outsde of the area (n the neghborhood cty); a substantal number of obs n the model area are occuped by people who lve outsde the model area (n the neghborhood cty). Therefore, t s approprated to consder such small urban areas as open systems, whch s not n accord wth the assumpton of ITLUP. The second wdely used urban model (MEPLAN) based on an nput-output framework s sutable for regonal or ntercty modelng (Hunt and Smmonds, 1993; Hunt, 1994). Ths model s more approprate for nterurban areas (Parsons, 1998). It s questonable whether ths model s approprate for small urban areas (Lemp, et al, 2007). In both ITLUP and MEPLAN, the plannng zone n the land use model typcally conssts of several TAZs assocated wth the transportaton model. Informaton exchange such as travel tme and household dstrbuton between plannng zones and TAZs wll cause substantal nformaton loss for small urban areas. Also, by aggregatng several TAZs nto one plannng zone, these models produce only a few plannng zones n a small urban area. It s dffcult to develop the land use model wth few plannng zones because of the small sample sze. The recently developed urban model (UrbanSm) requres ntense data at dsaggregate spatal level such as parcels. It requres over a thousand parameters and tens of thousands of varable values to develop and calbrate the model. Very few regons or metropoltan areas routnely collect all of ths data, not to menton small urban areas. Most ntegrated urban models use the tradtonal four-step travel demand model as the transportaton model. Few efforts have been made to ntegrate the combned trp dstrbuton-assgnment transportaton model and the land use model. The combned trp dstrbuton-assgnment model has been successfully formulated by researchers. It has 27

46 not been developed and calbrated for a real applcaton wthn the context of ntegrated urban models. Exstng ntegrated urban models requre a substantal budget and professonal personnel to perform the land use model. Small urban areas are typcally not able to afford the budget and professonal crew needed to develop these land use models. The ntegrated land use and transportaton model framework descrbed n ths dssertaton s desgned to develop an affordable and easy-to-mplement land use model based on avalable data, whch can be appled to both metropoltan areas and small urban areas. Chapter 5 compares the proposed land use model to the exstng land use models. The three components of ths framework are the transportaton model, the land use model, and the nteracton between these two models, whch wll be dscussed n the followng chapters. 28

47 CHAPTER 3 DATA COLLECTION AND PREPARATION The development of land use and transportaton models demands extensve data collecton and preparaton, ncludng land-use structure data, household and employment dstrbuton data, and transportaton network and performance data. Ths chapter wll dscuss data collecton and data preparaton. The data collecton secton descrbes the data sources used for the model development. The data preparaton secton focuses on the development of transportaton performance data. 3.1 DATA COLLECTION Land Use Data Descrpton Woodford County n Kentucky was selected to test the proposed model framework. Ths county s located between Lexngton (the second largest cty n Kentucky) and Frankfort (Kentucky s captal). There are two towns, Versalles and Mdway, located on the maor hghways of US60 and US62. The rest of the county conssts of rollng farmland and tmber stands. In the process of land use and transportaton plannng, an urban area s spatally dvded nto small zones for the purpose of analyss. In the proposed ntegrated land use and transportaton model framework, both land use and transportaton models are establshed at the same spatal level: TAZ. The TAZ confguraton of Woodford County s llustrated n Fgure 3.1. The county contans 78 TAZs. 29

48 Fgure 3.1: Woodford County TAZ Confguraton The study area has a populaton of 23,208, wth 8,893 households and 9,486 obs for the base year of Multple data sources exst for developng the proposed ntegrated model U.S. Census survey data provdes the household and populaton dstrbuton at census block level and the spatal commutng pattern. Dun & Bradstreet (D&B) employment survey data provdes the number of employments/obs n each census block. A TAZ s typcally composed of several census blocks. Therefore, the data at census block level are aggregated nto TAZ level for the ntegrated model development. Land use parcel data s obtaned from the Woodford County Plannng Commsson. It provdes area coverage by dfferent land use type n each TAZ, such as the area/footprnt of resdental land use, moble home and mult-famly resdental land use, agrculture and preserved agrculture land use, ndustral land use, commercal land use, professonal offce and nsttutonal land use, vacant land use, and other land use. These data wll be used for the land use model development. 30

49 3.1.2 Transportaton Network Data One of the most mportant goals of developng a transportaton model s to evaluate transportaton system performance. In dong so, detaled transportaton networks need to be represented n the model. The detaled transportaton network for ths study area s based on a road network map downloaded from the Kentucky Transportaton Cabnet s (KYTC) webste. The requred network attrbutes for the transportaton model development consst of functonal classfcaton, number of lanes, speed lmt, and traffc count. The road network for Woodford County by functonal classfcaton s shown n Fgure 3.2. Fgure 3.2: Woodford County Roadway Network by Functonal Classfcaton 31

50 US Hghway 60 lnkng Frankln, Woodford County, and Fayette County provdes the moblty for workers to commute wthn reasonable travel tme among these countes. Wth scenc horse farms and gently rollng hlls, t has become the promnent corrdor servng Woodford County. Interstate 64 and Bluegrass Parkway (Route 9002 n the map) has one nterchange n Woodford County, provdng easy access to maor nterstate and parkway systems n Kentucky for local resdents. The transportaton network consdered n ths study conssts of approxmately 251 mles of road. The mleage of each functonal class s llustrated n Table 3.1 wth the percentage of each functonal class over total mleage of all roads. Table 3.1: Functonal System Mleage Functonal System Mleage Percent of Total Mleage Rural Interstate % Rural Prncpal Arteral % Rural Mnor Arteral % Rural Maor Collector % Rural Mnor Collector % Urban Prncpal Arteral % Urban Mnor Arteral % Urban Collector % Local Road % Total % 3.2 TRANSPORTATION SYSTEM DATA One of the three components n the proposed ntegrated land use and transportaton model s the combned trp dstrbuton-assgnment transportaton model. A crucal step n developng ths model s to calbrate the model. The calbraton requres an OD trp table and an OD travel tme table. The OD trp table s usually obtaned by conductng a household travel survey; unfortunately, an OD survey s not conducted by most small urban areas such as ths study area because t s dffcult and expensve. Snce an observed OD trp table s unavalable, ths study uses an estmated OD trp table and a 32

51 travel tme table. These tables can be generated from the output of the Woodford travel demand model, whch s developed usng the tradtonal four-step method and default parameters recommended by NCHRP Report 365 (Martn et al, 1998). The procedure for developng ths Woodford travel demand model (WTDM) s shown n Appendx 3-A. The estmated OD trp and travel tme tables are regarded as beng reasonable snce WTDM has the satsfactory error bound between the observed traffc volume and the modeled traffc volume. Percent Root Mean Squared Error (PRMSE), as defned n equaton 3.1, s used to measure the dfference between the observed and the modeled traffc volumes. PRMSE Where N (ˆ v N n n v ) v n n / N 2 / N 3.1 vˆ n : Estmated traffc volume on traffc count staton n v n : Observed traffc volume on traffc count staton n N : Total number of traffc count statons n the area The acceptable PRMSE n common practce s under 30% (Kentucky Transportaton Cabnet, 2004). The PRMSE of WTDM s 25.7%. The comparson between the modeled and the observed traffc volumes on each traffc count staton s shown n Appendx 3-B. The estmated base-year OD trp table and OD travel-tme table are shown n Table 3.2 and 3.3. These tables wll be regarded as the observed OD trp and travel tme tables for the development of the combned trp dstrbuton-assgnment model. It s mportant to note that trps n Table 3.2 are vehcle trps per day. In addton, the OD trp table s symmetrcal because WTDM s a daly model wth the assumpton that trps orgnatng from a TAZ wll return to ths TAZ n the same day. In these two tables and other tables n ths dssertaton, TAZ s abbrevated as Z; for example, TAZ 1 s expressed as Z1. Snce there are 78 TAZs n ths study area, t s dffcult to show all 33

52 OD trps between each two OD pars, so only 21 TAZs are selected to demonstrate the OD trp table for llustraton purpose. OD trps between two TAZs are nternal trps. Also, a number of trps on the transportaton network are assocated wth external TAZs located outsde the study area. These trps are regarded as external trps that have at least one end outsde the study area. The external trps are also estmated n WTDM n Appendx 3-A. Estmated external trps wll be regarded as gven varables or background traffc n the combned trp dstrbuton-assgnment transportaton model development. After the requred data s generated, the transportaton model development s then dscussed n Chapter 4. The land use model s dscussed n Chapter 5, and the nteracton between these two models s presented n Chapter 6. 34

53 Table 3.2: Estmated OD Trp Table Trps Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z13 Z14 Z15 Z16 Z17 Z18 Z19 Z20 Z78 Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z

54 Table 3.3: Estmated OD Travel Tme Travel Tme Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z13 Z14 Z15 Z16 Z17 Z18 Z19 Z20 Z78 Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z

55 CHAPTER 4 TRANSPORTATION MODEL DEVELOPMENT The proposed ntegrated model ncludes three components: a transportaton model, a land use model, and the nteracton between these two models. Transportaton demand s drven by human socal actvtes, whch nvolves makng trps to satsfy needs. Transportaton models assgn these trps generated by households and employments to between TAZs to the road network. The resultng traffc flow patterns are then used to estmate transportaton performance measures. Takng transportaton performance measures and land use structure varables nto consderaton, the regresson-based land use model s developed to dentfy those varables that have a sgnfcant mpact on household and employment dstrbuton, and to fnd the approprate combnaton of these sgnfcant varables to estmate household and employment dstrbuton. The nteracton between the land use model and the transportaton model s then nvestgated by two dfferent methodologes: feedback model confguraton and smultaneous model confguraton. The nteracton between these two models wll strengthen the consstency between the land use model output and the transportaton model output by showng that household/employment dstrbuton s n accord wth transportaton system performance. Ths chapter outlnes the steps to develop the combned trp dstrbutonassgnment model. In state-of-the-art transportaton modelng, three categores of transportaton models have been formulated: the tradtonal four-step travel demand model, the combned trp dstrbuton-assgnment model, and the actvty-based model. The tradtonal four-step travel demand model has been wdely put nto practce by plannng agences; ths model was ntroduced n ITLUP framework n Chapter 2 and s dscussed n Appendx 3-A. The actvty-based transportaton model s desgned to smulate second-by-second movements of each ndvdual person and each vehcle across transportaton networks, whch requres very detaled actvty locaton data and household travel survey data. The actvty-based transportaton model s stll n development and s not broadly accepted by plannng agences. The combned trp 37

56 dstrbuton and assgnment model has been successfully formulated (Wlson, 1970; Sheff, 1992), but t has rarely been put nto practce n the feld of ntegrated urban models. The transportaton model developed n ths dssertaton wll adopt the combned trp dstrbuton-assgnment model. Ths model s the frst to utlze the combned transportaton model n the operatonal ntegrated urban model feld. Also the combned trp dstrbuton-assgnment model framework provdes a feasble platform to smultaneously formulate the land use model and the transportaton model, whch wll be dscussed n smultaneous model confguraton n Chapter COMBINED TRIP DISTRIBUTION-ASSIGNMENT MODEL Model Formulaton As mentoned n Chapter 3, the study area contans 78 TAZs, whch are connected to each other through the transportaton network. The combned trp dstrbutonassgnment model s desgned to estmate the number of trps between each two TAZs (trps refer to vehcle trps per day n the followng dscusson) and assgn these trps to the transportaton network. transportaton model are defned below. The varables as well as the set assocated wth ths Each TAZ serves as both orgn and destnaton for trps; a trp has two ends, orgn and destnaton. Let I denote the set of orgn TAZs, and J denote the set of destnaton TAZs. The components of both set I and set J are the 78 TAZs n the study area. Let O denote the trps orgnatng from TAZ, ( I ); let D denote the trps destned to TAZ, ( J ); let t denote the number of trps between orgn and destnaton, ( I and J ). Each OD s connected by road segments and there are multple paths that travelers can use. Consder the road network; let A denote the set of lnks (road segments) n the study area. tt denotes free-flow travel tme on lnk a, ( a A ), whch can be f a 38

57 calculated by lnk length dvded by free-flow speed. CP a denotes the capacty of lnk a, ( a A). v a denotes the traffc volume on lnk a, ( a A); tt a denotes the congested travel tme on lnk a wth traffc flow v a on ths lnk, ( a A ). The wdely used Bureau of Publc Road (BPR) functon s adopted as lnk mpedance functon for relatng travel tme to traffc volume: paths connectng each OD par; ( I and J f v a 4 s a ( va ) tt a tt a ( ). There are multple CPa R denotes the set of paths from orgn to destnaton, ). R denotes the set of complete paths whch connect all OD pars n the study area, therefore R R, ( I and J ). hr denotes the number of trps on path r, ( r R). Snce a path between an OD par usually conssts of several lnks, the relatonshp between lnks and paths needs to be defned. ar denotes the ar ncdence coeffcent to descrbe the relatonshp between path and lnk; 1 f lnk a ar s on path r ; otherwse 0 ; therefore v ar a h r, ( a A rr and r R ). Researchers have conducted extensve studes n the formulaton of a combned trp dstrbuton-assgnment model (Sheff, 1992; Boyce et al, 1988, Evan, 1976). The combned trp dstrbuton-assgnment model has a computatonal advantage snce results can be obtaned relatvely faster than by usng the tradtonal four-step model. Also, ts performance s sgnfcantly better than the tradtonal four-step travel demand model n comparng model results (Zargar et al, 2008). Meng et al (2000) descrbed an ntegrated urban model by lnkng a combned trp dstrbuton-assgnment model wth a Lowrybased land use model for home to work trps. However, the combned trp dstrbutonassgnment model n ther study s only tested usng assumed parameters and s not calbrated at all. Ths chapter presents the complete calbraton and applcaton of the combned trp dstrbuton-assgnment model based on a real network. A combned trp dstrbuton-assgnment model can be formulated as the followng optmzaton program (Sheff, 1992). 39

58 Mn a va 1 s ( w) dw a 0 ( t ln t t ) 4.1a S.T. t O ( I ) 4.1b t D ( J ) 4.1c rr h r t ( I, J ) 4.1d v ar a h r ( A rr a ) 4.1e h 0 ( I, J, r R ) 4.1f r In ths formulaton (equaton 4.1a-f), O and 40 D are gven varables; t and v a are unknown varables that can be obtaned after solvng ths optmzaton problem. Lnk mpedance functon ( s ( v a a f v a 4 ) tta tta ( ) CPa ) s used n ths orgnal formulaton. However, n ths study area, only nternal trps between each OD par nsde the study area are consdered; external trps are consdered as gven varables and dscussed n the last chapter. The assgnment of these external trps onto networks produces background traffc volume (or preloaded traffc) on each lnk. The orgnal lnk mpedance functon has to take ths background traffc volume nto consderaton. Let BG a denote the background traffc volume resultng from external trps on lnk a, ( a A ). The orgnal lnk mpedance functon wll be transformed nto f v a BGa 4 s a( va ) tta tta ( ) as the modfed BPR functon, whch wll be used CPa n ths study. The frst tem n the obectve functon s the sum of ntegrals of lnk mpedance functon. Ths tem does not have any physcal meanng; t s only constructed to satsfy user equlbrum condtons. User equlbrum condtons state that all used paths

59 between each OD par must have equal travel tme and no road user can mprove hs/her travel tme by swtchng paths (Wardrop, 1952). The second tem n the obectve functon does not have any physcal meanng ether. Ths tem ensures that trp dstrbuton has greatest number of states durng the procedure of allocatng trp generaton n each TAZ ( O, each OD par ( t, I and J I and D, J ) nto ) (Wlson, 1970). In ths tem, s an emprcally determned parameter based on the observed data whose value s greater than 0. The procedure of obtanng the value of wll be dscussed n the secton on model calbraton. Constrant 4.1b denotes that trps orgnatng from are the summaton of trps from to all other destnaton TAZs. Constrant 4.1c represents that the trps termnatng n destnaton are the summaton of trps from all other orgns to ths destnaton. Constrant 4.1d refers to flow conservaton, whch states that the summaton of all path flows that connect an OD par s equal to trp exchange between ths OD par. Constrant 4.1e refers to defntonal constrant, whch descrbes network structure by formulatng the relatonshp between path flow and lnk flow. The non-negatvty constrant 4.1f ensures that path flow s always greater than or equal to zero, whch makes the soluton of ths program physcally meanngful snce there s no negatve trp n the real world. The combned trp dstrbuton-assgnment model wth the orgnal BPR functon n the obectve functon can meet user equlbrum condtons, has trp dstrbuton functons n the gravty form. These have been dscussed n several studes (Sheff, 1992; Boyce et al, 1988, Evan, 1976). The purpose of the followng secton s to prove the combned trp dstrbuton-assgnment model wth the modfed BPR functon can stll arrve at the same results as those wth the orgnal BPR functon User Equlbrum Condtons and Trp Dstrbuton Functon The purpose of ths secton s to prove that the optmalty condton of ths program can satsfy user equlbrum condtons, and to derve the trp dstrbuton functon n the proposed combned trp dstrbuton-assgnment model. The trp 41

60 dstrbuton functon can be used to determne the value of through the model calbraton process. To derve the optmalty condtons of ths optmzaton program, the Lagrangan of ths mnmzaton problem can be formulated as equaton 4.2. L a v 0 a ( D 1 sa ( w) dw t ) ( t ln t u ( t rr t h ) r ) rr ( O r h r t ) 4.2,, u, r are the Lagrange multplers, denotng the dual varables assocated wth each correspondng constrant. In defntonal constrant 4.1e (ncdence relatonshp between lnk flow and path flow), the dervatve of lnk flow wth respect to a partcular path flow equals to an ncdence (0 or 1). v a h r h r rr h r ar 1 0 f lnk a s otherwse on path r The frst tem n the obectve functon s the sum of ntegrals of the lnk mpedance functon. The dervatve of ths tem wth respect to the lnk flow can be wrtten as follows: v a a va 0 s ( w) d a w s ( v a a ) tt a tt f a v ( a BG CP a a ) 4 So the frst-order condton for ths mnmzaton program governng h r, t can now be explctly expressed as: L h r a ar s ( v ) u 0 4.3a a a r 0 ( 0 ) 4.3b r h r r L t (ln t ) / u 0 4.3c 42

61 The dervatve of obectve functon wth respect to the path flow comes ar ar ar to sa( va) tt a u r ; tta s the congested travel tme on path r a a a accordng the defnton. Equatons (4.3a-b) ndcate that the optmalty condton of ths program can meet user equlbrum condtons as below: ar If h r 0, then r 0 the travel tme on path r, sa( va ) u ar If h r 0, then r 0 the travel tme on path r, sa( va ) u Snce path r belongs to OD par from to, t ndcates all used paths (path flow greater than zero) from to have the equal travel tme of u, and all unused path (path flow equal to zero) have hgher travel tme than u or the same travel tme as u. The mnmal travel tme between an OD par s equal to the Lagrange multpler u. These optmal condtons ndcate that no road user can mprove hs/her travel tme by swtchng paths. a a 4.4. Equaton 4.3c s used to derve OD trps, whch can be transformed nto equaton t e ( u ) 4.4 Ths expresson s then substtuted nto constrants 4.1b and 4.1c respectvely; the followng results are derved: ( u ) e O e ( u ) e O ( u ) e D e ( u ) e D 4.5a 4.5b To further smplfy, set: 43

62 e 1 A ( u ) ( u ) ( u O e D e D B e ) ( u ) 1 e 1 B e D e 1 ( u ) 1 ( u ) ( u ) O e e O A e 1 u expressed as: Substtute e, e nto equaton 4.4, and the OD trps from and to can be t u A B O D e 4.6 The travel mpedance functon between OD pars s characterzed by exponental decay form of u f ( u ) e, n whch the s a parameter determned durng the calbraton procedure. Trp dstrbuton functon 4.6 wll be used n the calbraton procedure to determne value based on the observed OD trp and travel tme tables provded n Chapter 3. After the calbraton, the determned value wll be put nto the obectve functon of ths combned transportaton model for future forecastng. It s noted that both A ( u ) 1 and e B ( u ) e 1 are balancng factors wthout any physcal meanng (Wlson, 1977). Equaton 4.6 ndcates that the trps between an OD par from to s drectly proportonal to the number of trps orgnatng from and the number of trps destned to, and nversely proportonal to travel tme between ths OD par Model Soluton The convexty and the unque soluton wth respect to lnk flow and OD trp of the combned transportaton model have been dscussed n some studes, where the orgnal 44

63 BPR functon s n the obectve functon (Sheff, 1992; Boyce et al, 1988, Evan, 1976). The purpose of the followng secton s to prove that the proposed combned trp dstrbuton-assgnment model wth modfed BPR functon s stll a convex optmzaton program and has a unque soluton wth respect to lnk flow and OD trp. In order to prove ths program has one and only one optmal soluton, t s suffcent to prove that the feasble regon by the constrants s convex and the obectve functon s strctly convex. The constrants are consttuted by lnear equalty equatons; therefore, the feasble regon s convex. The non-negatve path-flow constrant does not affect the property of convexty, t only needs to prove strct convexty of the obectve functon. The varables n the obectve functon nclude lnk flow ( v a ) and OD trps ( t ); convexty can be proven wth respect to these two varables. We can set Z( v, t ) a a va 1 s ( w) dw a 0 ( t ln t t ) 4.7 It can be seen that t s greater than zero, and that va wll be greater than zero based on the relatonshp between path flow and lnk flow. The strct convexty of the obectve functon can be proven by demonstratng the Hessan matrx (the matrx of the second dervatve of the obectve functon wth respect to these two varables) s postve defnte. The dervatve of Z v a, t ) wth respect of lnk flow on lnk a and b can be demonstrated as below. ( va sa ( w) d w sa ( va v ) 0 a a tt a 4.8a 2 Z v v tt a( v v ttb ( vb ) ) vb a b b 0 a for a b otherwse 4.8b f vb BGb 4 tt b ( ) f tt b ( v ) CP b b 0.6tt b vb BGb 3 ( ) v v CP CP b b b b 0 4.8c 45

64 46 The dervatve of ), ( v a t Z wth respect to the OD trps from to and the OD trps from r to s can be demonstrated n equaton 4.9. Snce t and are both greater than 0, t rs 1 s greater than 0. otherwse s r and for t t t t t Z rs rs rs ln It s noted that 0 2 v a t Z and 0 2 t v a Z snce they are dfferent categores of varables (Sheff, 1992). Therefore, all the off-dagonal elements n the Hessan matrx are zero. All the dagonal elements n the Hessan matrx can be obtaned from equatons (4.8a-c and 4.9). So the Hessan matrx can be explctly wrtten as equaton nn rs n n n b b b a a a a t t t v v t v v t v v t t v Z ) ( ) ( ) ( ), ( Snce all the dagonal elements n ths matrx are strctly great than zero and other elements n the matrx are zero, the Hessan matrx s strctly postve defnte. Thus the obectve functon s strctly convex. Also, the feasble regon by the constrants s convex as well. As a consequence, ths mnmzaton program has a unque optmal soluton wth respect to the lnk flow and OD trp.

65 The results llustrate that there s only one flow pattern and OD trp pattern assocated wth solvng ths mnmzaton problem. It s worth notng that the strct convexty of the obectve functon s set up wth respect to the lnk flow and OD dstrbuton nstead of path flow. The convexty wth respect to path flow s not guaranteed, whch shows that path flows are not unque, whch was dscussed n detal n the lterature (Sheff, 1992). One of the maor goals n transportaton model development s to apply the model to the study area and forecast the traffc volume on the road network. To acheve ths goal, the gven parameters ncludng O, D and need to be determned based on socoeconomc data and the observed OD trp and travel tme tables n the base year. Ths can be accomplshed by model calbraton procedure, whch s dscussed n the followng secton. 4.2 Model Calbraton After the proposed combned trp dstrbuton-assgnment model s formulated, the next step s to calbrate the model to obtan the approprate value of the parameters. After calbraton, the model can be used for future forecastng wth avalable data nput such as soco-economc data Trp Generaton Model Calbraton As dscussed n the model formulaton, O and D are gven parameters and are the row totals and the column totals n Table 3-2. It can be seen that the row totals are equal to the column totals or O D because ths transportaton model s a daly model n ths study. The daly model assumes that the trps that orgnated from a TAZ eventually come back to ths TAZ, whch results n O D. It s worth mentonng that O D s not related to the closed/open system at all. It does not matter f the model 47

66 area s a closed or open system; the daly model always has O D wth trps that orgnated from a TAZ eventually comng back to ths TAZ. For example, the study area s an open system, whch wll be dscussed n the next chapter; substantal obs n the study area are occuped by workers outsde the study area, and a sgnfcant number of workers n the study area are employed outsde the study area. However, the trps orgnatng from a TAZ, whether they are gong to the study area or outsde the study area, wll come back to ths TAZ at the end of the day snce t s a daly transportaton model. Snce trps ( O / D ) are related to urban actvtes such as workng and shoppng, all these actvtes are generated by household and employment. Let H denote the number of households n TAZ, ( I ); let E denote the number of employments n TAZ, ( J ). O and employments. between D are hghly correlated wth the number of households and The trp generaton calbraton attempts to quantfy the relatonshp O / D and household and employment, whch wll be used to estmate the values of O / D n the future. The scatter plot between trp generaton ( O / D ) and household/employment ( H / E ) s llustrated n Fgure 4.1 and Fgure 4.2. Fgure 4.1: Relatonshp between Trp Generaton and Household 48

67 Fgure 4.2: Relatonshp between Trp Generaton and Employment The number of trps generated n each zone n the base year s shown n Table 4.1 along wth the number of household and employment, where O / D are from the observed trp table, and H / E.are from the census data. The multple lnear regresson technque s used to establsh the statstcal relatonshp between trp generaton and urban actvtes n terms of household and employment (Rosner, 2005). The regresson equaton can be expressed as equaton ˆ O 1H 2 E 4.11 Where Ô : The estmated number of trps orgnated from zone, 1 2 : The emprcally determned parameters usng the observed base year data It s assumed that the ntercept of ths equaton equals zero snce a zone wthout any household or employment could not generate any trps. For regresson development, the regresson coeffcents of 1 and 2 are also known as partal slope coeffcents. It ndcates the change of response varable of H / E respectvely, wth other explanatory varables fxed. Ô correspondng to one-unt change n 49 The estmaton of the regresson coeffcents can be acheved by the least square method, whch s carred out

68 wth statstcal software. The least square refers to makng the square of dfference between the observed value of O and the estmated value of Ô as small as possble. Ths estmaton can be clearly expressed as the mnmzaton of O H E n denotes the total number of TAZs (78). n ; The regresson coeffcents fttng the lnear model do not guarantee the results are sutable for the purpose of explanaton. Whether the regresson model s able to sgnfcantly explan the varablty n the response varable s the frst statstcal test pursued, whch tests f the model s sgnfcant at a certan confdence level. The degree of assocaton between the response varable and the explanatory varables s the second statstcal test to be pursued, whch determnes how accurately the model s able to make predctons. It also reflects the degree to whch the regresson model explans the varablty of the response varable. The thrd statstcal test determnes whether the regresson coeffcents are sgnfcant at certan confdent levels such as 95 percent. Total sum of square (Tot SS) s defned as gross measure of varablty of the response varables, whch can be decomposed nto regresson sum of squares and resdual sum of squares. Regresson sum of squares (Reg SS) refers to the varablty n the response varable nterpreted by the regresson model. Resdual sum of squares (Res SS) represents the varablty n the response not accounted for by the model. The relatonshp among these three square tems can be wrtten as: n 1 n n O O O ˆ O O Oˆ 1 Tot SS= Reg SS + Res SS 1 It s further defned that Reg MS = Reg SS/k, Res MS = Res SS/(n-k-1) and Tot MS = Tot SS/(n-1). The O s the mean of observed value of the response varable or computed by n O O 1. The k s the number of explanatory varables. n 50

69 Table 4.1: Trp Generaton, Household, and Employment n Each Zone TAZ H E H O / D TAZ 51 E O / D

70 Frst, the statstcal test for the model sgnfcance s performed at 95 percent confdence level by usng f statstc test. The hypothess can be expressed as H 0 : If the value of F = Reg MS/Res MS s greater than f k, nk 1, (or equvalently report p-value s less than 0.05 from the statstcal software), the H 0 hypothess s reected, whch determnes that the model s sgnfcant n estmatng the response usng the collectve explanatory varables. After verfyng the model sgnfcance, goodness of ft s examned, whch refers to the fracton of the varablty n the response accounted for by the regresson model. In ths multple lnear regresson, the adusted R square s used n udgng the degree to whch the model can explan the varablty n the response varable, whch s defned by 1-Res MS/Tot MS. The hypothess for the coeffcent of each explanatory varable s further tested usng t test, whch examnes f one explanatory varable s sgnfcant n predctng the response after controllng for other explanatory varables. Let L HH n 1 H 2 n 2 2 ( H ) / n ( n 1) s X 1, and H 0. If the value of 0 : 1 1 t Res MS/ s greater than t (or equvalently the compute reported p- nk1,1 0.05/ 2 L HH value s less than 0.05), the hypothess test s reected. It ndcated the coeffcent for ths explanatory varable s sgnfcant at 95 percent confdence, whch also means ths varable s useful n predctng the response. The model statstcs output for ths trp generaton model calbraton s lsted n Table 4.2, followed by the regresson equaton

71 Table 4.2: Trp Generaton Regresson Model Statstcs Trp Generaton Model Statstcs Varables Estmate t-test p-value H (Household) E (employment) Adusted R Square 0.91 (Model) F Stat (Model) p-value O D H E 4.12 The prmary goal of ths regresson analyss s to obtan the statstcally sgnfcant model for estmatng the response varable. As seen from the model statstcs, 91 percent of (the values of Adusted R Square) varaton n the trp generaton can be generally explaned by the combnaton of household and employment. The F statstc shows that the model s qute sgnfcant at 95 percent confdence level wth p-value substantally lower than Thus, the explanatory varables are collectvely sgnfcant n forecastng. The t statstcs show that the coeffcent of each explanatory varable s sgnfcant at 95 percent confdence level too, whch shows that each explanatory varable s sgnfcant n the model. Therefore, ths regresson model s good for the purposes of explanaton and estmaton. The observed base-year trp generaton for each zone are compared wth the estmated trps n Fgure 4.3, where horzontal axs denotes observed trps and vertcal axs represents estmated trps. 53

72 Fgure 4.3: Comparson between Observed and Estmated Trp Generaton Trp Dstrbuton Model Calbraton As dscussed n secton 4.1.2, that plays an mportant role n dstrbutng OD trps s emprcally determned based on the observed base-year data. The observed OD trp and travel tme tables (Table 3.2 and 3.3) are utlzed for ths model calbraton. Trp dstrbuton model calbraton refers to the process of determnng value, whch ensures that the modeled trp length dstrbuton s as close as possble to the observed trp-length dstrbuton. A tral-and-error (teraton) process s employed n ths calbraton process. The calbraton process compares the modeled mean travel tme wth the observed mean travel tme n each teraton untl these two factors reach a convergence (Calper Corporaton, 2004). Let c denotes the observed travel tme between OD par from to, ( I ) and ( J ). The observed mean travel tme for the study area s defned tc asc*. The calbraton procedure s constructed as below (Calper Corporaton, T 2004). Take the nverse of the observed mean travel tme as the ntal value of nto the travel mpedance functon; the ntal value can be regarded as 1. 54

73 Apply the trp dstrbuton model of equaton 4.6: t A B O D e u assocated wth the observed trp table. O and D. Ths wll create a new modeled OD Calculate the new modeled mean travel tme C 1 usng the same formula as C * based on the new modeled OD trp table. If the convergence C C ( * 1% ) s reached, the procedure stops; otherwse, update the value C* of as follows: At (+1)th teraton, the updated parameter can be calculated accordng to the followng formula 1 ( C C ) * 1 ( C C C * 1 C 1 ). If =1, C11 2 C * After updatng the value of, return to the next teraton The calbraton procedure stops after eght teratons; the output s the optmal value of (0.1993), whch s larger than zero correspondng to the dscusson of value n model formulaton. 4.3 MODEL TEST The value and the relatonshp between O / D and H as well wth obtaned from the model calbraton wll be substtuted nto the combned transportaton model. The next step s to sort out the relatonshp between lnks and paths for the study area n order to represent the transportaton network structure. It s noted that there could be many paths connectng each OD par n the network, most of whch are not reasonable for travelers to choose. Travelers heurstcally take only a few of the shortest paths nto consderaton. For ths study, the frst three shortest paths between each OD par are taken nto account for formulatng the network structure. For each OD par, the frst three shortest paths are chosen based on travel tme on the paths. After the relatonshp E 55

74 between lnks and paths are obtaned, the combned trp dstrbuton and assgnment model can be formulated. Mn a va 0 s ( w) dw a ( t ln t t ) 4.13a S.T. t O H E 4.13b t D H E 4.13c rr h r t 4.13d v ar a h r 4.13e rr h f r Algorthm As prevously dscussed, ths program conssts of nonlnear obectve functons and lnear equalty constrants. The strct convexty of the obectve functon and lnear qualty constrants ensure that ths program has a unque global optmum n terms of lnk flow and OD trp. Ths program wll be solved by means of an nteror pont algorthm. A few software packages have been developed to mplement ths algorthm, such as LOQO, KNITRO, etc. LOQO and KNITRO are utlzed to seek the soluton of ths program. Ths algorthm has been developed over the last two decades. It has emprcally been shown that ths algorthm s effcent and robust n solvng large non-lnear programmng problems (Waltz et al, 2004). The logc behnd ths algorthm s to change constraned optmzaton problems nto unconstraned problems by placng equalty constrants nto the obectve functon wth multplyng Lagrange multpler. Inequalty constrants wll be placed nto the obectve functon wth barrer functons. Barrer functons are desgned to prevent the soluton from departng the feasble regon. 56

75 After placng all constrants nto the obectve functon along wth Lagrange multplers and barrer functons, the obectve functon becomes Lagrangan form for ths optmzaton program. The frst order Karush-Kuhn-Tucker (KKT) condton can then be derved for ths optmzaton problem, whch results n the standard prmal-dual system and conssts of a seres of equatons. Then the algorthm s developed to solve ths seres of equatons to satsfy KKT condtons for optmalty. There are many varatons n the nteror pont algorthm assocated wth computng search step and barrer functon. For example, LOQO and KNITRO dffer from each other on the method of search step, although both of them use the nteror pont algorthm. The methodologes n these software packages are brefly ntroduced. Vanderbe (1998) ncorporated a type of nteror pont algorthm n the LOQO software package. The logarthm type of barrer functon s adopted to remove nequalty constrants. After formulatng KKT condtons for optmalty program, Newton s method assocated wth feasble search drecton s used to solve ths program. In the case of the combned transportaton model program, all the constrants are lnear equalty constrants except the non-negatvty constrants n terms of path flow. A Lagrangan can be easly formulated wth addng the Lagrangan multpler for the equalty constrants and barrer functon for the nequalty constrants. Waltz et al (2004) proposed another type of nteror pont algorthm to solve large-scale nonlnear optmzaton problems. Ths algorthm s ntegrated n the KNITRO software package. It follows the same procedure to formulate the Lagrangan form as LOQO. It also utlzes the same type of barrer functons to elmnate nequalty constrants by placng them nto the obectve functon as LOQO. The only dfference between these two algorthms les n the search step n solvng the equatons of KKT condtons (or prmal-dual). KNITRO conducts a lne search or a trust regon search as ts prmary step. The lne search method s to calculate steps by factorng prmal-dual systems of equatons; the trust regon method s to compute steps by a conugate gradent teraton. The Lagrangan form of the combned transportaton model programmng can be wrtten as below, assocated wth the nteror pont algorthm. 57

76 L a v 0 a ( D 1 sa ( w) dw t ) ( t u ( t ln t rr t ) h ) r rr ( O ( h r r t w ) r ) rr Ln( w ) Here w 0s a vector of slack varables for the path set n the system, and s r the barrer parameter assocated wth the logarthm type of barrer functon. r Model Test The combned trp dstrbuton-assgnment model s tested on a realstc study area of Woodford County, Kentucky. Ths area has been descrbed n Chapter 3 and conssts of 78 zones whch produce about 6006 OD par. There are 723 lnks and 18,018 paths n ths network system. Ths optmzaton program can be solved by both solvers of LOQO and KNITRO, snce a unque global optmal soluton for ths program exsts. Both solvers do not have any specal requrements about startng pont. In KNITRO, any startng pont could be selected or KNITRO can compute one (Waltz et al, 2004). LOQO could fnd a globally optmal soluton f the problem s convex; otherwse, t could fnd a locally optmal soluton near to a gven startng pont (Vanderbe, 1998). However, these two solvers behave dfferently wth respect to the startng pont n seekng the optmal soluton for the proposed program. Several startng ponts have been tred on KNITRO and LOQO. It was found that KNITRO always can fnd the optmal soluton no matter what the startng pont s. For example, KNITRO was able to converge to the optmal soluton even wth zero as the startng pont. LOQO s more senstve to the startng pont than KNITRO. It often faled to converge to the optmal soluton when the startng pont was not near to the optmal soluton. For example, one startng pont was the observed OD trps n Tables 3-2 and the other startng pont was 0; LOQO can only fnd the optmal soluton wth the startng pont of the observed OD trps, and t faled wth zero as the startng pont. Wth the same starng pont such as the observed OD trps, KNITRO converged to 58

77 the optmal soluton a lttle slower than LOQO. These two algorthms wll contnue to be used n Chapter 6 to solve another optmzaton program. The optmal soluton ncludes OD trps and lnk volume. Lnk volume and Volume/Capacty (V/C) rato can be used to dentfy the defcency along the transportaton network, demonstrated n Table 4.3. Snce there are too many lnks over the network, only the frst twenty lnks wth the most traffc flow are selected for llustraton purposes. Table 4.3: Selected Lnk Attrbutes and Assgned Flow Lnk Flows Background Assgned Capacty V/C L L L L L L L L L L L L L L L L L L L Fgure 4.4 shows the frequency dstrbuton of the V/C rato. Results shows that the most traffc s concentrated on the US Hghway 60 snce ths road provdes servce to a large quantty of through traffc, whch s constent wth the observaton. Result statstcs shows that the study area overall s not congested at all, wth an average V/C 59

78 rato of Only 3 percent of road segments n the network carry traffc flow over ther capacty. Eght percent of the segments have a V/C rato between 0.6 and 1. Most of the segments carry traffc well under ther capacty. Fgure 4.4: V/C Rato Frequency Dstrbuton Based on the model outputs, other transportaton measures can be developed such as congested travel tme between each OD par and travel tme to downtown, whch wll be used n the land use model development. The next chapter develops the land use model for estmatng household and employment dstrbuton. 60

79 CHAPTER 5 LAND USE MODEL DEVELOPMENT The proposed land use model s desgned to forecast the number of households/employments that wll be located n each plannng zone. It s comprsed of two sub-models: household and employment dstrbuton models. In ths study, land use plannng zones have the same spatal confguraton as TAZs. Ths ndcates that the land use model and the transportaton model are establshed at the same spatal level. Ths confguraton dffers from exstng ntegrated urban models ITLUP and MEPLAN. In those models, a land use plannng zone conssts of several TAZs. Aggregaton of TAZs nformaton nto the land use plannng zone resulted n loss of nformaton such as travel tme between TAZs. In addton, there are only a few TAZs n ths study area; nformaton loss durng aggregatng TAZs nto the land use plannng zone s sgnfcant for the purpose of analyss. Ths chapter frst ntroduces the reasons that exstng land use models cannot be appled and the characterstcs of the study area. A modelng approach for estmatng household/employment dstrbuton at the spatal TAZ level s then dscussed. Dfferent categores of factors assocated wth land use structure and transportaton measure are dentfed from avalable data sources. Multple regresson equatons are developed to fnd a better combnaton of these factors for the purposes of explanaton and estmaton. The model s developed usng a relatvely straghtforward statstcal technque, makng t easy to understand and develop usng the lmted resources avalable n a small urban area. 5.1 MOTIVATION Regonal growth has touched small urban areas (generally defned as communtes wth a populaton less than 50,000), resultng n deteroratng traffc condtons. However, 61

80 MPOs, whch coordnate land use plannng and transportaton plannng, are only establshed n large urban areas wth more than 50,000 n populaton. In recent years, small communtes have become more concern about growth. These concerns ncreased nterest n nvestgatng the nterrelatonshp between land use and transportaton plannng, to encourage smart growth and mtgate traffc congeston. However, for smaller urban areas, exstng tools for modelng the nteracton between land use and transportaton systems orgnally desgned for large urban areas, are not usable. As dscussed n Chapter 2, urban economc models, e.g., MEPLAN, based on nput-output frameworks are only sutable for regonal or ntercty modelng and not for small urban areas. The recently developed urban model UrbanSm, based on dscrete choce theory, requres very detaled data at a much dsaggregated level such as parcel level. In comparson wth UrbanSm, the proposed land use model s easy to use and affordable to mplement. For example, UrbanSm has to use GIS to produce a parcel level database, and SAS or SPSS to calbrate the model; the proposed land use model can be easly calbrated n Mcrosoft Excel. The data nputs for UrbanSm nclude regonal control totals, exstng land use, future land use plans, households, employments, envronment constrants, development costs, and accessblty. Envronment constrants and development costs are not typcally avalable n plannng commssons. The proposed land use model does not requre these two varables. If UrbanSm was appled to the study area at 200x200 meter parcel level wth 10 varables, t requres 123,500 data records (number of varables multpled by number of parcel cells) for model calbraton; the proposed land use model requres only 780 data records (number of varables multpled by the number of TAZs). The land use model n the most wdely ntegrated model ITLUP consders the model area as a relatvely closed system. It ndcates that the maorty of obs n the model area are occuped by workers who lve n the model area, and the maorty of workers from local households work n the same area. However, n the study area, a sgnfcant number of obs (48% of total obs) are occuped by workers outsde the study area; a sgnfcant number of workers from local households (55% of total workers) work outsde the study area. 62

81 Fgure 5.1 shows local resdents spatal commutng pattern based on data from Kentucky State Data Center. It ndcates where workers from local households are workng, and where workers who are employed n ths area lve. Only 45 percent of the workers who resde n ths study area work n ths area. Ffty-fve percent work outsde the study area: 35 percent work n Fayette County, whch s a regonal economc center; 11 percent work n Frankln County, where the state captal s located wth many state employment opportuntes; 9 percent work n other countes or states. Ffty-two percent of the obs n ths study area are occuped by workers from local households. Forty-eght percent are occuped by workers outsde the study area: 18 percent by workers who lve n the metropoltan area of Fayette County, 6 percent by workers from Frankln County, and 24 percent by workers from other countes or states. Fgure 5.1: Commutng Patterns of the Study Area It s obvous that the ITLUP s not sutable for ths study area because t cannot separate obs occuped by resdents of outsde the study area from obs occuped by Woodford resdents. Unrealstc assumptons have to be made when the ITLUP s forced to be appled to ths study area. The ITLUP can only focus on the 45 percent of area resdents who work nsde the study area, and the 52 percent of obs that are occuped by households from nsde the study area. Assumptons made by the ITLUP model were that n each TAZ, 45 percent of area resdents work nsde the study area, and 52 percent of local obs are occuped by workers who lve nsde the study area. A prelmnary study 63

82 was conducted to estmate household dstrbuton usng the ITLUP. Results show that the ft between the observed household dstrbuton and the modeled dstrbuton s low, wth R square 0.56 even only for those workers employed nsde the study area. The household dstrbuton results from the ITLUP model s lsted n Appendx 5-A. It can be seen that exstng land use models are not applcable for ths small urban area due to ther lmtaton and the area s characterstcs. The obectve of the proposed land use model s to ft ths small urban area s characterstcs and take nto consderaton the lmted resources avalable n small urban areas. The next secton descrbes the process of developng a sutable land use model that can be used n ths small urban area as well as n large urban areas. It s mportant to note that prelmnary analyss shows that household/employment densty s a better ndcator for household/employment dstrbuton model development than the number of households/employments for. Therefore, the land use model n the followng dscusson uses the household densty model and employment densty model. 5.2 VARIABLE SPECIFICATION Many varables affect household and employment dstrbuton, ncludng demographc and bult-envronment varables. Ths study consder two basc categores of varables: land use structure and transportaton measures Land Use Structure Varables Land use patterns of Woodford County were analyzed frst to examne land-use composton n each zone. In order to elmnate the mpact of the zone sze, fractons of land use are used nstead of land areas of each type of land use. The fracton of a type of land use s defned as the rato of ths land use area over the total area of ths TAZ. Eght types of land use are consdered n ths study: resdental, moble home and mult-famly resdental, agrculture and preserved agrculture, ndustral, commercal, professonal 64

83 offce and nsttutonal, vacant, and other land use. In addton, land use mx ndex (also known as land use balance, or entropy) defned n equaton 5.1 s also ncluded. It s a functon of land use fractons suggested by Kockelman (1997). n MxIndex 1 Fr Ln( Fr ln( n) ) 5.1 where n s the total number of land use types under consderaton, and Fr s the fracton of land use type. The value of mx ndex ranges from 0 to 1, where 0 nfers that there s only one type land use and 1 ndcates that all eght types of land use have the same share n a TAZ Transportaton Measures Transportaton measures descrbe the transportaton system characterstcs for each TAZ, as well as ts accessblty to dfferent actvtes. Factors under ths category are developed based on the lterature of urban economcs, urban plannng and urban socology (Waddell et al, 2003a; Waddell et al, 2003b). Ths lterature recognzes many transportaton measures, provdng nspraton for the development of transportaton measures n ths dssertaton. Transportaton measures for ths study nclude dstance to maor hghways, travel tme to downtown, travel tme to adacent employment centers, and accessblty measures. Dstance to maor hghways refers to the length of road segments that connect a TAZ centrod to an on/off ramp or ntersecton of the nearest maor hghway. Ths measure ndcates how accessble a TAZ s to US60/US62, Interstate 64, and the Bluegrass Parkway. Travel tme to downtown s defned as the congested travel tme from a TAZ to the downtown of Versalles, because ths downtown has a large number of servce and commercal actvtes. The congested travel tme s generated after runnng the combned trp dstrbuton-assgnment model. Ths measure reflects the degree to whch households n a TAZ are able to access servce and commercal actvtes n the downtown area. 65

84 There are two maor employment centers adacent to Woodford County, connected through the nter-urban facltes of US 60 and US 62. One s the Lexngton metropoltan area; the other s the state captal (Frankfort) wth many government obs. The travel tme to adacent employment center factors nclude both travel tme to Lexngton and travel tme to Frankfort. These factors descrbe the accessblty of a TAZ to employment centers. Accessblty s used to measure the degree to whch people n a TAZ reach other actvtes or a busness n a TAZ s reached. Many accessblty measures have been developed for dfferent applcatons such as access to actvty wthn tme threshold, logsum accessblty measure, etc. (Mller, 2004). For example, the functon of the access to actvty wthn tme threshold s to add up all opportuntes (.e., obs or households) that le wthn the travel tme threshold (.e., 15 or 30 mnutes). The functon of logsum measure for a TAZ s to logsum all opportuntes as a functon of households or employment, and the travel mpedance as a functon of travel tme between ths TAZ and other zones. For the household densty model, accessblty measures the degree of ease wth whch the resdents of a TAZ can make trps to other zones n order to accomplsh ther actvtes. It s drectly proportonal to reachable opportuntes and nversely proportonal to travel tme for reachng those opportuntes. The combned trp dstrbutonassgnment model n Chapter 4 produced the travel mpedance functon and the congested travel tme between each OD par, whch are used to develop the accessblty functon. Based on the concept ntroduced by Wllams (1977), the accessblty functon for the household densty model s formulated n equaton 5.2. h c ACC e E 5.2 where h ACC : The accessblty measure for the household densty model : The emprcally determned coeffcent n the combned trp dstrbutonassgnment model as dscussed n Chapter 4 66

85 For the employment densty model, accessblty measures the degree of ease wth whch a busness n a TAZ can attract trps from other zones for ganng benefts (e.g., attractng people to work or shop n ths TAZ). Ths s drectly proportonal to the number of households at orgnatng zones and nversely proportonal to travel tme between ths TAZ and orgnatng TAZs. Smlarly, the accessblty functon for the employment densty model can be formulated n equaton 5.3. e ACC e c H 5.3 where e ACC : The accessblty measure for the employment densty model 5.3 CORRELATION ANALYSIS In ths secton, the relatonshp between household/employment densty and each factor under the category of land use structure and transportaton measure s explored. Land use structure varables nclude each type of land use fracton ( X 1,, X 8 ) and land use mx ndex ( X 9 ). Transportaton measures nclude dstance to maor hghways ( X 10 ), travel tme to downtown ( X 11), travel tme to Lexngton ( X 12 ), travel tme to Frankfort ( X 13) and accessblty for the household densty model and the employment densty model ( X 14 and X 15 respectvely). All factors as explanatory varables are summarzed n Table 5.1 along wth two response varables. Numercal values of these varables are lsted n Appendx 5-B. Land use structure data are from the data sources as dscussed n Chapter 3; transportaton measures are developed based on the output of the combned trp dstrbuton-assgnment model. 67

86 Table 5.1: Varable Descrpton Notaton Descrpton Response Varables Y Household densty (Households/mllon ft 2 ) 1 Y2 Employment densty (Jobs/mllon ft 2 ) X1 X X X X X X X X X X X X X X Explanatory Varables Moble home and mult-famly land use fracton Resdental land use fracton Professonal offce and nsttutonal land use fracton Commercal land use fracton Industral land use fracton Agrculture and preserved agrculture land use fracton Vacant land use fracton Other land use fracton Land use mx ndex Dstance to maor hghways (mle) Travel tme to downtown (mn) Travel tme to Lexngton (mn) Travel tme to Frankfort (mn) Accessblty measure for household densty estmaton Accessblty measure for employment densty estmaton Correlaton analyss s performed to dentfy the lnear assocaton between the response and explanatory varables. Correlaton coeffcent reflects the drecton and strength of the lnear relatonshp between the two varables. The correlaton coeffcent between Y and X can be computed by the followng equaton. r Y, X Here s Y, X 5.4 ( n 1) s Y s X r Y, X s the correlaton coeffcent between these two varables. s Y, X denotes the covarance between these two varables; t can be calculated as n sy, X ( Y Y )( X X ) where X and Y are the means of X and Y respectvely. 1 68

87 s Y, s X are the sample standard devatons of Y and X respectvely: s Y n 1 ( Y Y ) n 1 2 and s X n 1 ( X n 1 X ) 2 ; n s the sample sze, whch s the total number of TAZs n ths study area. The value of the correlaton coeffcent ranges from -1 to +1; a plus sgn represents a postve lnear relatonshp between the two varables; a mnus sgn ndcates that the two varables are negatvely correlated. The larger the absolute value, the stronger the lnear assocaton that exsts between the two varables Household Densty Correlaton Analyss The scatter plots between household densty varables and each explanatory varable are shown n Fgure 5.2a-b. They provde vsual ndcaton of the relatonshp (lnear, non-lnear) between each explanatory varable and the response varable. Correlaton analyss s then performed to fnd maor factors that have a sgnfcant nfluence on household densty. Each cell n Fgure 5.2a-b shows the relatonshp between the response varable and the correspondng explanatory varable. The plots apparently demonstrate that there are nonlnear correlatons between household densty and ndustry land use fracton, agrculture and preserved agrculture land use fracton, dstance to maor hghway, and travel tme to downtown, all of whch look lke an nversely proportonal curvature. Therefore, household densty s decreasng wth the ncrease of ndustral land use fracton, agrculture and preserved agrculture land use fracton, dstance to maor hghway and travel tme to downtown. The relatonshp between the response and other explanatory varables are dffcult to udge based on the plots. Possble transformatons such as logarthm, nverse, square, and exponental transformatons were tested to fnd the transformaton form that has the strongest correlaton wth household densty. The transformaton wth the strongest degree of assocaton was chosen for further analyss. Varables of ndustry land use fracton, agrculture and preserved agrculture land use 69

88 fracton are not transformed nto nverse form snce there are zero values for these varables that dsable nverse transformaton. Ultmate transformaton forms for varables of dstance to maor hghway, travel tme to downtown, travel tme to Lexngton, and travel tme to Frankfort are nverse form; lnear assocaton s the strongest among all transformaton forms for other varables. Fgure 5.2a: Scatter Plot between Household Densty and Land Use Structure Varables Fgure 5.2b: Scatter Plot between Household Densty and Transportaton Measure The correlaton coeffcents between household densty and each explanatory varable are presented n Table 5.2. Among all explanatory varables, professonal offce and nsttutonal land use fracton, commercal land use fracton, ndustral land use fracton, vacant land use fracton, other land use fracton, dstance to maor hghway, travel tme to Lexngton, and travel tme to Frankfort are nsgnfcant varables because 70

89 these varables have correlaton coeffcent values lower than 0.4, whch s used to udge the strength of correlaton n ths dssertaton. Other explanatory varables are sgnfcant because they have correlaton coeffcent values hgher than 0.4. TABLE 5.2 Correlaton Coeffcents for Household/Employment Densty Correlaton X1 X 2 X3 X4 X5 X6 X7 Coeffcent Y Correlaton X8 X9 X10 X Coeffcent 11 X 12 X13 X14 Y Correlaton X1 X 2 X3 X X 4 5 X6 X7 Coeffcent Y Correlaton X8 X9 X Coeffcent 10 X 11 X 12 X13 X15 Y Among land use structure varables, the resdental land use fracton varable has the most sgnfcant relatonshp wth household densty, whch has a correlaton coeffcent value of It also s the most sgnfcant varable among all explanatory varables. Ths ndcates that changng the resdental land use fracton wll have a sgnfcant nfluence on household densty n ths study area. The moble home and mult-famly land use fracton varable s also strongly correlated wth household densty. It can be seen that the agrculture land use fracton has a negatve mpact on household densty; household densty decreases wth an ncrease of the agrculture land use fracton. Although land use mx seems to have a postve mpact on household densty, we need to be cautous wth ths measure f t appears n the fnal model. The mpact of ths measure on household densty s complcated under certan crcumstances. For example, the correlaton coeffcent shows that a lower value of land use mx (whose value ranges from 0 to 1) should contrbute to a lower value of household densty n a TAZ. However, ths s not the case when a TAZ has only resdental land use. In ths crcumstance, household densty has a hgher value although the value of land use mx s the lowest 71

90 zero. Therefore, land use mx can only be appled to those TAZs that have both resdental land use and other types of land use. Among transportaton measure varables, travel tme to downtown and accessblty show a strong correlaton. Correlaton coeffcents show that households tend to lve n more accessble zones; the zones closer to the downtown area have greater household densty Employment Densty Correlaton Analyss The employment densty correlaton analyss follows the same procedure as household densty. The scatter plot between employment densty and each category of varables s drawn and shown n Fgure 5.3a-b. Analyss was performed to dentfy sgnfcant factors that are strongly correlated wth employment densty. Fgure 5.3a: Scatter Plot between Employment Densty and Land Use Structure Varables Fgure 5.3b: Scatter Plot between Employment Densty and Transportaton Measures 72

91 Each cell n Fgure 5.3a-b shows the relatonshp between employment densty and the correspondng explanatory varable. It s observed that there s a nonlnear relatonshp between employment densty and moble home and mult-famly land use fracton, resdental land use fracton, agrculture and preserved agrculture land use fracton, dstance to maor hghway, and travel tme to downtown, all of whch appear to have a nversely proportonal curvature. Ths sgnfes that employment densty decreases wth the ncrease of moble home and mult-famly land use fracton, resdental land use fracton, agrculture and preserved agrculture land use fracton, dstance to maor hghway, and travel tme to downtown. The relatonshp between employment densty and other explanatory varables s unclear based on ther plots. Possble transformatons such as logarthm, nverson, power, and exponental are tested to fnd the desrable transformaton form. Varables of moble home and mult-famly land use fracton, resdental land use fracton, and agrculture and preserved agrculture land use fracton are not transformed nto nverse form snce there are many zero values for these varables, makng nverse transformaton mpossble. The ultmate transformaton forms for varables of dstance to maor hghway, travel tme to downtown, travel tme to Lexngton, and travel tme to Frankfort are nverse form, whch are utlzed n further analyss. The correlaton coeffcents between employment densty and each explanatory varable are dsplayed n Table 5.2. Half of the explanatory varables are nsgnfcantly correlated wth the employment densty varables snce correlaton coeffcent values are lower than 0.4. These varables nclude moble home and mult-famly land use fracton, resdental land use fracton, professonal offce and nsttutonal land use fracton, ndustral land use fracton, vacant land use fracton, travel tme to Lexngton, and travel tme to Frankfort. Among land use structure varables, the commercal land use fracton s strongly correlated wth employment densty. The correlaton coeffcent between the agrculture land use fracton and employment densty shows that t exerts a negatve mpact on employment densty. Land use mx ndex also has a sgnfcant nfluence on employment 73

92 densty, whch shows that employment densty rses wth the ncrease of land use mx. Attentons should be pad f t appears n the fnal model, because the mpact of ths measure on employment densty s complcated under certan crcumstances. For example, the correlaton coeffcent shows that a lower value of land use mx (whose value ranges from 0 to 1) wll result n a lower value of employment densty. However, ths s not the case when a TAZ has only commercal/servce/ndustry land use. In ths crcumstance, employment densty has a hgher value although the value of land use mx s the lowest zero. Therefore, land use mx can only be appled to those TAZs that have both commercal/servce/ndustry land use and other types of land use. Among transportaton measure varables, dstance to maor hghway has the strongest correlaton wth employment densty, wth a correlaton coeffcent value of It also s the most sgnfcant factor n all explanatory varables. Employment densty tends to declne wth an ncrease n dstance to maor hghway, whch suggests that employment has an nclnaton to locate along maor hghways. Travel tme to downtown and accessblty are strongly correlated wth employment densty, too. Employment densty seems to decrease wth the ncrease of travel tme to downtown and ncrease wth the ncrease of accessblty. It ndcates that obs tend to be located around the downtown area and n those TAZs wth hgher accessblty. 5.4 REGRESSION MODELING ANALYSIS The explanatory varables that are strongly correlated wth the response varables wll be consdered n model development. These explanatory varables are canddate varables for multple lnear regresson model development. A model wth all these explanatory varables ncluded may not be the best based on statstcal tests. Statstcal technques are used to fnd an optmal subset of canddate varables. These technques nclude forward selecton, backward elmnaton, and stepwse selecton (Rosner, 2005). 74

93 5.4.1 Statstcal Technques Forward selecton procedure begns wth only an ntercept n the model. Frst, a sngle explanatory varable model s dentfed from all possble one-varable models whch yeld the smallest Res SS as defned n Chapter 4. In ths study, the sgnfcance level s 0.05, so p-value for ths varable must be less than If p-value for the frst selected value s less than 0.05, ths varable s ncluded n the model; otherwse, none of the canddate varables should be ncluded n the model. The next step s to ft all possble two-varable models wth the frst varable n the model. The second varable s dentfed, whch yelds the largest further reducton n Res SS. The p-value for the second varable s also requred to be less than the sgnfcance level. Ths procedure contnues untl a large p-value over 0.05 s obtaned or, much less commonly, untl all explanatory varables are ncluded n the model. Backward elmnaton procedure starts by ncludng all explanatory varables n the model. A sngle varable s then dentfed whose removal wll cause the smallest ncrease of Res SS. Ths varable wll be removed f ts p-value s larger than 0.05; otherwse, t suggests that all canddate varables should reman n the model. If the frst selected varable s removed, the procedure goes on to dentfy the second explanatory varable whose removal wll lead to the smallest ncrease n Res SS. Ths process contnues untl the p-value of each varable n the model s smaller than 0.05, whch ndcates that none of the canddate explanatory varables should be removed from the model. Stepwse selecton procedure s the hybrd of forward selecton and backward elmnaton. It starts out the same way as forward selecton. Each tme a new explanatory varable s ncluded n the model based on the forward selecton method, backward elmnaton wll be conducted to test f any of the prevously added explanatory varables can be removed from the model. Durng regresson model development, collnearty may appear among explanatory varables. Strong correlaton between explanatory varables produces the collnearty. For example, there s a strong correlaton between travel tme to downtown and accessblty durng household densty model development; ther correlaton 75

94 coeffcent s Collnearty wll have a negatve mpact n estmatng the coeffcent of explanatory varables. An approprate combnaton of explanatory varables wll be chosen to rule out collnearty. Collnearty wll be dagnosed usng statstcs VIF (Varance of Inflaton Factor) for each explanatory varable. For example, VIF for 2 explanatory varable X 1 s defned as 1/(1- R ) 1. regresson model, where X 1 wll be treated as 2 R 1 s calculated from the auxlary the response varable and other explanatory varables stll reman as explanatory varables. There s no specfc threshold value for VIF to determne collnearty. A rule of thumb s to pay attenton to collnearty when VIF for an explanatory varable s greater than 10 (Rosner, 2005). For example, VIF of X 1 s larger than 10, whch ndcates that ths explanatory varable can be removed from the model snce t s approxmately a lnear combnaton of other explanatory varables. Forward, backward and stepwse selecton procedures are mplemented n the SPSS software package. These three procedures generate three canddate regresson models. The adusted R square and VIF wll be used to udge these competng canddate models Household Densty Model Development Household densty model development s to fnd the approprate combnaton of explanatory varables that can be used to estmate household densty for each TAZ. Durng the model development, the aggregaton of smlar explanatory varables s conducted to seek better estmaton. For example, resdental land use fracton s added nto moble home and mult-famly land use fracton to create total resdental land use fracton snce they belong to the same category of land use. It shows that total land use fracton can provde a better estmaton for household densty wth bgger adusted R square. In order for the regresson model to be more physcally meanngful, the constant s excluded from the model. Unreasonable estmaton can take place f the constant stays 76

95 n the model. For example, some households are estmated for a TAZ because of the constant even f ths TAZ has no resdental land use. After evaluatng three canddate models from forward, backward, and stepwse selecton procedures, the followng lnear equaton out of the stepwse selecton procedure s chosen because t has the best ft for the data. The statstcal outputs of the household densty model are lsted n Table 5.3. Household Densty (totalresdental land use fracton) (accessblty) Table 5.3: Household Densty Model Statstcs Varables Estmate t-test Sg.(p-Value) Total resdental land use fracton Accessblty Adusted R Square 0.87 F Stat Sg. 0 Results show that 87 percent of varaton (Adusted R square 0.87) n household densty can be explaned by the combnaton of total resdental land use fracton and accessblty measure. All statstcs for ths household densty model are sgnfcant at 95 percent confdence level. The f statstc for the regresson model sgnfcance shows that the explanatory varables are collectvely useful n predctng household densty. The t statstc for the coeffcent of each explanatory varable shows that each varable s useful n forecastng the response after controllng other explanatory varables. As expected, total resdental land use fracton has a strong and postve mpact on household densty; household densty tends to ncrease wth ts ncrease. Accessblty also plays an mportant role n estmatng household densty; households tend to lve n zones wth hgher accessblty. We need to be cautous when applyng ths model snce each of these two explanatory varables has ts own physcal meanng n the urban plannng envronment. For example, accessblty measure always has a value larger than zero, whch can create a stuaton where the estmated value of household densty for a 77

96 zone s always larger than zero even when there s no resdental land use at all n ths zone. Ths s not consstent wth realty n urban plannng. Therefore, ths model s only appled nto these zones whose total resdental land use fracton s larger than zero. For each of those zones wth no resdental land use, household densty s set to zero. In summary, ths model s able to assess the role of transportaton decson and land use polcy n household dstrbuton snce t ncludes both transportaton and land use explanatory varables. The comparson between the observed household densty and the estmated household densty s shown n Fgure 5.4. Fgure 5.4: Comparson between Observed and Estmated Household Densty Employment Densty Model Development The employment densty model s developed by followng a smlar procedure smlar to the household densty model. The aggregaton of smlar explanatory varables s examned durng model development. For example, professonal offce and nsttutonal land use fracton, commercal land use fracton, and ndustral land use fracton are aggregated together to form the employment land use fracton varable. Smlarly, the constant s excluded from the model. After evaluatng the canddate models from forward, backward, and stepwse selecton procedures, the 78

97 followng lnear equaton out of stepwse s chosen to represent the employment densty model. The statstcal outputs of the employment densty model are lsted n Table 5.4. EmploymentDensty 9.411/(dstance to maor hghway) (land use mx ndex) Table 5.4: Employment Densty Model Statstcs Varables Estmate t-test Sg. Dstance to maor hghway Land use mx Adusted R Square F Stat Sg. 0 The model output shows that 60.6 percent of varaton n employment densty can be explaned by ths regresson model. F statstc for the regresson model s sgnfcant at 95 percent confdence level; and t statstcs for the coeffcents of both explanatory varables are sgnfcant at 95 percent confdence level. The model shows that the zones closer to maor hghways tend to have denser employment than those farther from maor hghways. It s mportant to note that employment dstrbuton typcally has a hstorcal trend, or t s more exogenous than endogenous n the context of urban plannng. For example, the EMPAL model dscussed n Chapter 2 allocates employments nto each plannng zone based on prevous employment dstrbuton. Ths hstorcal relatonshp between current employment dstrbuton (2000) and prevous employment dstrbuton (1995) s further explored. It s found that current employment dstrbuton s closely related to prevous employment dstrbuton (1995). The employment dstrbuton model wth prevous employment dstrbuton as the explanatory shows an extraordnary hgh adusted R square of Therefore, the followng lnear equaton s selected to be the fnal employment densty model n ths study. The statstcal outputs of the employment densty model are lsted n Table 5.5. All the statstcs for both the model and the explanatory varables are sgnfcant at 95 percent confdence level. 79

98 Employment Densty (Prevous employmentdensty) Table 5.5: Employment Densty Hstory Model Statstcs Varables Estmate t-test Sg. Prevous employment densty R Square F Stat Sg. 0 The comparson between the observed and the estmated employment densty s shown n Fgure 5.5. Fgure 5.5: Comparson between Observed and Estmated Employment Densty The household and employment densty models are able to estmate the number of households and employments n each zone (TAZ) by multplyng zone area, whch s the crtcal nput to the proposed combned trp dstrbuton and assgnment model as dscussed n Chapter 4. On the other hand, the output of the combned trp dstrbuton and assgnment model produce congested travel tme on the network, whch s an mportant nput to household densty model. The nteracton between these two models wll be dscussed n detal n the next chapter. 80

99 CHAPTER 6 THE INTERACTION 6.1 OVERVIEW After the combned transportaton model and the land use model have been developed and calbrated as dscussed n the last two chapters, the thrd component of the proposed ntegrated model framework (nteracton between the land use model and the transportaton model) s examned n ths chapter. As dscussed n the last two chapters, the land use model output serves as the nput to the transportaton model, and vce versa. Ths generates the nteracton between these two models. In ths study, the nteracton s desgned to acheve consstency between the land use model outputs and the transportaton model outputs. Consstency s acheved when the transportaton model outputs put nto the land use model are able to produce the same land use model outputs as those ntally put nto the transportaton model, and vce versa. In the exstng ITLUP framework, a feedback loop between the DRAM/EMAPL model and the tradtonal fourstep transportaton model s formulated to reach ths consstency as dscussed n Chapter 2. In ths dssertaton, two dfferent procedures are developed to acheve consstency between the land use model outputs and the transportaton model outputs. One s feedback model confguraton, whch solves the land use model and the transportaton model teratvely. The other s smultaneous model confguraton, whch formulates the land use model and the transportaton models nto one optmzaton problem. In both confguratons, use equlbrum condtons are satsfed. 81

100 6.2 FEEDBACK MODEL CONFIGURATION Most exstng operatonal ntegrated urban models take lagged transportaton model output n terms of travel tme as the nput for land use models to estmate household/employment dstrbuton. Ths does not take nto consderaton the consstency between land use model output and transportaton model output. Only ITLUP uses a feedback loop to teratvely solve ts land use model and transportaton model to reach consstency. In ITLUP, the transportaton model s a tradtonal four-step travel demand model, and land use models are DRAM/EMPAL. Feedback model confguraton n ths dssertaton can be brefly descrbed as follows: After solvng the transportaton model, the transportaton model output such as travel tme s nput to the household dstrbuton model. The household dstrbuton model outputs subsequently become nputs to the transportaton model to re-estmate the travel tme, whch wll be put back nto the land use model agan to re-estmate the household dstrbuton. Ths feedback loop contnues untl pre-defned convergence s reached Formulaton The developments of the combned trp dstrbuton-assgnment model and the regresson-based land use model have been dscussed n Chapter 4 and 5 respectvely. Ths secton descrbes how to formulate the nteracton between them. The combned trp dstrbuton-assgnment transportaton model has been developed as llustrated n Equaton: 4.13a-f. The model outputs can be used to generate a varety of transportaton performance measures for decson-makers to evaluate the transportaton system. In addton, one transportaton measure s congested travel tme between TAZs ( c ), whch s a key nput to the household dstrbuton model n ths study. In the land use model, the fnal employment dstrbuton model as descrbed n Table 5.5 does not nclude any transportaton measures or land use structure varables, whch wll be regarded as exogenously determned n ths study. 82 The household

101 dstrbuton model has been developed as a functon of total resdental land use fracton and accessblty measure as descrbed n Table 5.3. The number of households n each TAZ can be estmated based on ths household dstrbuton model wth the followng equaton: H Area ( X X ) 0.224E e ] 6.1 [ 1 2 c where Area s the area of TAZ for I ; t s usually a constant durng the urban plannng process. The number of households n each TAZ ( H ) s a key nput to the transportaton model. A feedback loop s formed between the land use model and the transportaton model snce one model s output serves as nput to the other model. The feedback loop model confguraton s llustrated n Fgure 6.1. An teratve approach s establshed between the land use and transportaton models n feedback model confguraton. The approach nvolves solvng the land use model and the transportaton model teratvely based on each other s outputs n the prevous round. The household dstrbuton model (equaton 6.1) s solved to obtan the number of households n each TAZ ( H ); then, s substtuted nto the transportaton model (equatons 4.13a-f). Congested travel tme c H s obtaned after solvng the transportaton model. c s then put nto the household dstrbuton model to re-estmate model agan to re-estmate convergence crtera are reached. H ; re-estmated H s put back nto the transportaton c. Ths feedback loop contnues untl predefned In ths study, the predefned convergence crtera are specfed as: n two consecutve teratons, (1) less than 5 percent of OD pars have OD trp varaton more than 5 percent; (2) less than 5 percent of lnks have lnk flow varaton more than 5 percent; and (3) less than 1 percent of zones have household dstrbuton varaton more than 5 percent. For example, the varaton wth respect to OD trp varable at k-th k k1 t t teraton s calculated as the equaton: 100. All three condtons have to be k1 t 83

102 satsfed before the procedure stops. The consstency between the land use model outputs and the transportaton model outputs s regarded as beng acheved once the predefned convergence crtera are met. Land use polcy, combned transportaton model calbraton Household Dstrbuton Model (6.1) Employment Dstrbuton Combned Transportaton Model (4.13a-f) Congested travel tme NO Household dstrbuton, lnk flow and OD trp dstrbuton converge? YES STOP Fgure 6.1: Feedback Model Confguraton Numercal Example Household dstrbuton model equatons (6.1) can be solved when nput varables are ready. The combned trp dstrbuton-assgnment model (4.13a-f) can be solved usng ether KNITRO or LOQO as dscussed n Chapter 4. The specfc steps nvolved n solvng the feedback model are outlned below. 84

103 Determne Set ntal values E by solvng the employment dstrbuton model k 1 c whch can be obtaned from the base year transportaton model; and set k=1 where k means k-th teraton Solve the household dstrbuton model to obtan Solve the combned trp dstrbuton and assgnment model to attan t, c k k k H k v a, Check the convergence crtera wth respect to k H, k v a, k t ; f they are satsfed, stop the teraton; otherwse, substtute k 1 c, and repeat the procedure k c nto step 2 to replace The household dstrbuton model and the combned trp dstrbuton-assgnment model are resolved teratvely. KNITRO or LOQO are used to solve the combned trp dstrbuton-assgnment model. Both solvers are able to successfully fnd the optmal solutons for ths transportaton model. KNITRO always can fnd the optmal soluton for the combned transportaton model no matter where the startng pont s; however, LOQO can fnd the optmal soluton only f the startng pont s close to the optmal soluton, such as usng the base year data as the startng pont. The base year data assocated wth the soco-economc and transportaton network s plugged nto ths ntegrated model to test the model performance. Although the convergence between the household dstrbuton model and the combned transportaton model s not guaranteed n theory, ths feedback model converges quckly for the study area. The convergence s attaned after three teratons between the land use model and transportaton model. Durng these three teratons, the convergence s reached accordng to the pre-defned convergence crtera. For the lnks wth bg varatons on lnk flows between the frst and second teratons, the varatons were becomng smaller n the next teraton. For the lnks wth smaller varaton than the convergence crtera between the frst and second teratons, the varaton changed very lttle n the next teraton and stll 85

104 remaned under the convergence crtera. There s no maor fluctuaton on the varatons as to lnk flows, OD trps, and household dstrbuton between these three teratons. After three teratons, pre-defned convergence crtera have been entrely satsfed for the base year scenaro. Results wth respect to lnk flow, OD trp, and household dstrbuton n the last two teratons are reported. Snce there are too many OD pars and lnks, only the frst twenty lnks wth the most traffc flow and the frst twenty OD pars wth the hghest OD trps are chosen to be dsplayed n Table 6.1. The results show that no lnk has lnk flow varaton of more than 5 percent n the last two teratons, no OD par has trp dstrbuton varaton greater than 5 percent, and only 26 OD pars out of 6006 pars (0.4 percent) have trp dstrbuton varaton of more than 1 percent. Wth respect to the household dstrbuton varable, none of the TAZs has the number of household varaton more than 5 percent. It can be seen that consstency between the land use model outputs and the transportaton model outputs s acheved after the predefned convergence crtera are met. However, consstency s not acheved between the frst and the second teratons because the predefned convergence crtera are not reached. For example, between the frst and the second teratons, 6.9 percent of lnks have flow varaton of more than 5 percent, whch does not satsfy the pre-defned convergence crtera; 10.2 percent of OD pars have trp dstrbuton varaton of more than 5 percent, whch does not meet the convergence crtera; 6.4 percent of TAZs have the number of household varaton of more than 5 percent, whch falls out of the convergence crtera. In addton, ths consstency ndcates that a dynamc equlbrum between land use and transportaton systems s reached. Households are satsfed wth ther locatons and travel tme to work and other actvtes after teratvely household dstrbuton. Transportaton systems can accommodate travel demand and serve travel needs at an acceptable level. The model outputs such as lnk volume can be used to help decson-makers evaluate overall performance of the exstng road network along wth lnk capacty. V/C rato s a proper ndex to measure the degree to whch network capacty s able to accommodate travel demand. Results show that the test area has a qute low level of congeston, wth average V/C rato of

105 Table 6.1: Selected Feedback Model Output Lnk Lnk Flow (thrd teraton) Lnk Flow (second teraton) Change between two teratons(percent) Orgnaton Destnaton OD Trps OD Trps Change between two teratons (percent) Zone Household (thrd teraton) Household (second teraton) L Z74 Z L Z75 Z L Z72 Z L Z73 Z L Z36 Z L Z56 Z L Z65 Z L Z64 Z L Z76 Z L Z78 Z L Z64 Z L Z62 Z L Z75 Z L Z76 Z L Z56 Z L Z72 Z L Z73 Z L Z56 Z L Z37 Z L Z36 Z Change between two teratons (percent) 87

106 Average V/C rato s based downward because t s observed that a large proporton of lnks are lghtly traveled. Therefore, frequency dstrbuton of V/C rato s presented n Fgure 6.2 to reflect the level of network congeston. V/C rato statstcs show that there are no extremely congested lnks on the network. Only 5 percent of lnks have V/C ratos larger than 1, whch ndcates that 95 percent of lnks carry traffc under ther capactes. Ffty-nne percent of lnks are lghtly loaded by showng a V/C rato of less than 0.3; 21 percent of lnks have a V/C rato between 0.3 and 0.6; 15 percent of lnks have a V/C rato between 0.6 and 1. Fgure 6.2: Frequency Dstrbuton of V/C Rato from Feedback Model Future Model Applcaton Ths secton s to test the feedback ntegrated model performance on future scenaros. One potental resdental land use development s evaluated usng ths feedback model framework. One maor development decson s beng made to TAZ 36: a subdvson development wll change the resdental land use fracton from 36.4 percent 88

107 to 46.4 percent. Ths TAZ s near the board of Versalles along maor road US60. The locaton of TAZ 36 s dsplayed n Fgure 6.3. Fgure 6.3: Development Area Resdental land use fracton (46.4 percent) s substtuted nto the household dstrbuton model along wth the base year travel-tme matrx to prelmnarly estmate future household dstrbuton. The estmated future household dstrbuton s subsequently put nto the transportaton model to forecast the future travel-tme matrx. The estmated future travel-tme matrx s agan substtuted nto the household dstrbuton model to re-estmate future household dstrbuton. Ths feedback loop between the land use model and the transportaton model contnues untl the specfed convergence crtera are reached. The convergence s reached after three teratons. The results show that n the future, the number of households n TAZ 36 wll ncrease, and the number of households 89

108 n neghborhood TAZ 56 wll decrease. The number of households n TAZ 36 wll ncrease from 1,180 to 1,440 due to the augmentaton of resdental land use area. Addtonal trps generated by the newly added 260 households wll use surroundng road networks, whch leads to the decrease of accessblty n neghborhood TAZ 56. Therefore, the number of households n neghborhood TAZ 56 wll be reduced from 1,654 to 1,653 as a result of lower accessblty n comparson to the base year. The reason there s no sgnfcant household change n TAZ56 s because of a mnor change n accessblty measure n ths TAZ. Ths mnor change n accessblty s assocated wth an nsgnfcant dfference between future traffc flow and base year traffc flow over the network. Overall, the new 260 households do not have a sgnfcant mpact on the congeston level of the network because t s not congested ether n the base year or n the future. For example, the road segment of US 60 along the development area has a daly traffc volume of 16,779, and the V/C rato s 0.76 wth ts daly capacty of 22,000 n the base year. Wth the newly added households n TAZ 36, daly traffc flow on ths segment wll be 16,832 and the V/C rato wll be The traffc flow on each lnk along wth the V/C rato for the future scenaro s estmated. The comparson on V/C rato frequency dstrbuton between the base year and the future s llustrated n Fgure 6.4. It can be seen that the new development n TAZ 36 does not have a maor mpact on traffc flow dstrbuton compared wth base year. The comparson shows that the future year average V/C rato ncreases slghtly to 0.33 from 0.32 n the base year. Therefore, there s no sgnfcant dfference n congeston level between the base year and the future. The comparson also shows that the percent of congested lnks ncrease from 5 percent n the base year to 5.3 percent n the future. Ths ndcates that the newly added 260 households n TAZ 36 generate a bt more congested lnks n the future because these new households travel to other TAZs to acheve ther needs. Addtonally, the comparson shows that the percent of the lnks whose V/C rato s between 0 and 0.3 ncreases from the base year 59.3 to the future 60. Ths mples that the OD trps are redstrbuted because of the new development n TAZ 36, whch produces a lttle more lnks wth less traffc compared to the base year. 90

109 Fgure 6.4: Comparsons of V/C Rato Frequency Dstrbuton between the Base Year and the Future Smlarly, ths feedback ntegrated model can be used to evaluate the mpact of alternatve transportaton proects on ths study area n the future. Although the convergence can be heurstcally reached for ths study area, there s no guarantee that ths feedback model s always converged n theory for other study areas or applcatons. It s encouraged to attempt to elmnate the feedback loop by reformulatng the model. The next secton proposes an approach to smultaneously solve the land use model and the transportaton model nstead of usng an teratve procedure, whch creates another methodology of examnng the nteracton between the land use model and the transportaton model. 6.3 SIMULTANEOUS MODEL CONFIGURATION Integraton of the regresson-based land use model and the combned trp dstrbuton-assgnment model can be nvestgated under a smultaneous model structure. Smultaneous model confguraton refers to solvng the land use model and the 91

110 transportaton model at the same tme rather than usng an teratve procedure as shown n the feedback model confguraton Smultaneous Model Framework As dscussed n the feedback model confguraton, H serves as an nput to the combned transportaton model. If household dstrbuton model equaton 6.1 s put nto trp generaton constrants 4.13 b-c, equatons 4.13b-c wll be transformed nto the followng forms: 6.2a t O c { Area [ ( X1 X 2 ) E e ]} E 6.2b t D c { Area [64.762( X1 X 2 ) E e } E O and D turn nto functons of total resdental land use fracton, TAZ area, employment dstrbuton, and congested travel tme ( c ) as llustrated n equatons 6.2a and 6.2b. All varables n O and D equatons 6.2a-b are gven except congested travel tme ( c ). A challenge for formulatng the smultaneous ntegrated model les n the formulaton of c, the mnmum congested travel tme between an OD par form to. It s the result of solvng the user equlbrum transportaton model such as the combned transportaton model 4.13a-f. Under user equlbrum condtons, all used paths have equal and mnmum travel tme; unused paths do not carry any trp and have a hgher travel tme; no road user can mprove hs/her travel tme by swtchng paths. In the smultaneous ntegrated model framework, there s no use equlbrum transportaton model to offer c. An alternatve formulaton needs to be found for c. Accordng to user equlbrum condtons, c s the travel tme on used paths; therefore, c can be formulated f the used path set can be found. Chen and Bernsten (2004) proposed a methodology to fnd the used path set for toll road modelng. Ths method makes use of a maxmum entropy model proposed by Larsson, et. al (2001), whch s used to fnd the 92

111 most lkely path flow pattern under the constrants of a user equlbrum lnk flow pattern. In ths entropy model formulaton, the equlbrum lnk flow pattern s regarded as the macro state. The path choces of ndvdual travelers are defned as a set of mcro states. A varety of mcro states wll gve rse to the same macro state. All mcro states are equally probable to take place due to the assumpton that an ndvdual traveler s behavor s the same n choosng the shortest paths. Based on the well-known entropy concept, the path flow pattern that engenders the greatest number of mcro states under the constrants of macro state s the most lkely path flow pattern. The maxmum entropy model can be formulated n equatons 6.3a-d (Larsson et al, 2001). Max h Lnh r 6.3a rr Subect to r rr h r t 6.3b h 0 6.3c r v 6.3d h ar r rr a Ths optmzaton program 6.3a-d has strctly convex obectve functon, as well as lnear constrants. In ths program, equlbrum lnk flow pattern ( v a ) and OD trps ( t ) are gven varables generated from the outputs of the combned trp dstrbutonassgnment transportaton model 4.13a-f. Ths program has a unque global optmal soluton wth respect to path flow. The optmal soluton s the most lkely path flow pattern under user equlbrum lnk flow pattern. It s mportant to menton that the most lkely path flows out of the entropy model (6.4a-d) are always greater than zero ( h 0 ) because of the logarthm type of obectve r functon (6.4a). Under the optmal soluton, all path flows are greater than zero, and none of them are equal to zero. However, from the perspectve of transportaton engneers/planners, any path whose path flow s less than 1 s consdered the unused path, snce trps are always larger than 1 n realty. The paths wth flows more than or equal to 93

112 1 wll be regarded as the used paths. Therefore the reasonable used path set can be extracted from the most lkely path flow pattern n conuncton wth ths reasonable threshold/tolerance (1). Let UR denotes the used path set between orgn and destnaton, for I, J ; and UR represent the used path set n the whole study area, whch s the unon of UR. After obtanng the most lkely path flow pattern by solvng the entropy maxmzaton problem (6.3a-d), pattern. Thus, c can be formulated n equaton 6.4. UR and UR are derved from the most lkely flow c ar s ( v ) For r UR 6.4 a a a I, J Equaton 6.4 ndcates that all used paths between OD pars (from to, for ) have equal and mnmal travel tme ( c ). In an attempt to formulate the smultaneous mode framework, t s worth recallng the transportaton model formulaton (4.13a-f). va 1 transportaton model: Mn sa ( w) dw ( t a In the obectve functon of the ln t t ), the term va sa( w) dw does not have any economc or behavoral meanng; t s strctly a 0 constructed as a mathematcal formulaton to obtan user equlbrum condtons (all the used paths between OD pars have equal and mnmal travel tme). In the smultaneous model formulaton, the unused paths have been removed by the most lkely path flow pattern and reasonable threshold; the formulaton of c (equaton 6.4) has guaranteed user equlbrum condtons. Therefore a v 0 a s ( w) dw s removed from the obectve functon. a After dentfyng the used path set ( UR and UR ) and formulatng c, the smultaneous model can be formulated as the followng optmzaton program. 94

113 1 Mn ( t ln t t ) 6.5a Subect to t O c { Area [ ( X 1 X 2 ) E e ]} 6.5b E t D c { Area [64.762( X 1 X 2 ) E e ]} E 6.5c rur h r t 6.5d v ar a h r 6.5e rur c ar s ( v ) For r UR 6.5f a a a h 0 6.5g r 1 The tem ( ( ln t t t ) n the obectve functon s to produce trp dstrbuton under the entropy concept as dscussed n Chapter 4. The solutons of ths smultaneous model (equatons 6.5a-g) have satsfed the same user equlbrum condton and entropy concept as the solutons of the combned trp dstrbuton-assgnment model. In ths smultaneous model framework, varables of Area X 1, X, are gven;, 2 t, c, va, are unknown varables whose solutons are the outputs of ths smultaneous model. The smultaneous model structure can be llustrated n Fgure

114 Land use polcy, combned transportaton model calbraton Smultaneous Integrated Model (6.5a-g) Employment Dstrbuton Model Household dstrbuton; lnk flow; Fgure 6.5: Smultaneous Model Confguraton Smultaneous Model Soluton Ths optmzaton program of the smultaneous model s a complcated nonlnear problem wth a nonlnear obectve functon, lnear equalty constrants, and nonlnear equalty constrants. The strct convexty of the obectve functon (equaton 6.5a) has been proven n Chapter 4. Equatons (6.5b, c, f) ncludng varable ( c ) are nonlnear equalty equatons. The exstence of nonlnear equalty constrants creates complexty for ths program because the feasble regon defned by these nonlnear equalty constrants s non-convex. Therefore, the global optmal soluton of ths optmzaton program s not guaranteed. However, a reasonable local optmal soluton can satsfy plannng needs from the perspectve of a transportaton planner/engneer f t can be attaned. The procedure to solve ths smultaneous model s dscussed usng base year data. The program starts wth solvng the combned trp dstrbuton-assgnment transportaton model (equatons 4.13a-f) usng base year data, whose outputs are lnk flow ( v a ) and OD trps ( t ). v a and t are then substtuted nto the entropy model (equatons 6.3a-d) to generate the most lkely path flow ( h r ). Based on the most lkely path flow ( h r ) and the reasonable threshold (1 trp), the used path set can be dentfed as 96

115 0 UR. 0 UR s placed nto the smultaneous model (6.5a-g) to forecast lnk flow, OD trp, and household dstrbuton. Snce the household dstrbuton model outputs and the transportaton model outputs are smultaneously obtaned, consstency between the household dstrbuton and the transportaton model outputs s reached. However, specal attenton needs to be pad to the used path set. It s possble for the set of used path to vary after solvng the smultaneous model. Once the smultaneous model s solved, the updated used path set (defned as 97 1 UR ) can be derved from the outputs of the smultaneous model by followng the same procedure as fndng ntal used path set 0 UR s dfferent from 1 UR, the updated used path set 0 UR. If the 1 UR wll be substtuted nto the smultaneous model (6.5a-g) agan to estmate lnk flow, OD trp, and household dstrbuton. The teratons wth regard to the used path set wll contnue untl the used path set s the same durng the last two consecutve teratons. UR s defned as the used path set at -th teraton. The procedure for solvng the smultaneous model s summarzed as follows: Solve the combned trp dstrbuton-assgnment transportaton model (equatons 4.13a-f) to obtan lnk flows and the OD trps Solve the most lkely path flow model (6.3a-d); use the reasonable threshold (1 trp) to dentfy the ntal used path set 0 UR Solve the smultaneous model (equatons 6.5a-g) usng the path set 1 UR to obtan lnk flow, OD trp, and household dstrbuton; set =1 where means -th teraton Solve the most lkely path flow model (6.3a-d) usng the outputs of the smultaneous model at teraton ; dentfy the updated used path set UR based on the reasonable tolerance Check the consstency between UR and 1 UR ; f they are entrely dentcal, stop the teraton, and report lnk flow, OD trp, and household dstrbuton; otherwse, substtute UR nto step 3 replacng 1 UR to repeat the procedure.

116 The smultaneous model framework s tested on the same network and zone structure of Woodford County as the feedback model framework. The nteror pont algorthm assocated wth solvers of KNITRO and LOQO s used to solve ths smultaneous model. Durng the procedure of searchng local optmal solutons for ths smultaneous model (equatons 6.5a-g), LOQO solver fals to converge no matter what startng pont s used. KNITRO solver succeeds n searchng local optmal solutons for ths smultaneous model. However, KNITRO can only converge to the local optmal solutons usng the reasonable startng pont. The reasonable startng pont refers to usng the base year data such as lnk flow and OD trp to solve the base year smultaneous mode, and usng the future year data (pre-estmated lnk flow and OD trp) for solvng the future smultaneous model. The future year data as startng pont wll be dscussed n the secton on Future Model Applcaton. The smultaneous model framework s appled to both base year and future year scenaros. Although the same used path set between two consecutve teratons s not mathematcally guaranteed, the same used path set s generated after two teratons for both base year and future model applcaton. A reasonable local optmal soluton for the base year s attaned after two teratons wth regard to the used path set. In the frst teraton, there s no sgnfcant change between the ntal used path set 0 UR and the frst teraton used path set For example, the paths wth number of trps greater than 5 s the same between 1 UR. 0 UR and 1 UR ; the varaton only takes place on those paths wth number of trps less than 5; 2 percent of paths do not appear n 1 UR because the number of trps on them are decreased from a lttle greater than 1 to less than 1. Durng the second teraton, the same used path set s reached between 1 UR and 2 UR. After the used path set s dentcal between the last two teratons, the outputs of the smultaneous model are reported as the fnal output. The outputs assocated wth lnk flow, OD trp and household dstrbuton are llustrated n Table 6.2. The same lnks, OD par, and household dstrbuton as the feedback model framework are selected to be 98

117 dsplayed. A comparson of the results between the feedback model and the smultaneous model wll be dscussed n secton 6.4. Table 6.2: Selected Smultaneous Model Output Lnk Lnk flow Orgnaton Destnaton OD Trps Zone Households L Z74 Z Z L Z75 Z Z L Z72 Z Z L Z73 Z Z L Z36 Z Z L Z56 Z Z L Z65 Z Z L Z64 Z Z L Z76 Z Z L Z78 Z Z L Z64 Z Z L Z62 Z Z L Z75 Z Z L Z76 Z Z L Z56 Z Z L Z72 Z Z L Z73 Z Z L Z56 Z Z L Z37 Z Z L Z36 Z Z Smlarly, the smultaneous model outputs can play the same role as the feedback model outputs n evaluatng overall performance of the exstng road network. Also, the V/C rato can be used to assess the level of congeston n the road network. The V/C rato frequency dstrbuton s llustrated n Fgure 6.6, whch shows that the study area has a low level of congeston wth an average V/C rato of

118 P ercentage of Lnks 70.0% Dstrbuton of V/C Ratos 60.0% 59.3% 50.0% 40.0% 30.0% 20.0% 18.4% 10.0% 11.9% 10.4% 0.0% V/C R ato Fgure 6.6: V/C Rato Frequency Dstrbuton from Smultaneous Model Output Fgure 6.6 shows that 10.4 percent of lnks have a V/C rato of between 1 and 1.7, whch ndcates no extremely congested lnks on the exstng road network percent of lnks carry traffc under ther capactes; 11.9 percent of lnks have a V/C rato of between 0.6 and 1; 18.4 percent of lnks have a V/C rato of between 0.3 and 0.6; and 59.3 percent of lnks have a V/C rato of under Future Model Applcaton Smlarly, the smultaneous model can be appled to future year scenaros. The same potental resdental land development as the feedback model s used for testng the smultaneous model framework, shown n Fgure 6.3. Fndng the used path set s the crtcal step n formulatng and solvng the smultaneous model. The base year used path set s most lkely dfferent from the future year used path set snce more trps are generated n the future due to the new land development. More trps are able to result n more used paths, some of whch may be unused n the base year. Prelmnary future year model testng has proven that a future 100

119 year model s not able to converge to a local optmal soluton when usng the base year used path set. Therefore, the future year used path set needs to be determned before runnng the future year smultaneous model. The future combned trp dstrbutonassgnment transportaton model s solved to assst n fndng the future year used path set. When solvng the future transportaton model, the future household dstrbuton as a key nput to the transportaton model s estmated usng the base year congested travel tme matrx. Based on lnk flow and OD trps from the future transportaton model output, equatons 6.4a-d are performed to obtan the most lkely path flow pattern. Reasonable tolerance (1 trp) s then used to dentfy the ntal used path set. These lnk flow and OD trps also wll be used as the startng pont to solve the future smultaneous model. The future year model s successfully solved after two teratons by showng the dentcal used path set between the frst and second teratons, and the convergence to a local optmal pont. The generated output such as household dstrbuton s shown n Fgure 6.7. Results show that the number of households n TAZ 36 ncreases from 1,173 n the base year (base year smultaneous model output) to 1,434 n the future due to the ncreasng resdental land use. The newly generated households wll produce addtonal trps (819) n comparson wth the base year. These addtonal 819 trps lead to a few more trps on neghborhood road networks, whch decrease the accessblty of neghborhood TAZs. The decreasng accessblty consequently reduces the number of households n these TAZs. For example, the number of households n neghborhood TAZ 56 wll be reduced from1,628 to 1,627. Ths very small decrease s a result of the small change n ts accessblty measure caused by the nsgnfcant change n traffc flow between the base year and the future. In ths case, future household dstrbuton does not have a sgnfcant traffc mpact on the network n comparson wth the base year. For example, the road segment of US 60 along the development area (lnk no.145) has a daly traffc volume of 17,297 (the base year smultaneous model output), wth a daly capacty of 22,000, and a V/C rato of n the base year; t has a daly traffc of 17,357, and a V/C rato of n the future. 101

120 Fgure 6.7: Future Household Dstrbuton From Smultaneous Model As can be seen, both the feedback model framework and the smultaneous model framework can be used to estmate the future traffc condton and household dstrbuton. The next secton wll compare these two model frameworks. 6.4 MODEL COMPARISON The feedback model framework and the smultaneous model framework have dfferent model structures, whch result n dfferent model outputs. Ths secton compares these two models assocated wth base year model outputs and model structure. 102

121 6.4.1 Model Structure Comparson The feedback model and the smultaneous model have some smlartes. Frst, both models can produce lnk flow, OD trp, and household dstrbuton output. Second, both model outputs are able to satsfy user equlbrum condtons whch state that all used paths between each OD par have equal travel tme and no road user can mprove hs/her travel tme by swtchng paths (Wardrop, 1952). Lastly, both models are capable of generatng consstency between the land use model output and the transportaton model output. However, the structure of the feedback model s dfferent from the smultaneous model. In the feedback model structure, the transportaton model and the land use model are separately developed and solved; the feedback soluton procedure s bult between them to resolve these two models. In the smultaneous model framework, the land use model s embedded nto the transportaton model constrants by addng the new varable c, whch converts the transportaton model nto the smultaneous model. In order to formulate c, the maxmum entropy model (6.3a-d) s frst solved to help n fndng the used path set. In the feedback model, the used path set does not take part n the formulaton at all; nstead, the frst three shortest paths are nput to the transportaton model. But n the smultaneous model, the used path set s crtcal nput; t s pre-defned based on the most lkely path flow pattern and then partcpates n the model formulaton. The used path set has already been determned before solvng the smultaneous model. In the feedback model, the transportaton model outputs show that hundreds of paths have path volume below 1. In the smultaneous model, the pre-defned used path set only conssts of the paths whose volume s not less than 1. In the feedback model framework, an teraton procedure s establshed between the transportaton model and the land use model. The teratons contnue untl the predefned convergence crtera are reached. Although there s no teraton procedure between the transportaton model and the land use model n the smultaneous model framework, there does exsts an teraton procedure between the smultaneous model and 103

122 the maxmum entropy model (6.3a-d); the teratons contnue untl the used path set s dentcal n the last two teratons. In the feedback model framework, land use model equatons can be easly solved; the transportaton model s formulated as an optmzaton program wth one and only one global optmal soluton. Both KNITRO and LOQO can successfully converge to the optmal pont; KNITRO s able to converge to the optmal pont no matter what the startng pont s. In the smultaneous model framework, there s no guarantee that the global optmal soluton exsts and can be found snce t s a complcated nonlnear optmzaton program. Only KNITRO solver s capable of convergng to the local optmal pont usng the approprate startng pont Model Output Comparson It s expected that the smultaneous model output wll be dfferent from the feedback model output to some degree because of the dfference n model structure. In the feedback model structure, the used path set s not nvolved n the model formulaton at all; the frst three shortest paths are nput to the transportaton model, and there are hundreds of paths n the model output wth a path volume below 1. However, n the smultaneous model structure, the used path set s pre-defned based on the most lkely path flow model; the used path set only ncludes the paths whose volume s not less than 1. Therefore, OD trps use fewer paths n the smultaneous model than the feedback model. Thus, the smultaneous model dstrbutes OD trps over fewer lnks than the feedback model overall. The dstrbuton of OD trps over fewer lnks causes the smultaneous model to produce more congested lnks and longer travel tme between OD pars than the feedback model. The longer travel tme generates less accessblty for each TAZ n general. Because of the smaller accessblty measure, the smultaneous model outputs show relatvely fewer households n each TAZ than the feedback model. The used path set comparson between the feedback model outputs and the smultaneous model outputs shows that there are certan dfferences between them. In the smultaneous model outputs, out of a total of 6,006 OD pars, 318 OD pars have two 104

123 used paths between them; all other OD pars have only one used paths. In the feedback model outputs, out of a total of 6,006 OD pars, 489 OD pars have two used paths, and all other OD pars have only one used path. In the outputs of both models, no OD pars has more than two used paths. The 318 OD pars n the smultaneous model outputs also have two used paths n the feedback model outputs. The feedback model outputs have an addtonal 171 OD pars wth two used paths. The outputs of these two models are compared wth regard to lnk flow, OD trp, and household dstrbuton usng base year data. The varaton s calculated to measure the dfference between these two model outputs. For example, the varaton as to OD f s t t trps s defned as: 100 s t, where the superscrpts s and f represent the smultaneous model and the feedback model respectvely. The comparsons of lnk flow, OD trp, and household dstrbuton as well as percent of varaton are lsted n Table 6.3. Frequency dstrbuton of V/C rato s shown n Fgure 6.8. The comparson assocated wth household dstrbuton s llustrated n Fgure 6.9. As to the lnk flow comparson between the two model outputs, certan dfference are expected because of dfferent model structure and model nputs. The comparsons show that 399 lnks out of a total of 723 lnks have lnk flow varaton below 5 percent; 189 lnks have lnk flow dfferences between 5 percent and 20 percent; 135 lnks have lnk flow dfferences between 20 percent and 50 percent; no lnks have lnk flow dfferences of more than 50 percent. As shown n Fgure 6.8, 10.4 percent of lnks from the smultaneous model have a V/C rato greater than one, whch s 5.4 percent hgher than the feedback model because of more congested lnks. Consequently, the smultaneous model generates a lower percentage of lnks wth smaller V/C ratos than the feedback model. For example, 18.4 percent of the lnks n the smultaneous model have a V/C rato of between 0.3 and 0.6, whch s 2.3 percent less than n the feedback model. In the smultaneous model, 11.9 percent of lnks have a V/C rato of rangng from 0.6 to 1, whch s 3 percent less than n the feedback model. Both models have the same percent of lnks wth a V/C rato below 0.3. The average V/C rato n the smultaneous model s 0.35, whle the average V/C rato n the feedback model s

124 Household dstrbuton comparson shows that the estmated total households from the smultaneous model are slghtly less than the feedback model. Ths causes the total number of OD trps from the smultaneous model to be lower than n the feedback model. Although the smultaneous model produces fewer total trps than the feedback model, V/C rato dstrbuton shows that the smultaneous model has hgher percentages of lnks wth a V/C rato of over 1. The fewer total trps from the smultaneous model are dstrbuted n a smaller porton of road segments compared to the feedback model. Ths s consstent wth prevous analyss showng that OD trps are dstrbuted over fewer lnks n the smultaneous model than n the feedback model due to the dfferent used path set. Fgure 6.8: Comparsons of V/C Rato Frequency Dstrbuton between Feedback and Smultaneous Model 106

125 Fgure 6.9: Comparsons of Household Dstrbuton between Feedback and Smultaneous Model 107

126 Table 6.3: Comparsons between Selected Feedback and Smultaneous Model Output Lnk Lnk flow (feedback model) Lnk flow (smultaneous model) Varaton between these two models (percent) Orgnaton Destnaton OD Trps (Feedback) OD Trps (Smultaneous) Varaton between these two models (percent)) Zone Household (feedback model) Household (smultaneous model) L Z74 Z Z L Z75 Z Z L Z72 Z Z L Z73 Z Z L Z36 Z Z L Z56 Z Z L Z65 Z Z L Z64 Z Z L Z76 Z Z L Z78 Z Z L Z64 Z Z L Z62 Z Z L Z75 Z Z L Z76 Z Z L Z56 Z Z L Z72 Z Z L Z73 Z Z L Z56 Z Z L Z37 Z Z L Z36 Z Z Varaton between these two models (percent)) 108

127 6.5 INTEGRATED MODEL CAPABILITY The proposed ntegrated model framework s composed of three components: the transportaton model, the land use model, and the nteracton between these two models, whch have been dscussed n Chapter 4, 5, and 6 respectvely. The nteractons between the land use model and the transportaton model are nvestgated by two dfferent methodologes: feedback model framework and smultaneous model framework. Both of these frameworks can be used to produce consstency between the land use model outputs and the transportaton model outputs. Based upon the estmated statstcal parameters, the proposed ntegrated model framework can provde feasble solutons assocated wth traffc flows and household dstrbuton. For example, the transportaton model calbraton shows that 91 percent of varaton n orgnatng/destned trps can be explaned by the trp generaton model as dscussed n Chapter 4. The orgnatng/destned trps are obtaned from the OD trp table n the outputs of the WTDM, whch has the satsfactory error bound between the observed traffc volume and the modeled traffc volume on 120 traffc count statons as dscussed n Chapter 3. Also, the land used model calbraton n Chapter 5 shows that 87 percent of varaton n household dstrbuton can be explaned by the land use model, whch demonstrates an acceptable error between the observed household densty and the modeled household densty. The proposed land use model ncludes land use structure varables such as moble home and mult-famly land use fracton and resdental land use fracton. It has the capablty of smulatng the mpact of changng land use structure on household dstrbuton. Also, the land use model ncludes transportaton measures n terms of travel tme; t allows the model to evaluate how household dstrbuton wll respond to network changes n the transportaton system. The transportaton model ncludes the varables of household and employment dstrbuton, network structure, and network attrbutes such as speed and capacty. It can evaluate the mpact of household and employment dstrbuton on transportaton system performance, and the mpact of network changes 109

128 such as road mprovements or new road development on transportaton system performance. The consstent soluton between the land use model output and the transportaton model output s obtaned usng ether the feedback model framework or the smultaneous model framework. It can demonstrate that household/employment dstrbuton s n accord wth transportaton system performance. The proposed model framework not only provdes procedures for evaluatng land use and transportaton polces, but also offers a clear mplcaton of dynamc equlbrum between land use and transportaton systems. For example, correlaton between household denstes and accessblty provded by transportaton systems can be used to estmate household dstrbuton assocated wth certan transportaton nvestments. The study focuses on the estmaton of household dstrbuton n a macro state. For example, the model outputs are the number of households n a TAZ nstead of whch ndvdual households are relocated for what reason or whch new household moves n. Also, current practces often estmate new transportaton facltes based on system performance measures such as V/C rato from travel demand model outputs, but do not take nto consderaton nduced travel demand due to household redstrbuton. The proposed model framework can be used to proect both new transportaton facltes and consequently nduced demand. In general, the model outputs mply a dynamc equlbrum between household dstrbuton and relevant transportaton system performance. The proposed model framework can be transferred to other areas for ther own applcatons. For example, the procedures for developng the land use model can be used n other areas for forecastng demographc dstrbuton. 110

129 CHAPTER 7 CONCLUSIONS AND FUTURE RESEARCH 7.1 CONCLUSIONS The growth of Amercan s urban area n the past few decades has been accompaned by transportaton problems such as congeston and polluton. These problems are not only caused by transportaton-system desgn but also are related to landuse plannng. There has been growng recognton that the nteractve relatonshp between land use and transportaton needs to be understood and analyzed n a consstent and systematc way. Integrated urban models have recently been ntroduced to examne the nteractve relatonshp between land use and transportaton. The general consensus n ths feld s that each model has ts own lmtatons because of ts specfc applcaton purposes. Ths dssertaton develops a new type of ntegrated land use and transportaton model framework: ntegraton of a regresson-based land use model and a combned trp dstrbuton-assgnment transportaton model. Ths new model can be appled to both metropoltan areas and small urban areas. The proposed new ntegrated model framework conssts of three components: the land use model, the transportaton model, and the nteracton between these two models. The combned trp dstrbuton-assgnment model servng as the transportaton model has rarely been examned n exstng ntegrated urban models. Ths dssertaton explores the formulaton, calbraton and applcaton of the combned trp dstrbuton-assgnment transportaton model n the context of an ntegrated model framework. The land use model s then developed usng correlaton and regresson analyss based on land-use structure factors and transportaton measures. Ths method has not been used n the current lterature of ntegrated urban models. The regresson equaton of the land use model s effectve n capturng the features of household dstrbuton. For 111

130 example, 87 percent of varaton n household densty can be explaned by the combnaton of total resdental land use fracton and accessblty measure. The nteracton between the land use model and the transportaton model s nvestgated by two model frameworks: feedback model framework and smultaneous model framework. Both of these are effectve n estmatng lnk flow, OD trp, and household dstrbuton n a consstent way. In the feedback model framework, a feedback loop s bult between the land use model and the transportaton model. The procedure can converge to pre-defned crtera after three teratons when ths framework s appled to both base year and future scenaros. In the smultaneous model framework, the combned trp dstrbuton-assgnment model s converted nto the smultaneous model by formulatng the land use model nto the transportaton model constrants. Ths s acheved by ntroducng the used path set. Iteratons wth regard to the used path set are examned n the smultaneous model. Model testng for the base year and the future shows that the same used path s obtaned after two teratons. It s worth mentonng that the calbrated parameters for the proposed transportaton model and land use model are only sutable for ths study cty. It cannot be transferred to other areas. For a specfc applcaton, t s recommended that the same methodology n the model framework can be utlzed to develop a regresson-based land use model, a combned trp dstrbuton-assgnment model, and the ntegraton of these two models. Ths dssertaton presents the frst nstance of ntegraton of a regresson-based land use model and a combned trp dstrbuton-assgnment transportaton model. It can be effcently solved usng modern computaton solvers and can be mplemented by both metropoltan areas and small urban areas wth lmted resources. 112

131 7.2 RECOMMENDATIONS FOR FUTURE RESEARCH The focus of ths study s to develop a framework for ntegraton of the regresson-based land use model and the combned trp dstrbuton-assgnment transportaton model. Contnued research to mprove the transportaton model and the land use model wll be of consderable beneft to the relablty and completeness of ths model framework. The proposed combned trp dstrbuton-assgnment model concentrated on estmatng total trps generated by each TAZ, rather than estmatng trps by purpose. Incorporatng trp purpose nto trp generaton s recommended, whch would gve a better understandng of travel behavor and may mprove the model's accuracy. The transportaton model s developed on a daly pattern; t s reasonable to assume that the number of trps orgnatng from a zone s equal to the number of trps destned to ths zone. However, they are not equal to each other on an hourly bass. It would be nterestng to develop a peak-hour transportaton model for ntegraton wth land use models. In the calbraton of the transportaton model, base year OD trps serve as key nputs derved from the tradtonal four-step travel demand model nstead of by observaton. It s recommended to use actual observed OD trps when data s avalable. Several deas that arose durng the research as well as durng the land use model analyss process could be worth nvestgatng more thoroughly. It s commonly recognzed that households wth dfferent levels of ncome show dstnct preference n choosng ther resdence locatons. For example, households wth hgh ncome prefer lvng n suburban areas n a bgger house wth a longer commutng dstance; low-ncome households prefer lvng close to downtown n a smaller house wth a shorter commutng dstance. So t s recommended that land use models could be developed for each category of household by ncome, and for each category of employment by ndustry type f addtonal data becomes avalable, whch may more accurately capture household/employment locaton choce preferences. The proposed land use model development analyzed a lst of land use and transportaton factors based on data avalablty. It would be nterestng to study more factors f data s avalable. For example, market force factors ncludng house prce, house sze, land value, terran, etc. 113

132 are worth beng explored snce they do play an mportant role n both household and employment locaton choce. 114

133 APPENDIX Appendx 2-A1: ITLUP Land Use Model Equatons DRAM Equatons: Nˆ, t Eˆ r n, t t k W h h, t, t h h k, t f (ˆ ck, t W f (ˆ c ) ) Where: ˆ N, t ˆ E, t : The estmated number of households n zone at tme t : The estmated number of employments n zone at tme t ˆ c, t : The congested travel tme between zone and at tme t f cˆ h (,t ) : Travel mpedance functon or accessblty functon n r t : Regonal actvty rato of households to employments at tme t W, : The attractveness functon of zone at tme t h t There are dfferent forms of travel mpedance functon such as exponental, nverse power and Gamma functon. Whch category of functon s used mostly reles on whch functon can effectvely ft the trp dstrbuton data. The modfed form of Gamma functon (a.k.a. Tanner functon) s recommended by Putman as llustrated below. Accordng to the curve of Tanner functon, most workers do not resde at locatons too far away from or too close to ther workplaces. There exsts a desred trp dstance from resdence to workplace. h f ( cˆ ch, t ) cˆ, t e dhcˆ, t 115

134 116 where h d h c, - Emprcally derved parameters The attractveness functon for household dstrbuton s expressed by the followng equaton. k k k k t k t t t N N L W } {1,,,, where t L, : The total land area of zone at tme t k t N, : The number of households n zone n the k ncome level at tme t k 1, : Emprcally estmated parameters EMPAL Equatons: 1, 1, 1, 1,, 1 1 1,,,, t e t k c c t k c c t t h t t E r e e W e W H r e e E op t op p t p op t op p t p where h t r : The regonal rato of employments at tme t to households at tme 1 t, 1 t H : The number of household n zone at tme 1 t, 1 t W : The attractveness ndex of zone at tme 1 t e t r : The regonal rato of employments at tme t to employments at tme 1 t : Emprcally derved parameter

135 The attractveness functon employment dstrbuton can be conveyed as the equaton below: W, t 1 where 1 E L 2, t 1 L : The total land area of zone, 1 2 : Emprcally derved parameters Appendx 2-A2: Quas-Gravty Model Equatons Mn a v 0 a subect to: t E s ( t) dt a 1 T t h h t t Ln T T S rr v h r t a h r rr ar h r 0 where: t : The number of trps from orgn zone to destnaton zone 117

136 h r : The number of trps on path r between zone and ; R s the set of path from zone to, I s the set of orgnaton zones and J s the set of destnaton zones s a ( v a ) : The travel cost on lnk a, whch s an ncreasng functon of lnk flow v a for a A ; A s the set of all lnks n the transportaton network ar : The ncdence coeffcent that descrbes the relatonshp between path and ar ar lnk, 1 f the lnk a s on path r ; 0 otherwse E : The number of employment or obs n zone h : The resdental beneft of choosng zone to lve n snce all zones are not equally attractve h : The mean beneft of lvng n the study regon Appendx 2-B: MEPLAN Model Equatons T n c D n c D Q wth n c m a T n c mn m g where : The ndex for land use zones m : The ndex for economc sector n : The ndex for economc sector n T c : The total volume of factor n consumed n zone n D c : The endogenous component of total volume of factor n consumed n zone n Q c : The exogenous component of total volume of factor n consumed n zone 118

137 mn a : The volume of factor n consumed n the producton of a unt of factor m n zone m T g : The total volume of factor m produced n zone After the volume of sector n consumed n zone s derved out, random utlty choce modelng n a spatal context s developed to seek the volume of sector n that wll be produced n zone. The followng formula s used to allocate ths producton. t n T n c exp[ ( T exp[ n n b n n ( Tb d n n d s n s Q n n n Q D )] n n D )] to zone where : The ndex for land use zones n t : The volume of economc sector n produced n zone and consumed n zone n : The dsperson parameter assocated wth economc sector n n T b : The cost of producng one unt of sector n n zone n d : The dsutlty assocated wth transportng one unt of sector n from zone n s : A sze term that accounts for a pror lkelhood that one unt of sector n produced n zone n Q : The exogenous component of zone-specfc dsutlty assocated wth producng sector n n zone n D : The endogenous component of zone-specfc dsutlty assocated wth producng sector n n zone 119

138 Appendx 2-C: Locaton Choce Model Equaton n fve-stage Urban Model The probablty ( P / h P / h exp[ ( WPh P )] S exp[ ( WPh P )] ) that the customer h wll choose lot can be depcted as be: where h represents customers; s the ndex for land lot (plannng zones), S s the set of land lots; WP s the wllngness to pay functon; P s the prce functon. s emprcally derved parameter. Appendx 3-A: Tradtonal Four-Step Travel Demand Model Development There are three maor steps n ths tradtonal travel demand model development for the study area: trp generaton, trp dstrbuton, and traffc assgnment. The step of mode splt s skpped due to data avalablty. Trp Generaton Internal Trp Generaton The model uses a cross-classfcaton trp method for trp generaton. The trp producton rate vares by household sze and ncome, and the trp attracton rate s manly assocated wth employment classfcaton and households. Household data s obtaned from the 2000 U.S. Census survey; employment data s provded by Dun & Bradstreet (D&B). In ths Woodford County model, households are categorzed nto low (<25th percentle), medum (25th-75th percentle) and hgh (>75th percentle) ncome group. The household ncome data s only avalable at the bgger spatal level of census block group. One census block group s composed of several TAZs. It s assumed that household ncome dstrbuton s even cross the TAZs n the same census block group. Ths ndcates that household ncome data s not adequately accurate n developng ths 120

139 travel demand model. The employment data were obtaned orgnally by category of standard ndustral classfcaton (SIC). The classfcaton system s llustrated as below Agrculture, Forestry, and Fshng Mnng Constructon Manufacturng Transportaton, Communcatons, and Utltes Wholesale Trade Retal Trade Fnance, Insurance, and Real Estate Servces Publc Admnstraton 99 Non-classfable Establshments For modelng purposes, employment data s dvded nto three dfferent groups because trp attracton rate s hghly related wth ndustry type. Accordng to NCHRP Report 365, the employment data s dvded nto the categores of Basc, Servce, and Retal. Each category s composed of correspondng ndustry types. Basc: Maor groups 1 through 51 and 91 through 99 Servce: Maor groups 60 through 90 Retal: Maor groups 52 through 59. Some verfcaton effort has been made to enhance the accuracy of the data as close to realty as possble. Control totals for Woodford County employment were obtaned from the Kentucky Cabnet for Economc Development (CED). The total number of employees as lsted by D&B s mostly consstent wth the CED record. The locatons of maor employment where the number of employees s more than 200 as ndcated by CED match wth those lsted by D&B at the TAZ level. The nputs for trp generaton can nclude the number of household by ncome and sze for each TAZ, the 121

140 amount of employment by basc, servce and retal type, and the producton and attracton rates. Trp Producton The trp producton s estmated for each dfferent trp purpose: Home Based Work (HBW), Home Based Other (HBO), and Non-Home-Based (NHB). The trp rate recommended by NCHRP Report 365 s used, as shown n Table A1. Usng the trp rates by ncome and household sze, the total trps by trp purpose can be estmated. For example, TAZ no.24 has 68 low-ncome households, 115 mddlencome households and 73 hgh-ncome households. The trp producton for ths TAZ s then estmated as: HBW trp productons = 68 x x x 1.84 = 381 trps HBO trp productons = 68 x x x 5.06 = 1105 trps NHB trp productons = 68 x x x 2.30 = 467 trps Therefore, the total trps produced from ths TAZ are 1953 per day. Table A1: Trp Producton Rate Household Income Group HHSIZE Rate_HBW Rate_HBO Rate_NHB Low Low Low Low Low >= Medum Medum Medum Medum Medum >= Hgh Hgh Hgh Hgh Hgh >=

141 Trp Attracton The number of trps attracted to a zone s estmated based upon the trp attracton rates as shown n Table A2. Trp attracton s estmated for the same three dfferent trp purposes as n trp producton. For llustraton purposes, trp attractons are estmated for the same TAZ, TAZ no.24, whch contans 256 households and 71 total obs wth 4 n basc, 67 n servce and none n retal sectors. Trp attractons are estmated as: HBW trp attractons = 1.45 x 67 = 97 trps HBO trp attractons = 9.00 x x x x 256 = 346 trps NHB trp attractons = 4.1 x x x x 256 = 210 trps Table A2: Trp Rate for Trp Attracton Input data HBW HBO NHB Total employment 1.45 N/A N/A Retal employment N/A Servce employment N/A Basc employment N/A Household N/A Snce trp producton and attracton are calculated usng dfferent formula and nput, the total trp producton s most lkely not equal to total trp attracton. A balancng effort s made by ntegratng nternal generaton wth external generaton based on the trp purposes. External Trp Estmaton Internal trp generaton deals wth the trps generated by households and employments nsde the study area. However, there are a number of trps on the transportaton network that are generated by household and employment outsde of the 123

142 study area. These trps are regarded as external trps; they can be defned as the trps that have at least one end outsde the study area. If both the orgn and destnaton of a trp are outsde the area, ths trp s consdered as a through trp or external-external trp. For example, a trp s made from Lexngton to Frankfort and pass through Woodford; ths trp s classfed as an external-external trp. When only one trp end s outsde the study area n ether orgn or destnaton, ths trp s categorzed as an nternal-external or externalnternal trp. For example, a trp s made from Lexngton to Woodford; ths trp s an external-nternal trp. External trp data s usually collected by conductng a roadsde ntercept travel survey. Unfortunately the study area does not mplement ths survey. In ths study, external trps wll be estmated based on observed traffc flow n the external statons and usng procedure recommended by NCHRP Report 365. External statons are located outsde Woodford County. External statons are located at the pont along a route where the Woodford County boundary lne was crossed. A total of 22 external statons were defned for the Woodford County area. Fgure A1 shows the locaton of external statons and connectons between external statons and road network. 124

143 Fgure A1: External Staton Dstrbuton There are two maor tasks ncluded n the estmaton of E-E, and E-I/I-E trps: (1) estmate percentage of E-E and E-I/I-E trps n the total traffc volume for each external staton; and (2) estmate trp dstrbuton of E-E between any two external statons. Estmate E-E/E-I Trp Splt The percentage of E-E trps at an external staton s calculated based on the characterstcs of ths external staton, ncludng the functonal classfcaton of the hghway where ths external staton s located, the average daly traffc volume at ths staton, the populaton of the study area, the connectvty to other external statons, and 125

144 the vehcle composton at ths external staton. Equaton A1 s used to estmate the percent of E-E trps at each external staton; results are dsplayed n Table A3. TTY I PA MA ADT 0.59 PTKS 0.48 PPS POP A1 where TTY : Percentage of E-E trps at external staton I : Interstate (0 or 1) PA : Prncpal arteral (0 or 1) MA : Mnor arteral (0 or 1) ADT : Average daly traffc at external staton PTKS : Percentage of trucks excludng vans and pckups at external staton PPS : Percentage of vans and pckups at external staton POP : Populaton of study area The number of E-E trps at an external staton can be obtaned by multplyng the percentage of E-E trps wth the average daly traffc (ADT) at ths staton. The E-I and I-E trps are then estmated by smply subtractng E-E trps from the average daly traffc for each external staton. The E-E and E-I trps estmated for each external staton are shown n Table A3. 126

145 Table A3: Through Trps and E-I Trps External Road Percentage E-E E-I/I-E ADT Staton Descrpton of E-E trps Trps Trps KY 1685 W US 421 W I 64 W KY 1681 W US 60 W KY 1681 W KY 1659 W US 62 W TR 9002 W KY 33 E KY 1267 E KY 169 E CR 1108 E CR 1107 E KY 1966 E US 60 E CR 1004 E KY 1681 E CR 1013 E US 62 E I 64 E KY 341 E Estmate E-E Trp Dstrbuton After the number of E-E trps at each external staton s determned, the dstrbuton of E-E trps between each two external statons s then estmated. Trp exchange between two external statons s hghly assocated wth the functonal classfcaton of the hghways connectng these two external statons, the percentage of E- E trps at the destnaton staton, route contnuty between orgn and destnaton, and the average daly traffc at the destnaton staton. The functonal classfcaton of the hghway connectng to the destnaton staton determnes whch formula wll be used. For example, percent dstrbuton of E-E trps from orgn staton to destnaton staton s estmated usng the followng equaton (A2) f the hghway at destnaton zone s classfed as prncpal arteral. 127

146 TTY PTTDES RTECON n 1 ADT ADT A2 where TTY : Percentage dstrbuton of E-E trps ends from orgn staton to destnaton staton ; or the percentage of E-E trps at orgn staton that wll end at destnaton PTTDES : Percentage of E-E trps n the traffc flow of destnaton staton RTECON : Route contnuty between and : Yes =1 and No=0 ADT : Average daly traffc at the destnaton staton After the percentage dstrbuton of E-E trps s obtaned by equaton A2, the number of trp exchanges between each two external staton can be calculated by multplyng E-E trps wth percentage dstrbuton. Ths wll create the OD matrx assocated wth external trp dstrbuton. However, the above equaton does not guarantee the number of trps from to s equal to the number of trps from to. Snce ths travel demand model s establshed to reflect average daly travel, t s reasonably assumed that the OD matrx should be symmetrcal. The next step s to produce a symmetrcal OD matrx by averagng value and value. In ths new symmetrcal OD matrx, t s very possble that row totals and column totals are not equal to E-E trps. The recommend soluton s to apply the Fratar technque to adust the OD matrx so that the total and column totals are consstent wth E-E trps estmated n Table A3 (Martn et al, 1998; Calper Corporaton, 2004). Estmate I-E/E-I Trps I-E/E-I trps are related to the households and employments nsde the study area. The trps generated n nternal zones by the households and employments are categorzed 128

147 by trp purpose such as HBW, HBO, and NHB. The I-E/E-I trps have to be analyzed by these trp purposes n order to be consstent wth the trps generated n nternal zones. NCHRP Report 365 suggests a breakdown of I-E/E-I trps by trp purpose. Table A4 lsts n the frst row the percentages of trp producton and attracton n E-I/I-E trps by trp purpose. Therefore, the number of trps by purpose and by producton/attracton at each external staton can be estmated, as shown n Table A4. Table A4: Trp Producton and Attracton of External Statons NCHRP 365 Recommendatons STATION I-E/E-I HBW_ HBW_ HBO_ HBO_ NHB_ NHB_ P A P A P A

148 Trp Balancng Snce trp producton and attracton are estmated ndependently, there s no guarantee that the area-wde total producton and attracton have the same numercal value as dscussed n secton Balancng s needed to ensure these two values are the same for the study area. Snce trp producton estmate s usually more accurate than attracton because of more relable data, the equaton A3 recommended by NCHRP Report 365 s used. P Pe CT A A3 p where CT p : The control total of trp producton P : Trp producton at each nternal TAZ P e : Trp producton at each external staton A e : Trp attracton at each external staton e Then, the balancng factor for trp attracton s computed as Factor CT p A where A : Trp attracton at each nternal TAZ For each nternal TAZ, trp attracton s then multpled by the balancng factor accordng to trp purpose to obtan the balanced trp attracton. Trp Dstrbuton Trp dstrbuton s the second maor step n the tradtonal four-step travel demand model. The trp dstrbuton model estmates the number of trps between each two TAZs. The E-E trp dstrbuton s calculated as descrbed n the prevous secton. 130

149 The I-I, E-I, and I-E trp dstrbutons are estmated usng gravty model embedded wth gamma functon form. The gravty model for transportaton plannng s based on the Newton s law of gravtaton, whch states that trps between two zones are drectly proportonal to the number of trps generated n these two zones and nversely proportonal to a functon of spatal separaton of these two zones (travel mpedance between them). The gravty model can be descrbed as equaton A4. t a P b A f c ) A4 ( where t : Trps between orgn and destnaton P : Trps produced by zone A : Trps attracted to zone a : The balancng factor for row b : The balancng factor for column f ( c ) : The mpedance functon between zone and zone c : The mpedance between zone and zone For the Woodford model, the mpedance s frst measured by free-flow travel tme between two zones. Once the traffc assgnment s performed, the congested travel tme wll replace the free-flow travel tme to re-run the model. The travel mpedance functon uses gamma functon, whch s often recommended n U.S. plannng practce because t fts well wth observed travel behavor (Calper Corporaton, 2004). The functon s defned mathematcally as equaton A5: c f ( c ) c e A5 where, and : derved parameters 131

150 The default parameters are used n ths study as lsted n Table A5. Note that parameter s a scalng factor and can be omtted. Table A5: Parameters for Impedance Functon Trp Purpose HBW HBO NHB The trps from gravty model are measured by person trps. Auto occupancy factors shown n Table A6 are needed to convert person trps to vehcle trps. Table A6: Auto Occupancy Factors Trp Purpose Auto Occupancy Factor HBW 1.11 HBO 1.59 NHB 1.66 trp purposes. An overall trp matrx can then be created by combnng all OD matrces for all Traffc Assgnment Traffc assgnment s the last maor step n the tradtonal four-step travel demand model. It s the process of assgnng nterzonal trps to the physcal roadway network. A detaled transportaton network specfcaton (such as node-lnk-path defnton, capacty, and speed lmt) s needed n addton to the OD matrx. The user equlbrum assgnment method s performed based on the assumpton that travelers are aware of the travel tmes (or costs) on all paths connectng ther orgns and destnatons and they always choose the path that mnmzes ther ndvdual travel tme (or cost). A BPR functon dscussed 132

151 n Chapter 4 s used to descrbe how travel tme on a lnk vares wth the traffc flow on ths lnk. Through solvng the equlbrum assgnment problem, the lnk flow pattern (and consequently travel tme on each lnk) can be found. There s no guarantee that the model output (.e., lnk flow) matches the measured traffc flow on the network after the frst run of the assgnment. Therefore, model calbraton s needed. Model Calbraton The man goal of calbraton s to ft the estmated traffc volume wth the observed traffc volume by adustng some parameters. The observed traffc volumes on roadways n Woodford County come from two sources: HIS extract for all count statons, and addtonal counts on segments of US 60, US 60X, US62 and KY33 collected by a KYTC transportaton study. A total of 110 road segments wth traffc counts are used n the calbraton process. The dstrbuton of these traffc count statons s shown n Fgure A2. The locatons where KYTC collected addtonal counts are shown n Fgure A3. Detaled counts from both sources are shown n the Appendx 3-B, along wth estmated traffc volume. 133

152 Fgure A2: Locatons of Traffc Count Statons 134

153 Fgure A3: Locatons of Addtonal Traffc Counts Collected by KYTC Percent Root Mean Squared Error (PRMSE), as defned n equaton A6, s used to measure the dfference between the observed and estmated lnk traffc volumes. PRMSE where N (ˆ v N n n v ) v n n / N 2 / N A6 vˆ n : Estmated traffc volume on traffc count staton n v n : Observed traffc volume on traffc count staton n N : Total number of traffc count statons n the area 135

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