Travel Demand Model Report City of Peterborough Comprehensive Transportation Plan Update Supporting Document Prepared for: City of Peterborough and Morrison Hershfield June 2012 Paradigm Transportation Solutions Limited 43 Forest Road Cambridge ON N1S 3B4
PROJECT SUMMARY PROJECT NAME:... CITY OF PETERBOROUGH COMPREHENSIVE TRANSPORTATION PLAN UPDATE SUPPORTING DOCUMENT TRAVEL DEMAND MODEL REPORT CLIENT:... MORRISON HERSHFIELD LIMITED 2440 DON REID DRIVE OTTAWA ON K1H 1E1 CLIENT PROJECT MANAGER:... BASSAM G. HAMWI, M.ENG., P.ENG.. PRINCIPAL & MANAGER TRANSPORTATION PLANNING PH: 613-739-3241 FAX: 613-739-4926 CONSULTANT:... PARADIGM TRANSPORTATION SOLUTIONS LIMITED 43 FOREST ROAD CAMBRIDGE ON N1S 3B4 PH: 519-896-3163 FAX: 1-866-722-5117 CONSULTANT PROJECT MANAGER... JAMES MALLETT, M.A.SC., P.ENG., PTOE REPORT DATE:... JUNE 2012 PROJECT NUMBER:... 081030
EXECUTIVE SUMMARY Paradigm Transportation Solutions Limited has prepared this Transportation Demand Modelling Report on behalf of Morrison Hershfield and the City of Peterborough. Paradigm Transportation solutions was part of the project team headed by Morrison Hershfield that was commissioned by the City of Peterborough to provide and update to the City s 2002 Transportation Master Plan. This report provides an overall review of the current model, its identified limitations, presents a comprehensive plan for addressing these shortcomings. In doing so, the inherent assumptions, procedures and processes used in this update are included. In addition, the report provides information with respect to the model network performance in the planning horizon years establish for the study (2006, 2021 and 2031) Paradigm Transportation Solutions Limited Page i
CONTENTS 1.0 EXISTING MODEL FRAMEWORK... 1 1.1 BACKGROUND... 1 1.2 STUDY GOALS AND OBJECTIVES... 1 1.2.1 ESSENTIAL / HIGH PRIORITY... 3 1.2.2 DESIRABLE / MEDIUM PRIORITY... 3 1.2.3 POTENTIAL FOR FUTURE EXPANSION / LOW PRIORITY... 3 1.3 MODEL OVERVIEW ASSESSMENT... 4 1.4 KNOWN ISSUES AND CONSTRAINTS... 4 1.5 ACTION ITEMS FOR UPDATE... 5 1.5.1 MODELLING FRAMEWORK... 5 1.5.2 TRIP GENERATION... 6 1.5.3 TRIP DISTRIBUTION AND MODE SPLIT... 6 1.5.4 TRIP ASSIGNMENT... 7 1.5.5 MODELLED SPEEDS... 7 2.0 MODEL FRAMEWORK ENHANCEMENTS... 8 2.1 DATA SOURCES... 8 2.2 TRAFFIC ANALYSIS ZONE RESOLUTION... 8 2.3 MODEL NETWORK RESOLUTION... 8 2.4 CENTROID CONNECTORS... 10 2.5 NETWORK ATTRIBUTES... 13 2.5.1 PHYSICAL ATTRIBUTES (LENGTH, LANES, AND POSTED SPEED)... 13 2.5.2 FUNCTIONAL CLASSIFICATION AND PLANNING CAPACITY... 13 2.5.3 LINK DELAY ESTIMATES... 15 3.0 MODELLING PROCESS... 17 3.1 TRANSPORTATION DEMAND MODELLING... 17 3.2 TRANSPORTATION MODEL OVERVIEW... 17 4.0 LAND USE... 20 4.1 DATA SOURCES... 20 4.2 LIMITATIONS AND ASSUMPTIONS... 20 4.3 TAZ FRAMEWORK... 20 5.0 TRIP GENERATION... 21 5.1 DATA SOURCES... 21 5.2 METHODOLOGY... 21 5.2.1 COMPARISON TO 2002 MODEL... 22 5.2.2 2006 TRIP GENERATION RATE COMPARISON... 22 5.3 CALIBRATION SUMMARY... 38 6.0 TRIP DISTRIBUTION AND MODE SPLIT... 39 6.1 DATA SOURCES... 39 6.2 METHODOLOGY... 39 6.3 GRAVITY MODEL CALIBRATION... 41 6.4 MODE SPLIT AND AUTO OCCUPANCY... 42 7.0 EXTERNAL PASSENGER VEHICLE TRAFFIC... 43 7.1 DATA SOURCES... 43 7.2 METHODOLOGY... 43 Paradigm Transportation Solutions Limited Page i
8.0 MODEL SPEEDS AND VDF EQUATIONS... 44 8.1 DATA SOURCES... 44 8.2 METHODOLOGY... 44 8.3 VDF DEVELOPMENT... 47 8.4 VDF CALIBRATION AND VALIDATION... 47 8.4.1 COMPARISON TO EXISTING VDF FUNCTIONS... 49 8.4.2 EXISTING VDF CALIBRATION CONCLUSION... 49 8.4.3 ADOPTED VDF ENHANCEMENTS... 49 8.5 RESULTS... 49 9.0 ASSIGNMENT... 512 9.1 METHODOLOGY... 52 9.2 VALIDATION... 53 9.2.1 SYSTEM-WIDE VEHICLE MILES OF TRAVEL (VMT)... 53 9.2.2 SYSTEM-WIDE TRAFFIC VOLUMES... 54 9.2.3 CORRIDOR VOLUMES... 57 9.2.4 LINK-SPECIFIC CALIBRATION... 623 10.0 MODEL VALIDATION CONCLUSION AND FUTURE ENHANCEMENTS... 64 10.1 VALIDATION CONCLUSION... 64 10.2 FUTURE MODEL ENHANCEMENTS... 64 10.2.1 TEMPORAL MODELS... 64 10.2.2 SPECIAL GENERATORS... 64 10.2.3 EXTERNAL TRAVEL DEMANDS... 64 11.0 BASE YEAR (2006) CONDITIONS... 65 11.1 DEFICIENCY DEFINITION... 65 11.2 BASE YEAR (2006) NETWORK PERFORMANCE... 66 11.3 BASE YEAR (2006) NETWORK LINK DEFICIENCIES... 68 12.0 LAND USE FORECASTS... 70 12.1 BACKGROUND... 70 12.2 POPULATION AND EMPLOYMENT PROJECTIONS... 70 13.0 FORECAST CONDITIONS... 77 13.1 TRAVEL DEMAND INCREASES... 77 13.1.1 INTERNAL-BASED TRAVEL DEMANDS... ERROR! BOOKMARK NOT DEFINED. 13.1.2 EXTERNAL TRAVEL DEMANDS... 81 13.1.3 TOTAL TRAVEL DEMANDS... ERROR! BOOKMARK NOT DEFINED. 13.2 COMMITTED ROAD NETWORK IMPROVEMENTS... ERROR! BOOKMARK NOT DEFINED. 13.3 FUTURE (2031) NETWORK PERFORMANCE... 83 13.4 FUTURE (2031) NETWORK PERFORMANCE... ERROR! BOOKMARK NOT DEFINED. 13.5 PERFORMANCE TRENDS... 89 13.5.1 Arterial and Collector Performance Trends... 86 APPENDICES Appendix A Population and Employment Growth Projections Appendix B Travel Demand Matrices Paradigm Transportation Solutions Limited Page ii
FIGURES FIGURE 1.1: CURRENT MODEL LIMITS... 2 FIGURE 2.1: TRAFFIC ANALYSIS ZONES... 9 FIGURE 2.2: MODEL NETWORK... 11 FIGURE 2.3: CENTROID CONNECTOR EXAMPLE (DOWNTOWN PETERBOROUGH)... 12 FIGURE 3.1: CITY OF PETERBOROUGH MODELLING PROCEDURE... 19 Figure 5.1: 2002 Model PM Peak Hour Auto Trip Generation Equations... 24 FIGURE 5.2: 2002 MODEL AUTO TRIP GENERATION EQUATIONS VS. 2006 TTS OBSERVED TRIPS... 25 FIGURE 5.3: 2002 MODEL AUTO TRIP GENERATION EQUATIONS VS. 2006 TTS... 26 FIGURE 5.4: COMPARATIVE DIFFERENCES FEBRUARY 2009 AND AUGUST 2009 DATA... 27 FIGURE 5.5: 2006 REVISED TRIP GENERATION EQUATIONS VS. 2006 TTS OBSERVED TRIPS... 28 FIGURE 5.6: TOTAL PREDICTED TRIPS VS. TOTAL OBSERVED TRIPS (2006)... 30 FIGURE 5.7: TOTAL PREDICTED TRIPS VS. TOTAL OBSERVED TRIPS (PRODUCTIONS AND ATTRACTIONS)... 31 FIGURE 5.8: PM PEAK HOUR AUTO TRIP CALIBRATION HBW PRODUCTIONS PREDICTED VS. OBSERVED... 32 FIGURE 5.9: PM PEAK HOUR AUTO TRIP CALIBRATION HBW ATTRACTIONS PREDICTED VS. OBSERVED... 33 FIGURE 5.10: PM PEAK HOUR AUTO TRIP CALIBRATION HBO PRODUCTIONS PREDICTED VS. OBSERVED... 34 FIGURE 5.11: PM PEAK HOUR AUTO TRIP CALIBRATION HBO ATTRACTIONS PREDICTED VS. OBSERVED... 35 FIGURE 5.12: PM PEAK HOUR AUTO TRIP CALIBRATION NHB PRODUCTIONS PREDICTED VS. OBSERVED... 36 FIGURE 5.13: PM PEAK HOUR AUTO TRIP CALIBRATION NHB ATTRACTIONS PREDICTED VS. OBSERVED... 37 FIGURE 6.1: SAMPLE TRAVEL IMPEDANCE FUNCTION... 40 FIGURE 8.1: TRAVEL TIME SECTIONS STUDIED... 46 FIGURE 8.2: OBSERVED SPEED VS. V/C RATIO... 48 FIGURE 8.3: OBSERVED AVERAGE TRAVEL SPEED VS. V/C AND EXISTING VDF FUNCTIONS... 50 FIGURE 8.4: OBSERVED AVERAGE TRAVEL SPEED VS. V/C AND VDF FUNCTIONS... 51 FIGURE 9.1: PM PEAK HOUR AUTO TRIP CALIBRATION PREDICTED VS. OBSERVED... 56 FIGURE 9.2: MAXIMUM ALLOWABLE DEVIATION ACROSS SCREENLINES... 58 FIGURE 9.3: SCREENLINES... 59 FIGURE 9.4: NORTH-SOUTH SCREENLINE CALIBRATION VOLUMES (PM PEAK HOUR)... 60 FIGURE 9.5: EAST-WEST SCREENLINE CALIBRATION... 62 FIGURE 11.1: BASE YEAR PERFORMANCE MEASURES... 67 FIGURE 11.2 2006 PM PEAK HOUR NETWORK LOS... 69 FIGURE 12.1: SUPER ANALYSIS ZONE (SAZ) STRUCTURE... 72 FIGURE 12.2: PROJECTED GROWTH IN POPULATION AND EMPLOYMENT (2006 TO 2031)... 73 FIGURE 12.3: RELATIVE GROWTH IN POPULATION AND EMPLOYMENT (2006 TO 2031)... 74 FIGURE 12.4: STUDY AREA POPULATION AND EMPLOYMENT TRENDS... 76 FIGURE 13.1: 2006 PM PEAK HOUR INTERNAL TRAVEL DEMANDS... 78 FIGURE 13.2: 2021 PM PEAK HOUR INTERNAL TRAVEL DEMANDS... 79 FIGURE 13.3: 2031 PM PEAK HOUR INTERNAL TRAVEL DEMANDS... 80 FIGURE 13.4: 2021 PERFORMANCE MEASURES... 84 FIGURE 13.5: 2021 PM PEAK HOUR NETWORK LOS... 85 FIGURE 13.6: 2031 PERFORMANCE MEASURES... 87 FIGURE 13.7: 2031 PM PEAK HOUR NETWORK LOS... 88 FIGURE 13.8: VKMT AND VHT GROWTH TRENDS... 90 FIGURE 13.9: ARTERIAL AND COLLECTOR SYSTEM... 91 FIGURE 13.10: ARTERIAL AND COLLECTOR PERFORMANCE (VKMT)... 92 FIGURE 13.11: ARTERIAL AND COLLECTOR PERFORMANCE (VHT)... 93 Paradigm Transportation Solutions Limited Page i
TABLES TABLE 2.1: PLANNING CAPACITIES... 14 TABLE 2.2: PLANNING CAPACITY ADJUSTMENTS MADE DURING CALIBRATION PROCESS... 14 TABLE 2.3: BPR VARIABLES... 16 TABLE 6.1: TRIP DISTRIBUTION CALIBRATION... 41 TABLE 6.2: MODE SHARE AND AUTO OCCUPANCY... 42 TABLE 8.1: AVERAGE LOADED SPEEDS VS. AVERAGE PEAK SPEED WITHIN FUNCTIONAL CLASSIFICATIONS... 47 TABLE 11.1: PLANNING CAPACITIES... 65 TABLE 11.2: LEVEL-OF-SERVICE AND V/C RELATIONSHIP... 66 TABLE 13.1: TOTAL TRAVEL DEMAND INCREASES... 81 TABLE 13.2: NETWORK ASSUMPTIONS WITHIN GROWTH AREAS... 82 Paradigm Transportation Solutions Limited Page ii
1.0 EXISTING MODEL FRAMEWORK 1.1 Background The City of Peterborough (COP) has maintained and continues to refine a transportation planning model which has been used to forecast future travel conditions along the City of Peterborough Roadway System. The model has undergone several revisions since its development in the mid-1980's. In 2003, a City of Peterborough model was developed using TransCAD software based on 1996 weekday PM peak hour conditions. Two horizon years (2011 and 2021) were developed for this model using land use forecasts provided by the City's Planning Department and officially endorsed by City of Peterborough Council. Since the study completion in 2002, the original TransCAD model has undergone revisions and updates. The first revision involved changes to the base assumptions as well as refinement of the modeling procedures in the West-Side corridor Analysis Review in 2003. The model remained an automobile-based model. As a result of work performed by the County of Peterborough, refinements were made and the TransCAD model was revised to incorporate additional information related to the County of Peterborough. Finally, the model has been adjusted to reflect the most recent land use forecast prepared by the City s Planning Department. Following this latest revision, travel demand scenarios were developed for 2011, 2021 and 2031. Traffic volumes were assigned to the horizon year networks and the resultant traffic volume forecasts were used to determine the travel demands on the Peterborough road network. The City's model has two key components: a supply component (road network) representing the characteristics of all of the significant roadways in the area and a demand component (trip matrix) representing the typical weekday PM peak hour traffic volume that flows through the network. The core area of the model update will be within the boundaries of the model area which extends into the County of Peterborough. However, significant transportation links to other municipalities (external links) are an important part of City's transportation infrastructure. The existing City of Peterborough model coverage shown in Figure 1.1 covers the entire City of Peterborough and includes area municipalities such as Lakefield and Bridgenorth. These municipalities vary from the populated centres with urban intensive features, to the Townships of Ottonabee and South Monaghan with a more rural & pastoral area setting. Tourism, industry and farming, as well as all the natural resources including mineral resources and environmental resources, make up Peterborough's economic diversity. 1.2 Study Goals and Objectives The primary goal of this study is to update the City of Peterborough model such that it can assist in variety of municipal decision making processes. These decision making processes were grouped into three categories based on their level of priority. The three categories are: Essential; Desirable; and Potential for Future Expansion. Paradigm Transportation Solutions Limited Page 1
Figure 1.1: Current Model Limits City of Peterborough Limit City of Peterborough Model Update Figure 1.1 Paradigm www.ptsl.com Model Limits Paradigm Transportation Solutions Limited Page 2
1.2.1 Essential / High Priority The ongoing work in Peterborough requires a suitably rigorous travel demand forecasting model that is capable of providing forecasts to be used in the following types of studies: Long Range Transportation Plans - For estimating major corridor deficiencies and- travel demand needs for new major facilities; Land Use and Growth Management Plans - Far evaluating transportation impacts of major changes in future land use and development; Area Municipal Transportation Plans - For determining municipal long range transportation plans; and Transportation Corridor studies - For evaluating alternative solutions within the identified corridor and also for providing sufficient output to aid in design of preferred alternative. 1.2.2 Desirable / Medium Priority In addition to the above minimum requirement, the ability to provide transportation planning input into the following types of studies is viewed as highly desirable: Traffic lmpact Assessments - For evaluating the impacts of proposed development on existing transportation facilities and services, for identifying improvements to transportation facilities and accommodating travel demands associated with development proposals; Travel Demand Management Strategies - For evaluating alternative methods of reducing or accommodating future travel demands within specified sub areas in Peterborough; Traffic Operational Plans - For evaluating traffic impacts and alternative traffic improvements in sub areas of Peterborough; and Setting of Development Charges - For identifying major improvements required to City of Peterborough road network and for assessing percentage increase in travel demand related to new development in the City and adjacent local municipalities. 1.2.3 Potential for Future Expansion / Low Priority Consideration to developing modules that could provide information with regard to the following should be given: Transit Plans - For identifying need for services between municipalities and within Peterborough and for providing ridership data for preliminary design of transit services; Air Quality Improvement Strategies - For estimating air quality impacts associated with alternative development and transportation plans and for monitoring changes in traffic and related impacts on air quality; and Emergency Response Planning - For planning alternative routing of traffic in instances where major roads or river crossings may be closed. Paradigm Transportation Solutions Limited Page 3
1.3 Model Overview Assessment The City of Peterborough model has undergone a number of transformations/updates since it was first developed. The current model can be likened to a photocopy of a photocopy. That is to say, that with each change/evolution of the modelling framework, some integrity has been lost at each step along the way. Indeed the model has evolved from a rigorous four-step transportation planning model to essentially an assignment tool. Based on this, it is clear that a fresh start approach is required in terms of the modelling framework as the current model does not adequately meet the requirements outlined above. 1.4 Known Issues and Constraints The City of Peterborough model was originally designed to prepare long range transportation plans for the Peterborough area utilizing travel demand forecasts to identify major transportation requirements over a 20-year horizon period. The City identified the following key issues and constraints: Traffic Assignment - Intersection delay is ignored in the current City of Peterborough model. Most traffic assignment procedures assume that delay occurs on the links rather than at the intersections. This is a reasonable assumption for highways and freeways but not for road corridors with extensive signalized intersections. There are a number of signalized intersections within the City of Peterborough model that involve highly complex movements and signal systems. These have been highly simplified in the current model. The current traffic assignment process does not modify control systems in an attempt to reach equilibrium. The use of sophisticated traffic signal systems, freeway ramp metering or enhanced network traffic control is not easily analyzed with conventional traffic assignment procedures. In the past transportation planning model networks were populated with road attribute data manually. This information can now be managed electronically with the added GIS component. Commercial Vehicle Travel - The City of Peterborough Count Program includes collection of detailed vehicle classification data which to date has not been fully utilized in the current City of Peterborough model. The project explored the need to more accurately and reasonably model commercial vehicle travel. Extent of Road Network - The current model assumes that all trips begin and end at a single point in a zone (the centroids) and occurs only on the links included in the model network. Not all roads/streets have been included in the current network nor have all possible trip origins and destinations been included. The current zone/network system is an oversimplification of reality and excludes some travel most notably shorter trips. Over-simplified Roadway Capacities - Determining the capacity of roadways requires a complex process of calculations that consider many factors. Travel forecasts in the City of Peterborough model have been oversimplified. For example, capacity is based only on the number of lanes of a roadway and its type (freeway or arterial). Emphasis on Peak Hour Travel - As mentioned above, forecasts are done for the PM peak hour on a typical weekday. A forecast for the peak hour of the day does not provide any information on what is happening the other 23 hours of the day, in particular during the AM peak hour and the mid-day conditions. A measure of the duration of congestion beyond the peak hour such as "peak spreading" is not determined. Further, travel forecasts are made for an 'average weekday'. Variation in Paradigm Transportation Solutions Limited Page 4
travel by time of year (summer vs. typical) or day of the week (weekday vs. weekend) was not currently considered. 1.5 Action Items for Update Based on the model review and the Terms of Reference for the study, the following key elements have been identified as requiring action in this update. 1.5.1 Modelling Framework The current City of Peterborough model has a number of fundamental features that needed to be reviewed in the project including the Traffic Analysis Zones (TAZ) and network resolution. These are the fundamental building blocks of the model. A well-designed TAZ system and comprehensive network structure (including centroid connectors) can greatly assist in providing reliable and meaningful forecasts. The TOR expressed concern with the current zone system and the state of the network including the coverage of the network and the network link characteristics. Based on the geographical size of City of Peterborough and the level of resolution necessary, it was determined that the TAZ s and network required a critical review and update. There were a number of important items that needed to be given consideration in this review: Longitudinal conformity - It is essential that any new TAZ system that is developed be able to be linked geographically back through the current zone system to provide the City with the ability to monitor changes in travel patterns and demands over time as well as to utilize previous land use and travel demand data. Road Network Complexity - There is an adage in transportation planning that states Travel knows no boundaries. This notion is important when considering the roadway network to be included in the model. In many ways the network that is developed should focus on the demands of the system rather than any self-imposed jurisdictional filter. That is, there may be local roads that are playing an important function and should be included. Similarly, there may be a series of local roads that feed together to load the City of Peterborough road network and should be included as a system rather than being represented by a centroid connector. Road Network Use - Understanding the nature of the road system and how it is used is very important in terms of providing an accurate traffic assignment. As with the above, traffic does not necessarily adhere to an assumed functional classification. For example, there may be links in the network that are classed as local in Official Plans that are performing a major collector function. Also it is important to understand that all arterials are not created equal and the model network needs to reflect this. Roadway Planning Capacity - Coupled with the above is the determination of roadway capacity. The TOR noted that there is perhaps an over-simplified view toward capacity in the current framework. While that may be accurate and should be thoroughly reviewed, there are also important features in the modelling framework such as the Volume-Delay Functions (VDF) and intersection delays that are very important in determining the true capacity of a corridor. In many cases, it is the intersections which govern the throughput of a corridor and it is incumbent upon the modelling framework to accurately reflect these to the maximum extent possible. Paradigm Transportation Solutions Limited Page 5
1.5.2 Trip Generation The absence of Trip Generation rates and equations in the current model severely limit the ability of the tool to produce accurate long-term forecasts of demand. The current tool relies on the 1996 Transportation Tomorrow Survey Demand matrices that have been Fratar-balanced into the horizon years. This approach has a number of limitations including: Low Sample - The demand matrix is based on roughly a 4.5% sample and has a significant number of no-observation cells. The Fratar technique cannot create demand; rather it simply factors demand where it exists in the base table. This is reasonable for short-term planning horizons where travel patterns are not likely to change much. It cannot reflect long-term changes in demand resulting from new development patterns, where no demand was observed in the base year without an artificial intervention. Fixed Demand Patterns - This technique is not responsive to reflect the changes in travel demand that might occur as result of infrastructure improvements. For example, the impact of a new arterial link, or improvements to the Highway 115, or other Highways that reduce travel times and therefore make commuting to the GTA from the area a shorter time trip, cannot be reflected by a Fratar-based model. There are other issues that have been identified with travel demand in the TOR that need be given consideration in the model update: Commercial Vehicle Travel: A significant amount of commercial travel demand relies on the Provincial Highway system through Peterborough area. In addition, there are a number of agricultural and industrial developments which generate commercial vehicle travel. Methods of estimating commercial travel demand needs to be considered in the update. Temporal Variation: Understanding time-varying demand is fundamental to understanding how the transportation system is utilized. The role that the transportation planning model can have in this regard needs to be reviewed. Many agencies are now carrying forward both AM peak hour and PM peak hour trip generation functions to attempt to capture the unique issues associated with each peak hour. The current model prepares PM peak hour forecasts which tends to be the highest hour of demand for the majority of the system but may be less accurate in areas of high industrial employment (which tend to have AM peak hour based issues) and high tourist activity (which tend to have Saturday peak hour issues). Tourism: The ability of the current model to accurately reflect peak travel demands in high tourist areas is an area of concern for the transportation planning in the area. The model update must review and consider means to determine whether the modelling tool is the appropriate method in forecasting this demand and secondly how it could get incorporated into the modelling structure. 1.5.3 Trip Distribution and Mode Split The current model does not employ any gravity-model based trip distribution methods as it relies on the Fratar technique to forecast future demand. Development of trip distribution functions will be required for a full four-step transportation planning model. The TOR also highlights the need to consider the role of mode split in the modelling framework. There are a number of issues that could potentially arise depending upon the approach ultimately undertaken. It is Paradigm Transportation Solutions Limited Page 6
recognized that there are specific areas which rely on public transport to provide effective transportation services. The degree to which this will play a role in the ultimate development of the model will need to be addressed in this effort. 1.5.4 Trip Assignment The current model framework relies on the traditional link-based approach to traffic assignment. This approach uses parameters related to the ratio of volume to capacity to assign delay to the link. This has a number of limitations; the most significant of which is that it ignores the impacts of intersections on capacity and consequently it is difficult to accurately model areas such as downtown Peterborough. The model update considered new and improved methods of estimating delay. This included a detailed review of the VDF functions available in the model. The model update also addresses the issues of advanced assignment techniques which give consideration to intersection delays and turn penalties. 1.5.5 Modelled Speeds At a project steering committee meeting of January 14, 2010 it was identified by that without confirmed and validated model speed estimation, the full evaluation of some of the parameters proposed for the evaluation of the alternatives could not be included in the benefit-cost analysis proposed for the evaluation of alternatives. At the meeting, it was identified that overall the model speed estimation that resulted from the calibration process to date had shown to well-represent typical conditions in Peterborough based on experience in developing models elsewhere. Despite these findings, the following issues were nonetheless identified: it was felt that the model VDF functions that were currently being used potentially underestimated the impacts of congestion in Peterborough, in particular for instances of high V/C ratios; the VDF functions currently in use within the model and previously used in the development of the 2002 TMP and West Side Analysis were not supportable in that they had not been validated for use in the Peterborough context; there was a desire to be able to forecast link speeds with a reasonable degree of precision to linkspecific segments; and there was a general lack of objective, observed speed data against which the VDF function and areaspecific, and link specific speeds could be tested and validated. It was agreed that in order to provide enhanced assessments of the relationship between speed and congestion in the context of the Peterborough network, it would be necessary to undertake a comprehensive data collection effort couple with detailed analyses of the average and free speed conditions. Paradigm Transportation Solutions Limited Page 7
2.0 MODEL FRAMEWORK ENHANCEMENTS This section documents the work undertaken to update the current modelling framework given the goals and objectives identified above, along with the identified issues and constraints. 2.1 Data Sources Within the modelling framework a number of data sources and methods were used in this update: City of Peterborough GIS database City of Peterborough maintains a single-line representation of the entire road network within the City. This is maintained within a Geographic Information System and is tied to a number of information sources which are important to transportation planning; Traffic Count Data The City of Peterborough conducts a comprehensive annual traffic counting program. The data are mapped to the road sections and intersections within the City of GIS structure and include automatic traffic recorder counts, intersection turning movement counts and classification counts; and County of Peterborough Model In cooperation with the City of Peterborough, the County of Peterborough provided its model network files to the project to ensure that the most recent changes completed in its TMP update were reflected in the City s work. 2.2 Traffic Analysis Zone Resolution The existing Traffic Analysis Zone System (TAZ) has been found in practice at City of Peterborough to be too coarse in many cases to provide reliable forecasts at the municipal level. Notable issues with the current TAZ structure included: TAZ boundaries were found to span barriers. While in most cases, these areas were undeveloped and would not generate travel demand, it did not provide adequate flexibility for changes over the long term. Indeed identification of areas that produce little or no trips is as important as those that are high generators; and Known growth areas were typically found to have large zones which would not be capable of reflecting potential future development scenarios without the development of a sub-area model. A comprehensive review of the TAZ framework was undertaken and the structure was modified accordingly. Figure 2.1 illustrates the refined TAZ structure that resulted from this effort. 2.3 Model Network Resolution The development of the TAZ structure described above was in part created through the addition of new roadways to the modelling framework. A thorough review of the entire City of Peterborough roadway infrastructure was undertaken. The City of Peterborough GIS formed that basis on which the model would be constructed. The model framework was developed as the locus of: Paradigm Transportation Solutions Limited Page 8
Figure 2.1: Traffic Analysis Zones City of Peterborough Model Update Figure 2.1 Paradigm www.ptsl.com Traffic Analysis Zones Paradigm Transportation Solutions Limited Page 9
All County of Peterborough roads; All City of Peterborough arterial roads; All City of Peterborough collector roads; All important local streets such as those that are effectively performing a function of collector roads; All known future new roads; and Potential roadway patterns in new growth areas. Outside of City of Peterborough, with co-operation from the County of Peterborough the model network was incorporated in its entirety. This provides an important potential policy variable for the City and allows the City to test important provincial policy directives with respect to the impact of new potential transportation corridors on the City of Peterborough road network. For example, the Highway 7 corridor route has been incorporated into the modelling framework to provide the City with information on the potential diversion to the corridor to or from City of Peterborough roads. Figure 2.2 illustrates the refined network structure that resulted from this effort. 2.4 Centroid Connectors As a direct result of the development of the TAZ structure, additional centroid connectors were added to the modeling framework. Coincident with this work, a review of the centroid connectors was undertaken. The following process and generalized rules were applied to the placement of centroid connectors: Centroid connectors should reflect the local road system wherever possible; No centroid connector should be directly connected into an intersection, unless it is representing a local road; In urban areas, centroid connectors should reflect access to and from major parking facilities; The number of centroid connectors should be limited to four for any particular zone, with one or two being preferred. Figure 2.3 provides an example of the assignment of centroid connectors in downtown Peterborough. Paradigm Transportation Solutions Limited Page 10
Figure 2.2: Model Network City of Peterborough Model Update Figure 2.2 Paradigm www.ptsl.com Model Network Paradigm Transportation Solutions Limited Page 11
Figure 2.3: Centroid Connector Example (Downtown Peterborough) City of Peterborough Model Update Figure 2.3 Paradigm www.ptsl.com Centroid Connector Example Downtown Peterborough Paradigm Transportation Solutions Limited Page 12
2.5 Network Attributes There are a number of roadway network attributes that are contained in the network file. These have been updated to reflect the nature of the modelling desired within the City. Important attributes include: Link Length the length of the link expressed in kilometres; Direction of Travel a flag used by the model to assist in assignment with 0 representing two-way flow, -1 and 1 representing one-way flow depending on the direction of the link s insertion into the network; Street Name as it appears in the City or County GIS Functional Classification the assigned functional classification (see 2.6.3); Alpha alpha variable in the BPR VDF formulation; Beta - beta variable in the BPR VDF formulation; Posted Speed legal posted speed on the link; User Assigned Free Flow Speed user-defined variable per direction (AB and BA) used to influence assignment; Free Flow Travel Time calculated travel time on link per direction (AB and BA) based on the User Assigned Free Flow Speed used to influence assignment; Number of Lanes number of lanes per direction (AB and BA) in the link; User Assigned Per Lane Capacity - user-defined variable per lane per direction (AB and BA) used to influence assignment; Capacity - calculated variable per direction (AB and BA) used to influence assignment; Existing PM peak hour traffic volumes per direction (AB and BA) as observed in the field. 2.5.1 Physical Attributes (Length, lanes, and posted speed) The number of travel lanes and posted speed data were obtained directly from the City and County GIS along with the direction of travel. Note one-way links are assigned values of 1 or -1 to indicate one-way travel with respect to the network topology. Link length is automatically calculated within TransCAD based on the Euclidean distance between the endpoints of each line segment. The network is based on the UTM NAD 83 projection contained in the City GIS. 2.5.2 Functional Classification and Planning Capacity Functional classification in transportation modeling is used to identify not only the intended function of a particular road, but also the actual function. It is important to realize that not arterial roads perform equally and in some cases, it is arguable that collector roads are performing minor arterial function. A thorough review of the network was performed by City staff to assign major and minor function to each of the arterial and collector links within the model framework. Paradigm Transportation Solutions Limited Page 13
The planning capacities assigned to each model link are based on the functional classification assigned to each link, along with the area type designation. Table 2.1 summarizes the generalized planning capacities assigned in the City of Peterborough Model. TABLE 2.1: PLANNING CAPACITIES Functional Classification Grade Peterborough WALTS WUTS SEMCOG Region of Waterloo Region of Niagara Region of Ottawa- Carleton Brantford St.Thomas London Freeway 1800 1850 1800 1850-1900 1800 1850 1800 1800 1800 1800 Freeway Ramps Fwy. To Arterial 1300 1300 n/a 1200-1300 900 1300 1200 1300 1300 1300 Fwy. To Fwy. 1500 1600 Highway Rural 1000 1100 1000 1100 1100 1200-1600 1000 1000 1100 Arterial High 800 900 800 850-950 900 900 1000 900 800 900 Medium 700 800 700 650-850 750 800 800 800 700 750 Low 600 n/a n/a n/a 650 n/a 600 n/a n/a Collector High 500 650 600 550-700 550 650 600 650 500 500 Medium 400 500 250 500-575 n/a 500 400 500 400 n/a Local 300 350 n/a n/a 400 350 400 350 300 n/a The entries in the table highlight the intended role of each class of facility within the various area types. For example a two-lane major arterial could carry up to 800 vehicles per lane per hour (e.g. Downtown Peterborough), while in areas such as Downtown Peterborough arterial facilities would only be expected to carry 700 vehicles per lane per hour. The generalized planning capacities noted above were modified during the model calibration process. Table 2.2 summarizes notable changes made during the calibration process along with the rationale for the change. TABLE 2.2: PLANNING CAPACITY ADJUSTMENTS MADE DURING CALIBRATION PROCESS Based Link Adjusted Link No. Street From/to Comment / Explanation Capacity Capacity 1 Parkhill Rd. West Brealey Drive to Wallis Drive 1600 veh/hr 700 veh/hr 2 Parkhill Road West Monaghan Road to Fairbairn Street 1400 veh/hr 1600 veh/hr 3 Monaghan Road McDonnel Street to Parkhill Road 1400 veh/hr 700 veh/hr This section of Parkhill is a two lane rural cross-section equivalent to the road segment west of Brealey. This section of Parkhill immediately east of Monaghan Road over the bridge operates the same as the link to the west. This section of Monaghan Road is striped as and operates as a two-lane facility. It has pavement of a four lane facility but doesn t operate as such. 4 Charlotte Street Monaghan Road to George Street 1400 veh/hr 700veh/hr This section of Charlotte Street operates as a wide two lane road. 5 Sherbrooke Street Glenforest Boulevard to Wallis Drive 800 veh/hr 1600 veh/hr 6 Sherbrooke Street Wallis Drive to Monaghan Road 1600 veh/hr 1400 veh/hr 7 Sherbrooke Street Monaghan Road to George Street 1400 veh/hr 700 veh/hr 8 Hunter Street Alymer Street to George Street 1200 veh/hr 600 veh/hr 9 Hunter Street East George Street to Rogers Street 1400 veh/hr 700 veh/hr 10 Chemong Road Parkhill Road to Sunset Boulevard 1600 veh/hr 1200 veh/hr 11 Chemong Road Towerhill Road to Milroy Drive 800 veh/hr 1600 veh/hr This section of Sherbrooke Street is a four lane arterial with few side street and driveway conflicts. This section of Sherbrooke is four lane but has numerous side street and direct residential driveway interfaces. This section of Sherbrooke Street operates as a wide two lane road. This section of Hunter Street is a two lane facility with on-street parking. This section of Hunter Street is a wide two lane facility with onstreet parking both sides of the road. This section of Chemong Road is base 4 lane however there are no turning lanes, lane geometry is narrow and significant number of uncontrolled commercial accesses. This section of Chemong Road is a four lane arterial with turning lanes at intersections. Paradigm Transportation Solutions Limited Page 14
2.5.3 Link Delay Estimates The link performance function is a mathematical representation of the relationship between flow (i.e. traffic volumes and travel cost (i.e. travel time) on any given link in the network. In the case of the City of Peterborough model link delay calculations are based on the BPR formulation. where: t: congested link travel time t f : link free-flow travel time v: link volume c: link planning capacity : calibration parameter : calibration parameter t t f 1 v / c (Equation 1) The BPR formulation is the default link performance function provided in TransCAD. In the case of Peterborough, the and parameters are assigned by functional classification. The default values are 0.15 and 4.00 respectively. To refine the calibration parameters, it was necessary to collect speed and travel time data across the Peterborough network, so that travel speeds could be verified by functional classification and by corridor. In order to calibrate and refine the VDF functions, a comprehensive dataset of traffic operating speeds are required for each functional classification and through a range of V/C values. It was important that data were collected on links that are experiencing as broad a range as possible to ensure that the VDF functions replicate the delay and speed conditions that are occurring on these links. In order that the V/C values could accurately be represented, the measured volumes on the links were used. Overall, data were collected on about 169 km of roadways. To ensure statistical reliability, three days of sampling was undertaken. To improve sampling efficiency, to provide a full range of V/C conditions and to respect timing and budgetary constraints, sampling was undertaken during the AM and PM peak periods. Section 8.0 of the report details the process undertaken to calibrate the VDF functions. Based on the result, the following suggested changes to the modelling framework were made: in general the link free speeds, be set to the average observed speed by functional class grouping (Arterial, Collector, Local), subject to calibration adjustments; and the BPR formulation be implemented such that the alpha constant reflects the function classification under consideration and the exponent on the V/C term remain at 4. Table 2.3 contains the values as assigned by functional classification. The importance of the BPR values is to create congestion on lower class facilities sooner, so that short-cutting is reduced. The shape of the functions creates delay on the lower class roads sooner than for the higher class roads, thus encouraging the assignment of traffic to the higher class facilities wherever possible. Paradigm Transportation Solutions Limited Page 15
TABLE 2.3: BPR VARIABLES Class Alpha Beta Freeway/Expressway 0.20 4 Arterial Highway (Rural Regional Road) 0.25 4 Major Arterial 0.30 4 Minor Arterial 0.35 4 Major Collector 0.40 4 Minor Collector 0.45 4 Local 0.50 4 Paradigm Transportation Solutions Limited Page 16
3.0 MODELLING PROCESS 3.1 Transportation Demand Modelling Transportation demand modelling has a history dating back to the late 1960 s, when the standard fourstage procedure (trip generation, trip distribution, mode split and assignment) was first introduced. These models were initially developed to assist municipalities in dealing with rapid automobile growth and the planning of new roadway infrastructure. In later years, the planning of transit systems became more important, which resulted in advances in transit modelling techniques. The last 40 years has seen much progress, but the basic inputs and outputs have not changed significantly. In general, the model inputs consist of: land use data allocated according to a set of traffic zones; and network data that describe all the physical characteristics of the road links and transit routes that connect these zones. The model outputs include estimates of travel volumes and travel times for: all origin/destination pairs by mode; and each link on the road and transit network. These outputs are used for many transportation-related activities including: strategic planning; transportation demand management analysis; highway and transit project evaluation; traffic and revenue studies; transit route planning and local site impact analysis. Despite the complex mathematical equations employed by the model, they represent a simplification of human travel behaviour. Many of the data inputs as well as the formulas used to estimate travel represent average conditions or behaviour, and cannot hope to replicate the real world in all its detail. Therefore, while the model produces remarkably accurate estimates of travel over the system in general, and reasonable comparisons with observed counts on many individual road and transit links, in some cases there will remain significant variations between observed and estimated values. To some extent, the model accuracy can be improved by introducing site-specific trip generation rates and enhanced traffic zone and network detail. For instance actual traffic attracted to a particular zone may be higher than estimated because the specific type of retail in that zone attracts more trips per foot than the average square foot of retail space. When detailed forecasts are required, a sub-area model can be developed for a specific area or municipality, using the City of model as a starting point. This step will result in improved model accuracy within the sub-area, such that the model outputs can be directly input to other software used for specific applications, such as the design and signal timing of intersections. 3.2 Transportation Model Overview The City of Peterborough transportation model is comprised of three main components: a traffic zone system and associated land use data; a base network; and a four-stage transportation modelling procedure. Paradigm Transportation Solutions Limited Page 17
City of Peterborough has been divided into a system of Traffic Analysis Zones (Figure 2.1). The zone size varies according to population and employment densities and geographical features and barriers. The updated TAZ boundaries are coincident with the Traffic Analysis Zones used the previous Transportation Master Plan and thus are a subset of the TAZ s and can be aggregated to compare longitudinal data over time. These boundaries also attempt to adhere to the federal government s census tracts and to municipal boundaries wherever possible. It must be noted that census boundaries are adjusted over time and may in time not remain consistent with these boundaries. Detailed demographic information has been developed for current and future years for each traffic zone. Also included in the zone system are external zones located at entry points to the Peterborough area to account for traffic entering, leaving or passing through the area. The second component is a digital base network that covers City of Peterborough (Figure 2.2). The auto network is comprised of all freeway, arterial and collector facilities within City of Peterborough and County of Peterborough (model the model area). Within the highly urbanized parts of City of Peterborough important local roads are also included. Each auto link contains information on the number of lanes, posted speed limit, and capacity. The digital auto network consists of approximately 1,847 nodes (intersections) and 2,419 links (road segments). The third component is the transportation modelling procedure that predicts the number of auto vehicle trips during the PM peak hour. This procedure is represented schematically in Figure 3.1. This diagram contains three types of boxes, which differentiate between policy input variables, sub-model algorithms and model outputs. The directional arrows indicate the flow of the modelling procedure through a series of sub-models, which are referenced according to the sections in this report. The boxes shaded in yellow represent major sub-models in the transportation demand estimation process, where this is described in more detail in the following sections: Trip Production and Attraction: estimate the number of person trips in each traffic zone for each trip purpose, based upon the population and employment demographics; Mode Split: estimates the mode of choice for a trip for each origin/destination (e.g. walk/bike, transit or auto) by using the relative share of Auto trips compared to Non-Auto trips; Trip Distribution: estimate the trip interchanges, of the number of person trips between zones, based upon trip impedance; Traffic Assignment: based upon the final trip matrices from the mode split stage, this step estimates route choice on the road network. Paradigm Transportation Solutions Limited Page 18
Figure 3.1: City of Peterborough Modelling Procedure Land Use Data Trip Production Trip Attraction HBW Prod HBO Prod NHB Prod HBW Attr HBO Attr NHB Attr Trip Balancing Auto Impedance Trip Distribution Total Trips Home-Based Work Home-Based Other Non Home-Based Vehicle Assignment Mode Split Auto Mode Share Auto Person Trips Total Vehicle Trips Auto Trips Auto Occupancy External Auto Trips City of Peterborough Model Update Figure 3.1 Paradigm www.ptsl.com Peterborough Modelling Procedure Paradigm Transportation Solutions Limited Page 19
4.0 LAND USE As outlined above, land use information is one of the primary inputs to the modelling process. It is used to create the projected amount of travel demand produced and attracted to any particular area within the City of Peterborough. This section of the report provides an overview of the demographic information used in this study. 4.1 Data Sources Data used in this update were provided by City of Peterborough Planning staff at the TAZ level and were obtained from the following sources: 2001 Census Canada Data The primary source of demographic (population and employment data) for this study was that which was available from the 2001 Census Canada database. Data provided to the City was made available at the Dissemination Area (DA) level and through GIS allocation procedures were used by planning staff to allocate to the TAZ structure. 4.2 Limitations and Assumptions The population data used in the modelling process is widely considered to be the most reliable source of information available as it is based on a virtually 100% sample. It should be noted that there are known issues with Census Data including: Under-reporting: Experience across Canada has shown that under-reporting of population and employment data does occur. In particular, work at-home, nomadic (no regular place of work or work in several locations) and student population data are affected. It addition, it should be noted that the Statistics Canada employment data is based on a 20% sample as only 1 in 5 households receive the long form census survey which requires detailed employment locations Data Suppression: Statistics Canada applies data suppression policies when the values for population or employment fall below a specified minimum threshold. In the sparsely occupied areas of Peterborough, this can affect the overall distribution of residents and jobs. 4.3 TAZ Framework In the scope of work identified for the project, a refinement of the TAZ structure to provide more refined assignments had been identified as a key deliverable. This process (Section 2.2 and Section 2.3) was seen as important to the overall improvement of the model. At the outset of the project, City of Peterborough Planning staff indicated that provision of population and employment data at any level more discrete than the TAZ structure would not be possible, therefore limiting the ability to provide a more discrete structure. Paradigm Transportation Solutions Limited Page 20
5.0 TRIP GENERATION As outlined above, the trip generation modules (productions and attractions) are the first modelling processes. They make use of the land use information to create the projected amount of travel demand produced and attracted to any particular area within the City of Peterborough. This section of the report provides an overview of the trip generation modules contained in the City of Peterborough model. 5.1 Data Sources The trip generation relationships are based on the following data sources: Transportation Tomorrow Survey This information is collected each census year and is based on a telephone survey of residents within the Greater Golden Horseshoe (GGH) area. It provides the City with a 24-hour database of travel patterns for all travel modes and four primary trip purposes; and Demographic Data The population and employment data produced by City of Peterborough staff provide the necessary independent variables for determining the trip generation relationships. In this case the independent variables included total population, total primary employment, total manufacturing employment, total institutional employment and total other employment 5.2 Methodology The trip generation sub-model determines the number of trips produced and attracted by each traffic zone. Separate production and attraction equations were developed for three typical PM peak hour trip purposes: Home-Based Work (HBW) Home-Based Other (HBO) Non Home-Based (NHB) These trip purposes are an aggregation of detailed trip purposes (e.g. work to home, work to dropping off passenger, work to shop) that exhibit common trip characteristics. These trip purposes have similar demographic generators, trip lengths and mode biases. The first step in developing trip generation rates and equations was to test the overall rigour of the data contained in the TTS database. The daily trips per capita were calculated based on the observed trips and the demographic information. Overall the person-trips per capita were estimated to be in the order of 2.5 person-trips per capita and about 6.5 trips per household. When compared to data collected across North America these values were found to be in the order of 8 to 10 person trips per household on a daily basis and 3-4 trips per person during the peak hour. This indicates that the TTS data experiences underreporting of trips in the order of 20-35% compared to experience across North America. Previous documentation in Peterborough indicated that the Data Management Group (DMG) at the University of Toronto who collected this information, has recognized the under-reporting of trips as an issue with the data as far back as 1996. Reports prepared for the 1996 survey data and suggest that non-home-based- Work travel was under-reported by 27% to 41% in 1996 which is significant. Another known issue with the TTS data is the temporal distribution of trips. Significant values of the trip making are coded to the quarter-hours. Therefore, determination of a single peak hour is highly sensitive to Paradigm Transportation Solutions Limited Page 21
whether a particular 15-minute is included. A common technique to avoid this concern is to use the PM peak period (i.e. 3:00 PM to 6:00 PM) and then apply a peak hour factor to obtain the peak hour data. For the City of Peterborough model, to avoid these two particular issues, the peak period was extended to include all trips coded between 3:44 PM to 5:16 PM. Overall this resulted in 0.30 person trips during the PM peak hour which is consistent with experience elsewhere across North America. Having established that there was sufficient overall trip-making contained in the database, linear regression techniques were used to test the relationship of various independent variables and combinations for each trip purpose. Several combinations of the independent variables, along with geographical stratification (i.e. urban, vs. rural) were assessed to determine which combination of independent variable(s) and geographical stratification provided the most statistically reliable model. 5.2.1 Comparison to 2002 Model In the 2002 Transportation Master Plan, trip generation functions were developed to produce PM peak hour Auto Driver trips. These were based on the 2001 TTS data. The first step in model calibration was to test these functions against the 2006 TTS data to determine if the functions were still relevant, or in need of an update. Figure 5.1 depicts the PM Peak hour Auto trip Demand production and attraction functions used in the 2002 study for each of the three trip purposes. The demographic data provided by the City in mid-february 2009 were then fed into the trip generation module to produce the estimated trips produced and attracted to each Superzone. The trip generation results were then compared to the data collected in the 2006 TTS. (Figure 5.2) Overall the predicted productions were within 4% of the observed values, while the predicted attractions were within 9%. In each case, there predicted values were underestimated. The industry-accepted measure of the Goodness of Fit of the observed versus the modelled trips is the Coefficient of Determination (R 2 ). The FHWA s Model Validation and Reasonableness Checking Manual 1 (MVRCM) identifies that the Coefficient of Determination (R 2 ) should be greater than 0.88. In the case of the Peterborough model, the Coefficient of Determination (R 2 ) was calculated to be 0.91 for the overall productions and 0.81 for the overall attractions, indicating a good degree of correlation between the predicted and the observed trips. (Figure 5.3) Based on the reviews of the preliminary results that were provided, it was felt by the project team that additional effort to gain increased precision in the model would be a prudent course of action. As such, additional effort was expended on updating the trip generation functions within the model. The results follow. 5.2.2 2006 Trip Generation Rate Comparison Using the same process that was followed in the 2002 TMP, automobile trip generation functions were developed for each trip type using the 2006 Transportation Tomorrow Survey Data and the revised demographic data provided by the City in mid-august 2009 2. (Figure 5.4) This process led to improved 1 Model Validation and Reasonableness Checking Manual, FHWA, Barton-Aschman Associates Inc. and Cambridge Systematics Inc., 1997. 2 City Staff updated/refined the 2006 base year population and employment data between February 2009 and August 2009 to reflect the City s the Growth Plan Policy initiative which was running contemporaneously with the study at the time. Paradigm Transportation Solutions Limited Page 22
overall precision with respect to the Trip Generation Functions. (Figure 5.5) process are discussed below: The results of this Paradigm Transportation Solutions Limited Page 23
Figure 5.1: 2002 Model Auto PM Peak Hour Trip Generation Equations HBO Attractions 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0 HBO Attractions 0 5000 10000 15000 20000 Population Trips = 124.79+0.059*Population R-squared = 0.76 HBO Productions 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0 HBO Productions Figure 5.1 2002 Model PM Peak Hour Auto Trip Generation Equations HBW Attractions Paradigm www.ptsl.com NHB Attractions 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0 0 1000 2000 3000 4000 5000 6000 Employment Trips = 24.581+0.094*Employment R-squared = 0.63 NHB Attractions 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0 0 5000 10000 15000 20000 Population Trips = 62.238+0.064*Population R-squared = 0.88 HBW Productions 1400.0 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0 HBW Productions HBW Attractions 0 1000 2000 3000 4000 5000 6000 Employment Trips = -15.111+0.185*Employment R-squared = 0.87 NHB Productions 700.0 600.0 500.0 400.0 300.0 200.0 100.0 0.0-100.0 0 1000 2000 3000 4000 5000 6000 Employment 0 5000 10000 15000 20000 Population Trips = 141.01+0.054*Population R-squared = 0.69 Trips = -13.623+0.113*Employment R-squared = 0.89 NHB Productions City of Peterborough Model Update Paradigm Transportation Solutions Limited Page 24
Figure 5.2: 2002 Model Auto Trip Generation Equations vs. 2006 TTS Observed Trips NHB Model 1, 2 HBW HBO Production Attraction Production Attraction Production Attraction SAZ Pop'n Emp't Pred. Obs. Pred. Obs. Pred. Obs. Pred. Obs. Pred. Obs. Pred. Obs. 1 700 4600 836 608 107 82 179 162 396 157 457 322 506 219 2 17820 6306 1151 993 1203 1606 1103 1508 497 1406 617 398 699 440 3 7592 6035 1101 1150 548 567 551 869 481 560 592 834 668 708 4 5800 2339 418 336 433 551 454 764 263 503 244 389 251 387 5 3985 767 127 104 317 531 356 248 170 335 97 50 73 85 6 7218 2628 471 519 524 551 531 478 280 475 272 270 283 215 7 3183 7615 1394 1137 266 105 313 759 574 429 740 656 847 491 8 14241 2873 516 656 974 768 910 1139 294 795 295 560 311 460 9 15114 3096 558 507 1030 964 957 1501 307 1280 316 683 336 707 10 3450 1111 190 254 283 155 327 413 190 181 129 141 112 52 11 0 2405 430 428 62 0 141 49 267 36 251 36 258 19 12 75 40-8 23 67 18 145 0 127 0 28 0-9 0 13 30 6-14 19 64 0 143 0 125 0 25 0-13 0 14 903 1755 310 232 120 32 190 50 228 33 190 51 185 18 15 3333 600 96 142 276 208 321 241 160 114 81 34 54 91 16 2892 700 114 201 247 357 297 175 166 143 90 73 65 69 17 1091 200 22 106 132 143 200 128 137 91 43 19 9 35 18 593 250 31 69 100 111 173 54 140 37 48 0 15 0 19 7284 2000 355 324 528 848 534 482 243 470 213 69 212 77 Total 95305 45326 8098 7807 7282 7598 7826 9018 5045 7045 4728 4585 4863 4072 1 Population Estimates for SAZ 1-14 from City of Peterborough staff, 15-19 from TTS 2 Employment Estimates for SAZ 1-14 from City of Peterborough staff, 15-19 from 2002 Master Plan with adjustments Figure 5.2 2002 Auto Trip Generation Equations vs. 2006 TTS Observed Trips City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 25
Figure 5.3: 2002 Model Auto Trip Generation Equations vs. 2006 TTS Productions Attractions 4000 3500 3000 2500 2000 1500 1000 500 0 3500 3000 2500 2000 1500 1000 500 0 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 4000 Coefficient of Determination (R 2 ) = 0.91 Coefficient of Determination (R 2 ) = 0.81 Figure 5.3 2002 Auto Trip Generation Equations vs. 2006 TTS City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 26
Figure 5.4: Comparative Differences February 2009 and August 2009 Data SAZ Feb. 2009 Data Aug. 2009 Data Absolute Difference Percent Difference Pop'n Emp't Pop'n Emp't Pop'n Emp't Pop'n Emp't 1 700 4600 636 4503-64 -97-9.1% -2.1% 2 17820 6306 18301 6152 481-154 2.7% -2.4% 3 7592 6035 6909 5945-683 -90-9.0% -1.5% 4 5800 2339 5967 2298 167-41 2.9% -1.8% 5 3985 767 4160 752 175-15 4.4% -2.0% 6 7218 2628 7670 2581 452-47 6.3% -1.8% 7 3183 7615 2009 7477-1174 -138-36.9% -1.8% 8 14241 2873 11883 2819-2358 -54-16.6% -1.9% 9 15114 3096 15201 3043 87-53 0.6% -1.7% 10 3450 1111 3211 1072-239 -39-6.9% -3.5% 11 0 2405 0 2335 0-70 0.0% -2.9% 12 75 40 114 39 39-1 51.5% -2.5% 13 30 6 27 6-3 0-8.9% 0.0% 14 903 1755 1223 1703 320-52 35.5% -3.0% 15 3333 600 4022 869 689 269 20.7% 44.8% 16 2892 700 2278 1013-614 313-21.2% 44.7% 17 1091 200 2315 516 1224 316 112.2% 158.0% 18 593 250 1803 1428 1210 1178 204.2% 471.2% 19 7284 2000 7770 2619 486 619 6.7% 31.0% Total 95305 45326 95499 47170 194 1844 0.2% 4.1% Figure 5.4 Comparative Differences February 2009 and August 2009 data City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 27
Figure 5.5: 2006 Revised Trip Generation Equations vs. 2006 Observed TTS SAZ Model Production HBW Attraction HBO Production Attraction NHB Production Attraction Pop'n Emp't Pred. Obs. Diff. Pred. Obs. Diff Pred. Obs. Diff. Pred. Obs. Diff Pred. Obs. Diff. Pred. Obs. Diff 1 636 4503 699 608 91 71 82-11 281 162 119 142 157-14 349 322 27 250 219 31 2 18301 6152 1064 993 72 1433 1606-173 1704 1508 196 1429 1406 23 748 398 350 716 440 276 3 6909 5945 962 1150-188 558 567-9 842 869-26 631 560 71 564 834-270 469 708-239 4 5967 2298 388 336 52 471 551-80 533 764-231 429 503-74 239 389-150 222 387-165 5 4160 752 136 104 32 326 531-205 296 248 49 246 335-89 81 50 31 89 85 4 6 7670 2581 442 519-76 603 551 53 678 478 200 558 475 82 288 270 18 275 215 60 7 2009 7477 1171 1137 34 188 105 83 578 759-180 349 429-79 623 656-34 464 491-27 8 11883 2819 505 656-151 927 768 159 1007 1139-131 859 795 64 370 560-190 376 460-84 9 15201 3043 561 507 53 1183 964 219 1269 1501-232 1097 1280-183 438 683-245 458 707-248 10 3211 1072 180 254-74 255 155 100 247 413-166 192 181 11 95 141-46 89 52 37 11 0 2335 357 428-71 14 0 14 91 49 41 17 36-19 155 36 119 102 19 83 12 114 39 0 23-23 13 18-5 -52 0-52 -62 0-62 -39 0-39 -39 0-39 13 27 6-6 19-25 6 0 6-60 0-60 -69 0-69 -43 0-43 -43 0-43 14 1223 1703 266 232 34 105 32 73 140 50 90 78 33 45 119 51 68 88 18 70 15 4022 869 153 142 11 316 208 108 294 241 53 240 114 127 89 34 56 93 91 2 16 2278 1013 165 201-36 183 357-174 173 175-2 125 143-18 76 73 3 66 69-2 17 2315 516 88 106-19 184 143 41 144 128 16 109 91 18 34 19 16 36 35 1 18 1803 1428 227 69 158 148 111 37 165 54 112 108 37 71 104 0 104 82 0 82 19 7770 2619 449 324 125 611 848-237 688 482 206 566 470 96 293 69 224 279 77 202 Total 95499 47170 7807 7807 0 7598 7598 0 9018 9018 0 7045 7045 0 4585 4585 0 4072 4072 0 City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Figure 5.5 2006 Revised Auto Trip Generation Equations vs. 2006 TTS Observed Trips Paradigm Transportation Solutions Limited Page 28
Overall Fit Overall the predicted productions were within 0% of the observed values, while the predicted attractions were within 0%. The Coefficient of Determination (R 2 ) overall was calculated to be 0.95. (Figure 5.6) For the trip productions, the value was calculated to be 0.91 for the overall productions and 0.97 for the overall attractions, indicating a very high degree of correlation between the predicted and the observed trips. (Figure 5.7) Home Based Work (HBW) A number of model constructs were tested to determine of the good-of-fit measures previous observed could be improved. The HBW productions were determined to be statistically related to both population and employment. The following equations were developed: HBW (productions) = 0.1558(Employment) + 0.0061(Population) - 6.75 HBW (attractions) = 0.0768(Population) + 0.004(Employment) + 4.2 Scattergram plots of the predicted versus observed values for the productions (Figure 5.8) and attractions (Figure 5.9) were prepared. The purpose of the exercised was to identify the closeness to the line X=Y that the data fell to identify the overall goodness of fit and identify any outliers. The graphics indicate a high degree of correlation between the predicted and observed values. The Coefficient of Determination for the productions was 0.94, while for the attractions it was 0.91. HBO A number of model constructs were tested to determine of the good-of-fit measures previous observed could be improved. The HBO productions were determined to be statistically related to both population and employment. The following equations were developed: HBO (productions) = 0.0657(Employment) + 0.0745(Population) - 62.73 HBO (attractions) = 0.0693(Population) + 0.0376(Employment) 70.91 Scattergram plots of the predicted versus observed values for the productions (Figure 5.10) and attractions (Figure 5.11) were prepared. The purpose of the exercised was to identify the closeness to the line X=Y that the data fell to identify the overall goodness of fit and identify any outliers. The graphics indicate a high degree of correlation between the predicted and observed values. The Coefficient of Determination for the productions was 0.89, while for the attractions it was 0.96. NHB A number of model constructs were tested to determine of the good-of-fit measures previous observed could be improved. The NHB productions were determined to be statistically related to both population and employment. The following equations were developed: NHB (productions) = 0.0852(Employment) + 0.0146(Population) 43.59 NHB (attractions) = 0.0205(Population) + 0.0623(Employment) 43.69 Scattergram plots of the predicted versus observed values for the productions (Figure 5.12) and attractions (Figure 5.13) were prepared. The purpose of the exercised was to identify the closeness to the line X=Y that the data fell to identify the overall goodness of fit and identify any outliers. The graphics indicate a high degree of correlation between the predicted and observed values. The Coefficient of Determination for the productions was 0.69, while for the attractions it was 0.72. Paradigm Transportation Solutions Limited Page 29
Figure 5.6: Total Predicted Trips vs. Total Observed Trips (2006) 8000 Coefficient of Determination (R 2 ) = 0.95 7000 6000 5000 4000 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Figure 5.6 City of Peterborough Transportation Master Plan Total Predicted Trips vs. Total Observed Trips (2006) Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 30
Figure 5.7: Total Predicted Trips vs. Total Observed Trips (Productions and Attractions) Productions Attractions 4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 0 0 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 Coefficient of Determination (R 2 ) = 0.91 Coefficient of Determination (R 2 ) = 0.97 City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Figure 5.7 Total Predicted Trips vs. Total Observed Trips Productions and Attractions Paradigm Transportation Solutions Limited Page 31
Figure 5.8: PM Peak Hour Auto Trip Calibration HBW Productions Predicted vs. Observed Coefficient of Determination (R 2 ) = 0.94 1600 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 Figure 5.8 PM Peak Hour Auto Trip Calibration HBW Productions Predicted vs. Observed City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 32
Figure 5.9: PM Peak Hour Auto Trip Calibration HBW Attractions Predicted vs. Observed Coefficient of Determination (R 2 ) = 0.91 1600 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 Figure 5.9 PM Peak Hour Auto Trip Calibration HBW Attractions Predicted vs. Observed City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 33
Figure 5.10: PM Peak Hour Auto Trip Calibration HBO Productions Predicted vs. Observed Coefficient of Determination (R 2 ) = 0.89 1600 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 Figure 5.10 PM Peak Hour Auto Trip Calibration HBO Productions Predicted vs. Observed City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 34
Figure 5.11: PM Peak Hour Auto Trip Calibration HBO Attractions Predicted vs. Observed Coefficient of Determination (R 2 ) = 0.96 1600 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 Figure 5.11 PM Peak Hour Auto Trip Calibration HBO Attractions Predicted vs. Observed City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 35
Figure 5.12: PM Peak Hour Auto Trip Calibration NHB Productions Predicted vs. Observed 1600 Coefficient of Determination (R 2 ) = 0.69 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Figure 5.12 PM Peak Hour Auto Trip Calibration NHB Productions Predicted vs. Observed Paradigm Transportation Solutions Limited Page 36
Figure 5.13: PM Peak Hour Auto Trip Calibration NHB Attractions Predicted vs. Observed 1600 Coefficient of Determination (R 2 ) = 0.71 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 1600 City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Figure 5.13 PM Peak Hour Auto Trip Calibration NHB Attractions Predicted vs. Observed Paradigm Transportation Solutions Limited Page 37
5.3 Trip Generation Calibration Summary The trip generation equations were generally overall found to have the highest reliability on the attraction side. The HBO attraction equation had an R 2 value of 0.96 and while the HBW attraction equation had an R 2 value of 0.91. NHB trips were generally found to have poor fits to the independent variables. The total amount of trips predicted on the attraction side was found to be virtually replicating the observed trips. Therefore, trip balancing to the attraction side was determined to provide the best results. Paradigm Transportation Solutions Limited Page 38
6.0 TRIP DISTRIBUTION AND MODE SPLIT As outlined above, the trip distribution module is used to allocate trips between all origins and destinations. They are generally based on a gravity model formulation, which is based on Sir Isaac Newton s Law of Universal Gravitation. The fundamental nature of the equation indicates that the relative attractiveness of any two zones is directly proportional to the population and employment in each zone and inversely proportional to the travel time separating them. This section of the report provides an overview of the trip distribution modules contained in the City of Peterborough model. 6.1 Data Sources The trip distribution relationships are based on the following data sources: Transportation Tomorrow Survey This information is collected each census year and is based on a telephone survey of residents within the Greater Golden Horseshoe (GGH) area. It provides the City with a 24-hour database of travel patterns for all travel modes and four primary trip purposes. 6.2 Methodology The most common method of distributing trips between any two given TAZ s used in transportation planning is the gravity model. The essence of the model is that the relative attractiveness of any two given TAZ s is directly proportional to the cross product of a measure of the propensity to create trips and inversely proportional to an impedance function. This is based on Sir Isaac Newton s Law of Universal Gravitation: Within the Peterborough modelling process, the trip distribution module estimates the number of person trips travelling between OD pairs for each trip purpose (HBW, HBO, NHB). The trip distribution models are developed for internal trip-making and do not include trips that originate or are destined to areas outside the City of Peterborough. A separate external trip matrix has is added to the final internal auto matrix prior to assignment. (see Section 7.0) Internal trip distribution is a multi-step process that starts with the calculation of travel impedances (or travel time in this case) between OD pairs. The impedance matrices are then used to calculate friction factors, which describe the propensity to travel between different locations. Friction factors are calculated for each trip purpose as they exhibit different trip length characteristics. A balancing algorithm is used to implement the gravity models and convert the trip production and attraction vectors into full OD matrices. Travel impedance is based on the travel time (including link delay and intersection delay) between any given two zones. Auto impedances were developed for each trip purpose for the City of Peterborough model. These impedances were then used to calibrate gravity models for each trip purpose. Gravity models are used to distribute the production and attraction vectors between OD pairs. The friction factors take the form of a negative exponential equation. The functions are calibrated to the Trip Length Distribution (TLD) curves for each trip purpose. As these values become less negative, the average trip lengths increase as illustrated in Figure 6.1. Paradigm Transportation Solutions Limited Page 39
Figure 6.1: Example of Gravity Model Travel Impedance Function 3.00 2.50 2.00 1.50 1.00 0.50 Fij Factor 0.00 0 5 10 15 20 25 30 35 40 45 50 Combined Travel Impedance (min) Figure 6.1 City of Peterborough Transportation Master Plan Sample Travel Impedance Function Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 40
Individual trip purpose matrices are then computed using the two-dimensional, or doubly constrained balancing procedures in TransCAD. Inputs to the gravity models include the balanced production and attraction vectors and the friction matrices. Each trip purpose is subject to the same iterative balancing process. The results of this sub-model are four trip purpose matrices that describe the travel between all origins and destinations. 6.3 Gravity Model Calibration Calibrating the gravity model consists of evaluating the parameters of the impedance function (or the values in the friction factor table) so that the gravity model reproduces, as closely as possible, the base year productions and/or attractions and the base year trip length distribution. TransCAD provides a procedure that calibrates a friction factor lookup table, a K-Factor matrix, and exponential, inverse power, and gamma impedance functions. Regardless of the model being calibrated, the calibration procedure requires: a base year P-A matrix; a base year impedance matrix; and a zone layer All of the calibration procedures use the base year P-A matrix and the impedance matrix to generate the Observed Trip Length Distribution (OTLD), and the aim is to calibrate the model such that this OTLD is reproduced as closely as possible. Table 6.1 shows the average calibrated trip lengths using the trip distribution parameters and friction factors developed for City of Peterborough. The calibrated parameters by purpose are: HBW 0.085 HBO 0.140 NHB 0.095 The entries in the table indicate that the functions are able to replicate the average trip lengths to within about 1.16% or about 15 seconds for HBW trips and to within 1/100 th of a minute for the other two trip types. TABLE 6.1: TRIP DISTRIBUTION CALIBRATION Trip Type Observed Average Travel Time (min) Predicted Average Travel Time (min) Difference (%) Home Based Work (HBW) 21.50 21.25-1.16% Home Based Other (HBO) 18.02 18.01-0.06% Non Home Based (NHB) 19.25 19.24-0.05% Paradigm Transportation Solutions Limited Page 41
Another measure of the accuracy of the distribution model is to compare the trip length frequency distributions of the estimated person trips from the model to the observed person trips from the household survey. The coincidence ratio is one such measure. The coincidence ratio is the ratio in common between two distributions as a percentage of the total area of those distributions. In general, the coincidence ratio measures the percent of the area that coincides between the two curves. This ratio for each trip purpose should be at least 60 percent. For Peterborough, all purposes exceed the 60 percent target. 6.4 Mode Split and Auto Occupancy Given the dominance and ubiquitous use of the auto share in City of Peterborough, the development of a mode split model was not deemed to be worthwhile and was outside the TOR for the study. Therefore, the resulting person trip demands were then converted to vehicle trips through the application of global auto person trip share and auto occupancy factors which were calculated from the TTS database. (Table 6.2) TABLE 6.2: MODE SHARE AND AUTO OCCUPANCY Purpose % Auto Persons Auto - Occupancy HBW 94.9% 1.03 HBO 91.7% 1.24 NHB 98.1% 1.14 Paradigm Transportation Solutions Limited Page 42
7.0 EXTERNAL PASSENGER VEHICLE TRAFFIC Passenger travel demand to, from and through Peterborough area is an important component of the traffic flows on the City of Peterborough road system. These data were collected from a number of sources and as illustrated in Figure 3.3 were added to the internally generated travel demands to complete the passenger travel demand matrices. 7.1 Data Sources Transportation Tomorrow Survey Data Travel demand to and from the west of Peterborough was supplemented with the O-D information available in the TTS database. 7.2 Methodology The above data sources provided the combined Internal-to-External (I-X), External-to-Internal (X-I) and External-to-External (X-X) travel demand portions of the travel matrices. These demands were subsequently added to the Internal-to-Internal (I-I) travel demands from the trip distribution and model split modules to complete the auto demand matrices. These data sources were used in the following manner: the TTS data were processed so that the origin-destination location information was consistent with the updated TAZs and both were imported into TransCAD matrices. Paradigm Transportation Solutions Limited Page 43
8.0 MODEL SPEEDS AND VDF EQUATIONS Through the modelling process enhancements to the Volume-Delay Functions and Model Speed estimation were made. These are described below. 8.1 Data Sources In order to calibrate and refine the VDF functions, a comprehensive dataset of traffic operating speeds was required for each functional classification and through a range of V/C values. It was important that data were collected on links that are experiencing as broad a range as possible to ensure that the VDF functions replicate the delay and speed conditions that are occurring on these links. In order that the V/C values were accurately represented, the measured volumes on the links were used. Figure 8.1 illustrates the location of 2008/2009 ATR data that was provided by the City of Peterborough. In addition, the red links illustrate the links measured for overall travel time (which included delay experienced at intersections) and mid-block operating speeds (a measure of free-flow speed). Overall, data were collected on about 169 km of roadways which was down as follows: Freeway Ramp Freeway Arterial Collector Local Private 1.9 km 13.5 km 89.3 km 48.8 km 14.3 km 1.0 km Given that there was an assumed average operating speed of about 40 km /h and that some deadheading was required to accomplish efficient routing of the network, it required about 4.5 hours to complete the sample the entire proposed network. To ensure statistical reliability, three days of sampling was undertaken. To improve sampling efficiency, to provide a full range of V/C conditions and to respect timing and budgetary constraints, sampling was undertaken during the AM and PM peak periods. 8.2 Methodology The data collected were used in a two-fold purpose. Firstly, the average travel speed which gives consideration to delay experienced at intersections was plotted against the V/C ratio measured for the section and used in the model. The link-based BPR functions were reviewed against these plots to determine if the BPR function is indeed the most applicable given the observed shapes of the delay curves. Where necessary, further assessment of BPR, Conical, Logit-Based, Acelik and generalized cost functions were conducted to determine if the shape of the observed volume-delay relationship better followed other curves. Following this assessment, the VDF functions were re-calibrated to the observed data to a statistically-valid degree. In addition to the above, the observed mid-block (undelayed) operating speeds were used as a surrogate for the free flow speeds (desired undelayed travelling speed) that are desired on the links. This method improved the overall estimates of delay using the refined VDF functions and contemporaneously refines the network assignment. Subsequently, for each roadway segment, the average loaded travel speed (one that Paradigm Transportation Solutions Limited Page 44
gives consideration to the delays experienced at intersections) were then compared to the calculated V/C ratio and plotted against the VDF functions that have been used in the model development. The average loaded speed by functional class from above was used as the starting speed for each functional class. Paradigm Transportation Solutions Limited Page 45
Figure 8.1: Travel Time Sections Studied Legend ATR Traffic Data Collected in 2008/09 Proposed Travel Time and Travel Speed Measurement Location City of Peterborough Model Update Figure 8.1 Paradigm www.ptsl.com Travel Time Sections Studied Paradigm Transportation Solutions Limited Page 46
8.3 VDF Development Figure 8.2 illustrates the scattergram of the overall average loaded speeds compared to the V/C ratio calculated for the roadway segment. Note that the V/C ratios are calculated based on the respective hourly volume that was provided for each of the 2009 ATR locations provided. That is, if the speed sample was measured at 2:30 PM, the volume data associated to 2:30 PM were used to calculate the V/C ratios. The assumed capacity for the link under question was extracted for the model. The information presented in Figure 8.2 shows that there is generally a wide variation in the average travel speed that is occurring on the links across all V/C values. However, there was a general trend of decreasing average speed with increasing V/C. The trend line shown on the graph generally indicates that the average travel speed reduces by about 0.7 km/h for each 0.1 change in V/C. 8.4 VDF Calibration and Validation The data collected for each roadway segment were reduced to extract the average travel time (including delays at intersections) and the average peak mid-block speed. Table 8.1 summarizes these two measures by functional classification. The entries in Table 8.1 show that: The overall average travel speed was 43.5 km/h, while the average peak speed was more than 53 km/h, or about 22% (10 km/h) higher; The average travel speed generally reflected the pattern of decreasing overall average speed with decreasing functional classification; and The average loaded speeds were generally lower than those suggested by the current model calibration. TABLE 8.1: AVERAGE LOADED SPEEDS VS. AVERAGE PEAK SPEED WITHIN FUNCTIONAL CLASSIFICATIONS Functional Class Average Average Travel Speed Peak Speed Freeway Average 89.4 102.0 Highway Average 43.8 66.2 High Capacity Arterial Average 46.6 54.4 Medium Capacity Arterial Average 43.6 52.6 Low capacity Arterial Average 38.3 48.1 High Capacity Collector Average 41.4 51.7 Low Capacity Collector Average 41.2 52.2 Local Average 35.7 50.9 Grand Average 43.5 53.2 Paradigm Transportation Solutions Limited Page 47
Figure 8.2: Observed Speed vs. V/C Ratio 90 80 70 60 Average Loaded Speed (km/h) 50 40 y = 7.0463x + 46.949 R² = 0.0126 30 20 10 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 V/C Ratio City of Peterborough Model Update Figure 8.2 Paradigm www.ptsl.com Observed Speed vs. V/C Ratio Paradigm Transportation Solutions Limited Page 48
8.4.1 Comparison to Existing VDF Functions The above data were then re-evaluated to determine the average loaded travel speed compared to the V/C ratio and plotted against the VDF functions that have been used in the model development. Figure 8.3 illustrates the average loaded speeds compared to the V/C ratio calculated for the roadway segment. The calculated average loaded speed by functional class from above was used as the starting speed for each functional class. The following observations are noted: the shape of the VDF function generally follows the observed average loaded speed pattern albeit it appears to be slightly flatter; and it appears that the effect of congestion begins to affect average loaded travel speed by a V/C of about 0.3. 8.4.2 Existing VDF Calibration Conclusion Based on the foregoing, it is concluded that: the average speeds within the current model are higher than those observed, indicating that global reductions in the free speeds are warranted; the existing model VDF functions generally well-represent the observed Speed-Delay relationships; potential improvements to the VDF function include improving the sensitivity to V/C to begin closer to a V/C of 0.3 and flattening of the VDF curve. 8.4.3 Adopted VDF Enhancements Based on the foregoing, the following are suggested changes to the modelling framework: in general the link free speeds, be set to the average observed speed by functional class grouping (Arterial, Collector, Local), subject to calibration adjustments; and the BPR formulation be implemented such that the alpha constant reflects the function classification under consideration and the exponent on the V/C term remain at 4. (Figure 8.4). 8.5 Results In the redevelopment of the Volume-Delay Functions, data were collected with respect to the average loaded travel speed. This information was used to refine the VDF equations within the model. The resultant model loaded speeds compare as follows: Overall the average loaded speed is within 9% of the observed average mid-block speed; For arterial roads, the average loaded speeds are within 12-15% of the observed average mid-block speeds; and For collector roads, the average loaded speeds are within 12-20% of the observed average mid-block speeds. Paradigm Transportation Solutions Limited Page 49
Figure 8.3: Observed Average Travel Speed vs. V/C and Existing VDF Functions 60.00 50.00 40.00 Loaded Speed (km/h) 30.00 20.00 10.00 High Capacity Arterial Medium Capacity Arterial Low Capacity Arterial High Capacity Collector Low Capacity Collector Local Observed Arterial Observed Collector 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 V/C Ratio City of Peterborough Model Update Figure 8.3 Paradigm www.ptsl.com Observed Average Travel Speed vs. V/C and Existing VDF Functions Paradigm Transportation Solutions Limited Page 50
Figure 8.4: Observed Average Travel Speed vs. V/C and Adopted VDF Functions 60.00 50.00 40.00 Loaded Speed (km/h) 30.00 20.00 10.00 High Capacity Arterial Medium Capacity Arterial Low Capacity Arterial High Capacity Collector Low Capacity Collector Local Observed Arterial Observed Collector 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 V/C Ratio City of Peterborough TMP Figure 8.4 Paradigm www.ptsl.com Observed Average Travel Speed vs. V/C and VDF Functions Paradigm Transportation Solutions Limited Page 51
9.0 ASSIGNMENT The final step in the modelling process is to assign the assembled auto vehicle demands to the roadway networks. The following describes this process. 9.1 Methodology The vehicle assignment sub-model determines the actual path taken by the vehicle trips. The main inputs to this step are the auto trip matrices and the road network. The following are traffic assignment methods encountered in transportation planning practice, all of which are available in TransCAD: All-or-Nothing Assignment (AON) - Under All-or-Nothing Assignment, all traffic flows between O-D pairs are assigned to the shortest paths connecting the origins and destinations. This model is unrealistic in that only one path between every O-D pair is used, even if there is another path with the same or nearly the same travel time or cost. Also, traffic on links is assigned without considering whether or not there is adequate capacity or heavy congestion; travel time is a fixed input and does not vary depending on the congestion on a link. Stochastic Assignment The assignment method distributes trips between O-D pairs among multiple alternative paths that connect the O-D pairs. The proportion of trips that is assigned to a particular path equals the choice probability for that path, which is calculated by a Logit route choice model. This method does not assign trips to all the alternative paths, but only to paths containing links that are considered "reasonable." A reasonable link is one that takes the traveler farther away from the origin and/or closer to the destination. The link travel time in this method is a fixed input and is not dependent on link volume. Consequently, the method is not an equilibrium method. Incremental Assignment - Incremental Assignment is a process in which fractions of traffic volumes are assigned in steps. In each step, a fixed proportion of total demand is assigned, based on All-or-Nothing Assignment. After each step, link travel times are recalculated based on link volumes. When there are many increments used, the flows may resemble an equilibrium assignment; however, this method does not yield an equilibrium solution. Consequently, there will be inconsistencies between link volumes and travel times that can lead to errors in evaluation measures. Also, Incremental Assignment is influenced by the order in which volumes for O-D pairs are assigned, raising the possibility of additional bias in the results. Capacity Restraint - Capacity Restraint attempts to approximate an equilibrium solution by iterating between all-or-nothing traffic loadings and recalculating link travel times based on a congestion function that reflects link capacity. Unfortunately, this method does not converge and can flip-flop back and forth in the loadings on some links. The capacity restraint method as implemented in some software packages attempts to lessen this problem by smoothing the travel times and by averaging the flows over a set of the last iterations. This method does not converge to an equilibrium solution and has the additional problem that the results are highly dependent on the specific number of iterations run. Performing one more or one less iteration usually changes the results substantially. User Equilibrium (UE) - User Equilibrium uses an iterative process to achieve a convergent solution, in which no travelers can improve their travel times by shifting routes. In each iteration network link flows are computed, which incorporate link capacity restraint effects and flow-dependent travel times. Stochastic User Equilibrium (SUE) - Stochastic User Equilibrium is a generalization of user equilibrium that assumes travelers do not have perfect information concerning network attributes and/or they Paradigm Transportation Solutions Limited Page 52
perceive travel costs in different ways. SUE assignments produce more realistic results than the deterministic UE model, because SUE permits use of less attractive as well as the most-attractive routes. Less-attractive routes will have lower utilization, but will not have zero flow as they do under UE. System Optimum Assignment (SO) - System Optimum Assignment computes an assignment that minimizes total travel time on the network. Under SO Assignment, no users can change routes without increasing their total travel time on the system, although it is possible that travelers could reduce their own travel times. This method can be thought of as a model in which congestion is minimized when travelers are told which routes to use. Based on experience in developing hundreds of models across North America, the User Equilibrium process models across has been found to provide the most reliable means of assigning trips. This step is implemented in TransCAD using the built-in assignment procedure User Equilibrium Assignment. This method is an iterative process. The first iteration loads trips on the shortest path between origin and destination and travel times are calculated based on the link volume delay functions. The next iteration reassigns a percentage of the trips to a second optimal path and so on until the network is in a state of equilibrium (usually requiring 30-60 iterations). Outputs from this stage include: origin/destination travel times, link travel times, link speeds and link volumes for autos. 9.2 Validation When validating the model s assignment, reliance was placed on the FHWA s Model Validation and Reasonableness Checking Manual 3 (MVRCM) to provide guidance with respect to the acceptable precision of the assignment modules within the planning model. Accordingly, assignment validation targets were set on three increasingly detailed levels of precision: System-wide (VMT and Volumes); Corridor Volumes (Screenlines); and Link Specific Volumes. 9.2.1 System-Wide Vehicle Miles of Travel (VMT) When evaluating the accuracy of the assignment, the first check was observed versus modelled Vehicle Miles of Travel (VMT). VMT is the product of the link volume and the link distance, summed over the desired geographic area and facility types. The observed VMT is a product of a comprehensive traffic count program. Since not every link in the network was counted for the validation year, estimates of observed VMT were developed. In the case of the Peterborough model, the primary source of observed VMT is the traffic count database maintained by City staff. It is important to note that these data have been used as provided to the project team. No attempts have been made to rationalize the count data between stations along arterials, or to normalize the data into a consistent weekday PM peak hour (e.g. Thursday PM peak hour in October). 3 Model Validation and Reasonableness Checking Manual, FHWA, Barton-Aschman Associates Inc. and Cambridge Systematics Inc., 1997. Paradigm Transportation Solutions Limited Page 53
It is important to note that a cursory review of the data has indicated that within individual count locations there is significant variation in the traffic counts within the data. In some cases this variations was observed to be as much as 30%. This variation can affect the assessment of the calibration, particularly at the screenline and link level. Further, data provided by City staff represented a sampling of about 250 locations within the City. According to the MVRCM, the modelled VMT should be within 5% of the observed VKMT on a network level. The observed traffic count data is insufficient to provide an overall assessment of the VKMT as the counts only cover about 9% of the estimated VKMT in the network. Nonetheless to assess the model s performance comparisons were made where observed data were available. The MVRCM also suggests that VKMT breakdown for populations such as Peterborough is typically as follows: Freeway/Expressway 33-38%; Major Arterial 27-33%; Minor Arterial 18-22%; and Collectors 8-12%. In the case of the Peterborough model, the VMT breakdown in the count data provided does not follow this distribution. It should be noted however, that these are based on that travel patterns in American cities where they have a more developed freeway network for commuter traffic. Peterborough also has an overall lower density than many similar size populations in the US. Overall the modelled VKMT for the all functional classes is within 1.5% of the observed VKMT. More specifically, the modelled VKMT for the arterial functional classes which comprise 73% of the model network is within 2.2% of the observed VKMT. Medium capacity arterials which comprise 62% of the model network are calibrated within 0.5% of the observed VKMT. 9.2.2 System-Wide Traffic Volumes Consistent with the MVRCM, the next level of validation of the highway assignment is the comparison of observed versus estimated traffic volume on the highway network. As noted above, the observed count data were derived from the traffic count data provided by the City. As indicated in the MVRCM, traffic volumes were validated at the system-wide level by first comparing the overall assignment performance The first level of validation was to compare observed versus estimated volumes for all links with counts. To compare the system-wide assignment performance, a scattergram of the counts versus the assigned volumes was prepared. The degree to which the scattergram follows a 45-degree line (i.e. observed = estimated) is a measure of the ability of the model to replicate the observed volumes. Figure 9.1 indicates that in the case of the Peterborough model, the observed and predicted volumes generally follow a 45-degree line. The industry-accepted measure of the Goodness of Fit of the observed versus the modelled volumes is the Coefficient of Determination (R 2 ). The MVRCM identifies that the Coefficient of Determination (R 2 ) should be greater than 0.88. In the case of the Peterborough model, the Coefficient of Determination (R 2 ) was Paradigm Transportation Solutions Limited Page 54
calculated to be 0.89, which exceeds this value indicating a strong degree of correlation between the modelled volumes and the observed traffic counts. Paradigm Transportation Solutions Limited Page 55
Figure 9.1: Scattergram Plot of Observed vs. Predicted Directional Volumes (PM Peak Hour) R 2 = 0.89 1400 1200 1000 800 600 400 200 0 Modelled 0 200 400 600 800 1000 1200 1400 Observed Figure 9.1 PM Peak Hour Auto Trip Calibration Predicted vs. Observed City of Peterborough Transportation Master Plan Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 56
Another important industry-accepted measure of the Goodness of Fit of the modelled volumes compare to the observed traffic volumes is the Root Mean Square Error (RMSE). This value is calculated as follows: The MVRCM does not provide strict guidelines with respect to the % RMSE values, though it is generally accepted that % RMSE values for models should be in the order of 35%. Referring to assignment results the % RMSE for the entire network is calculated at 30% which is consistent with these targets. In terms of absolute volumes, the average loading compared to the average count indicated that volumes were predicted within 9-38 vehicles per direction (varies by direction) on high capacity arterial sections which is excellent, 32-56 vehicles per direction (varies by direction) on medium capacity arterial sections which is very good and within 45-66 vehicles per direction (varies by direction) on low capacity arterial sections, which is also very good. Accuracy on the high capacity collectors was acceptable with the average error being 90-98 vehicles per direction (varies by direction) on and excellent on low capacity collectors with the average error being 31-55 vehicles per direction (varies by direction). On average across all functional classifications, the volumes were predicted within 24-62 vehicles per direction (varies by direction), which is very good. Therefore, based on the requirements outlined above, the system-wide calibration met FHWA and industrystandard requirements both in terms of VMT and traffic volumes. 9.2.3 Corridor Volumes Having satisfied the overall system-wide calibration targets, the next level of investigation carried out was at screenlines. Typically, screenlines run across the model from edge to edge with sub-groupings referred to as cut lines. In the case of Peterborough, a combination of screenlines and cutlines were used. The MVRCM provides guidance with respect to ADT volumes across screenlines and the maximum allowable deviation permitted. Figure 9.2 illustrates that lower volume screenlines have a higher allowable deviation (> 50%) than do higher volume screenlines (20%). Various agencies have established differing degrees of precision with respect to screenline assignments. For example, the State of Michigan uses 10% at screenlines for its statewide model. In the case of Peterborough, the MVRCM method targets which are based on the volume at the screen line were used to determine the acceptability of the assignment using the PM peak hour volumes rather than the ADT volumes and assuming the same relationship applies to the peak hour values. For Peterborough, seven screenlines were developed to verify the model assignment. Figure 9.3 illustrates the three screenlines used to verify north-south flows through the City (100, 300 and 500) and east-west through various sections of the City (200, 400, 600, 800 and 1000). Figure 9.4 illustrates the screenline calibration across the screenlines running east-west across the City which monitor the north-south flows. Overall the screenline located north of Parkhill Road (Screenline 100) was calibrated within 7-10% of the of the observed traffic volumes which is very good. All links meet the maximum allowable deviation criteria, except University Road southbound. Ackison Road and University Road experience among the highest deviations. Within this screenline, there appears to be overassignment on George Street. Paradigm Transportation Solutions Limited Page 57
Figure 9.2: Maximum Allowable Deviation Across Screenlines Source: NCHRP 255 p.41 (cited in FHWA, Calibration and Adjustment of System Planning Models, Dec. 1990) Figure 9.2 City of Peterborough Transportation Master Plan Maximum Allowable Deviation Across Screenlines Paradigm www.ptsl.com Paradigm Transportation Solutions Limited Page 58
Figure 9.3: Screenlines 600 400 200 Figure 9.3 Screenlines 100 300 500 City of Peterborough Transportation Master Plan Paradigm www.ptsl.com 800 1000 Paradigm Transportation Solutions Limited Page 59