THE OPERATIONAL ANALYSIS OF TWO-LANE RURAL HIGHWAYS

Transcription

1 THE OPERATIONAL ANALYSIS OF TWO-LANE RURAL HIGHWAYS van As, S.C. 1 and van Nekerk, A. 2 1 Traffc Engneer. 2 South Afrcan Natonal Road Agency Lmted. ABSTRACT A large proporton of the South Afrcan rural road network conssts of two-lane hghways. Some of these hghways are carryng relatvely hgh volumes of traffc wth the result that some roads are operatng at low levels of servce. Currently, the Hghway Capacty Manual of the Transportaton Research Board s used for the analyss of the operatons on these roads. Concern has, however, been expressed that the methodologes descrbed n the HCM may not be approprate or adequate for South Afrcan condtons. An alternatve model has been developed for the operatonal analyss of two-lane rural hghways. Ths model utlses queung theory to model platoons of traffc along a hghway. The average platoon length s determned whch can be utlsed to determne evaluaton crtera such as percentage followers and to predct travel speed. Ths model can also be used to model hghways wth wde shoulders where the shoulders are utlsed by vehcles to provde passng opportuntes. The Hghway Capacty Manual uses "Percent tme spent followng" as the measure of effectveness n the evaluaton of two-lane hghways. Ths measure has the lmtaton that t can not readly be observed n the feld. It s therefore proposed that ths should be replaced by "percentage followers", although a new measure termed "follower densty" should be used for the evaluaton of two-lane roads. 1. INTRODUCTION The majorty of rural hghways n South Afrca consst of two lanes. Many of these carry relatvely low volumes of traffc, but on some roads the traffc volumes are hgh wth the result that the roads are operatng at poor levels of servce. The operatonal analyss of two-lane hghways s currently beng undertaken by means of procedures provded n Hghway Capacty Manual (TRB, 2004). Concern has been expressed that the methodologes descrbed n the HCM may not be approprate or adequate for South Afrcan condtons. If ths s true, then t could have serous consequences n stuatons where capacty expansons are undertaken on the bass of nadequate analyss. The am of ths paper s to descrbe a new model that was developed for the operatonal analyss of two-lane hghways. A number of alternatve models, such as the HCM model as well as varous mcroscopc smulaton models, were evaluated and varous shortcomngs were dentfed. The new model was extensvely calbrated and valdated by means of feld observatons. The model has been appled to a major rural two-lane hghway (N4 between Belfast and Komatpoort) and was found to perform satsfactorly. Proceedngs of the 23 rd Southern Afrcan Transport Conference (SATC 2004) July 2004 ISBN Number: Pretora, South Afrca Proceedngs produced by: Document Transformaton Technologes cc Conference Organsed by: Conference Planners

2 One of the ssues dentfed durng the study s the measure of effectveness used for the evaluaton of two-lane hghways. The Hghway Capacty Manual uses "Percent tme spent followng", but ths measure has the lmtaton that t cannot readly be observed n the feld. It s therefore proposed that ths should be replaced by "percentage followers", although other measures are dscussed n ths paper. 2. AVAILABLE MODELS A number of alternatve traffc models are avalable for the operatonal analyss of two-lane hghways. Three such models were dentfed and obtaned for evaluaton durng the study. These models are the followng:! Hghway Capacty Manual model (TRB, 2000)! TRARR Mcroscopc smulaton program (Hoban et al, 1991)! TWOPAS Mcroscopc smulaton program (FHWA, 2003; St John & Harwood, 1986) The Hghway Capacty Manual model s probably the best known of the avalable models. The model was developed by Harwood et al (1999) on the bass of feld observatons and smulaton studes undertaken by the TWOPAS smulaton program. The TWOPAS program was specfcally developed for the smulaton of two-lane hghways. The program was orgnally developed for the Federal Hghway Admnstraton by the Mdwest Research Insttute (the orgnal name of the program was TWOWAF). The program was used n varous research studes and further mprovements and valdatons were made. Most recently, sgnfcant enhancements were made to the program as part of a project for developng the Hghway Capacty Manual model. The program has also been ncorporated n the Interactve Hghway Safety Desgn Model (IHSDM) developed for the Federal Hghway Admnstraton. TRARR s another program that was specfcally developed for the smulaton of two-lane hghways. The program was developed for the Australan Road Research Board (now ARRB Transport Research) n 1985 and The program was one of two (the other beng TWOPAS) whch was consdered as a bass for the development of the Hghway Capacty Manual. An extensve evaluaton by the Unversty of Calforna-Berkley ndcated that TRARR and TWOPAS had smlar capabltes. A problem wth TRARR s that t s apparently no longer supported by the ARRB (McClean, 2003). 3. MACROSCOPIC SIMULATION MODEL A new model that utlses macroscopc smulaton technques was developed durng the study. Ths model apples queung theory to smulate the change n queue or platoon length over the length of a road. The model conssts of a number of modules amed at calculatng varous aspects of traffc flow along a two-lane road. Two of the mportant modules are the followng:! Free flow speed module. Free-flow speed s estmated as a functon of parameters such as speed lmt, ntersectons, pavement wdth, curve radus, road gradent and the acceleraton and deceleraton capabltes of vehcles.! Platoon module. The change n platoon length s modelled over the length of the road. The platoon length depends on a varety of parameters such as traffc flow, speed dfferentals road wdth and other factors. The length of a platoon (or movng queue) s the number of vehcles n the platoon, ncludng the platoon leader. The mnmum platoon length s therefore one. Percentage followers s drectly

3 related to the average platoon or queue length by the followng relatonshp: PF = 100 (N - 1)/N n whch PF s the percentage followers and N the average platoon length. The platoon module models change n platoon length along a road n 20m ntervals. The average platoon length s establshed at each of these ntervals. A certan length s assumed at the start of the road, and a change n the length ( N) s modelled for each nterval. The change s added to the length (N ) at the start of the nterval to determne the length (N +1 ) at the end of the nterval: N +1 = N + N The change n platoon length ( N) s determne as the dfference of two components: N = N Catchup - N Overtake N Catchup s the ncrease n platoon length due to faster vehcles catchng up slower vehcles whle N Overtake s the decrease n the length due to overtakng of vehcles. Catchng up occurs on both no-passng zones as well as passng zones, whle overtakng would normally only occur on passng zones although t s possble to model "llegal" overtakng on such- zones. Where a wde shoulder s used for overtakng, the model provdes for some overtakng on no-passng zones. The ncrease n queue length due to catchng up s calculated by means of a formula orgnally developed by Normann n 1942, smplfed by Wardrop n 1952, and mproved by Mller n the 1960's. Further adjustments were made durng the project. The formula s as follows: In whch N Catchup = (1 H D Z Q Q ) V π D Z Q H V = Dstance nterval (20m) = Speed coeffcent of varaton, dependng on extent of queung = Flow rate n drecton of movement (vehcles per second) = Average followng headway (seconds), dependng on vehcle composton = Average travel speed (m/s), dependng on extent of platoonng The decrease n platoon length due to overtakng s calculated by means of the followng formula developed by Mller ( ): NOvertakng = N 1 S N V D S s the rate at whch vehcles overtake from a long platoon of vehcles. Varous researchers have developed varous formulae for S that depends on gap acceptance and opposng flow. These formulae, however, are very dffcult to calbrate. An alternatve approach for estmatng S was therefore developed durng the study. The alternatve method s based on the premse that, where t s possble, overtakng wll take place at a rate hgher than catch-up untl such tme equlbrum condtons are reached n whch the overtakng rate s equal to the catch-up rate. Equlbrum condtons occur when platoon length no longer changes along the length of a road and N Catchup s equal to N Overtakng. Ths means that S can be determned usng the followng formula:

4 Ve Ne S = N 1 e N D Catchup In whch N e s the equlbrum platoon length (ths N e s not a constant, t depends on traffc condtons). The reducton n platoon length due to overtakng can therefore be calculated as: N Overtakng = N 1 Ve N e V N N 1 e N Catchup The above formula therefore only requres an estmate of the equlbrum platoon length N e to establsh the reducton n platoon length due to overtakng. The advantage of the formula s that t s guaranteed to converge to the equlbrum platoon length, somethng that s very dffcult to acheve wth the orgnal Mller model. Small errors n the catch-up and overtakng rates can accumulate and result n a large error n the platoon length estmaton. The above approach reduces the possblty of such an error. The Hghway Capacty Manual (2000) provdes a model for the estmaton of the equlbrum platoon or queue length N e that has the followng form: N e 1 = Cons tan t (Q + Q j) e N e n whch Q and Q j s the flow and opposng flow n the two drectons of travel respectvely. An alternatve model was developed n ths study n whch the equlbrum platoon length s estmated as follows: N e = 1+ Cons tan t Q Q j The man dfference between the above models s that the HCM (2000) estmates equlbrum queue length as a functon of the sum of the two opposng flows of travel, whle the product of the two opposng flows of travel s used n the alternatve model. The square root of the opposng flow s also used to reduce the mpact of the opposng flow. The advantage of the alternatve model s that t s senstve to the drectonal splt. At 0/100 or 100/0 drectonal splts, the average platoon length s estmated as one (no followers) whch s conceptually more acceptable than the HCM model whch does not converge to zero followers (except when flows are zero n both drectons). The model was extensvely calbrated usng traffc data obtaned from TEL loggers as well as manual observatons. The observatons were undertaken under varous condtons, on varous types of roads and for varous volumes of traffc. A varety of relatonshps were developed n addton to those descrbed above and an attempt was made to take nto account all possble and relevant factors that may affect flow on a two-lane hghway. Due to the large number of factors and varables nvolved, t was not possble to calbrate all factors and some judgement was requred to quantfy these factors. Addtonal research would be requred to calbrate all the dentfed factors. A problem encountered durng the study s that there are not many two-lane roads avalable on whch the requred observatons can be made. A major effort was requred durng the study to dentfy such locatons. 4. MODEL EVALUATION The dfferent traffc flow models descrbed above were evaluated by means of the followng methods:! Senstvty analyss n whch a model s evaluated to establsh whether ts predctons are logcal and consstent.

5 ! Comparson wth other models wth the purpose of dentfyng possble major dfferences.! Comparson wth observed traffc operatons n whch the model s appled to a partcular road and stuaton and the predctons of the model are compared wth observatons of actual traffc operatons. A major problem that was dentfed wth all currently avalable models s that none of them provde for overtakng n whch the shoulder s used by the overtaken vehcle to move out of the way of followng vehcles (as customary n South Afrca). Observatons made durng the study ndcated that the utlsaton of shoulders has a major mpact on traffc flow on a two-lane road. It would be possble to calbrate the Hghway Capacty Manual model for such utlsaton of shoulders, but the two mcroscopc smulaton programs would requre extensve rewrtng of the program algorthms. 5. MICROSCOPIC SIMULATION MODEL EVALUATION A problem wth the mcroscopc smulaton programs s that they requre extensve calbraton of factors that can not be easly observed n the feld. Some factors nvolve human factors that can probably only be calbrated by means of a vehcle smulator. There are a number of factors, such as vehcle power-to-weght ratos, that can readly be calbrated by means of the feld observatons and some effort was made durng the study to calbrate the TRARR program. In spte of such calbraton, t was stll not possble to obtan satsfactory correlaton between the model and feld observatons. One of the problems encountered wth the TRARR program was that t becomes unstable when a long road secton s smulated. For example, f a long no-overtakng secton s smulated, the percentage followers frst ncrease along the secton (as expected) but then the platoons start breakng up and the percentage followers decrease. A further problem wth the program s that t s apparently no longer supported by the ARRB (McLean, 2003). For these reasons, the program can not be recommended for general applcaton. Major problems were experenced wth the verson of the TWOPAS smulaton program that was made avalable for evaluaton durng the study. The program contnually termnated wth error messages that could not be explaned. It appears f the program has lmted facltes for checkng nput data for possble errors wth the result that nvald calculatons are performed that lead to system errors. One of the problems dentfed wth the TWOPAS program s that t requres data n a pre-processed form. A further problem s that t uses mperal unts such as feet, mles and pounds. Ths means that a front- and back-end program would be requred to convert data to the format requred by TWOPAS and to convert results produced by the program to a format that can be more readly be nterpreted. Two such programs are avalable, namely IHSDM (FHWA, 2003) and UCBRURAL (Leman & May, 1996). The IHSDM program was obtaned but t was found to be somewhat cumbersome. It also dd not elmnate all data errors wth the result that TWOPAS stll termnated wth error messages. Due to ts lmtatons wth regard to the use of shoulders for overtakng, further attempts at gettng the program operatonal were abandoned. 6. HIGHWAY CAPACITY MANUAL MODEL EVALUATION The Hghway Capacty Manual (TRB, 2000) model provdes a relatvely smple procedure for the analyss of two-lane hghways. It would also be possble to extent the model to ncorporate the effect of wde shoulders on overtakng. The manual, however, warns that there are stuatons that are too complex to evaluate by means of the model and that a traffc smulaton model would be requred for such stuatons. In practce, many problem two-lane hghways that need capacty

6 analyss are precsely those that are too complex for the model. Fgure 1. Senstvty analyss of the HCM model - percent tme spent followng. Fgure 2. Senstvty analyss of the HCM model - travel speed.

7 The Hghway Capacty Manual was evaluated by means of a senstvty analyss as well as comparsons wth traffc observatons. The senstvty analyss, however, already ndcated some serous shortcomngs n the model. Some of the results of the senstvty analyss are shown n Fgures 1 and 2. The followng are a number of mportant problems dentfed n the fgures:! The HCM provdes two alternatve models or procedures for the analyss of two-lane roads, but the two procedures provde dfferent results, as shown n Fgure 1.! The model produces a percent tme spent followng greater than 100% (as shown n Fgure 1). Ths means that vehcles spent more tme followng than they are travellng.! The percent tme spent followng s sgnfcantly greater than zero at zero traffc flow (see Fgure 1). A zero or near-zero percent tme spent followng would have been more realstc.! Average speeds are sometmes very low, and can even be negatve when free-flow speeds are low such as on a steep upgrade. Ths problem s llustrated n Fgure 2. The above ndcates that the model provded by the Hghway Capacty Manual s not adequate to accommodate all varables and factors needed for the analyss of a two-lane hghway. The model may be used n smple applcatons, but fals f the applcaton becomes complex. The macroscopc smulaton model was extensvely evaluated by means of a senstvty analyss and comparson wth observatons and other models. Some of the results of the evaluaton are shown n Fgures 3 to 6. The model generally performed as expected whle a far comparson was obtaned wth traffc observatons. No serous flaws were dentfed durng the evaluaton. Addtonal research would be requred to calbrate all the parameters of the model, but t appears f the model can be used wth some confdence n most practcal applcatons. Fgure 3. Comparson of macroscopc model wth traffc observatons (narrow shoulders).

8 Fgure 4. Comparson of macroscopc model wth traffc observatons (wde shoulders). Fgure 5. Comparson of macroscopc and HCM models - percentage followers.

9 Fgure 6. Comparson of macroscopc and HCM models - travel speed. A comparson of the macroscopc and HCM models s shown n Fgures 5 and 6. Although a number of serous problems have been dentfed wth the HCM model, t does not mply that the model s always naccurate. There are stuatons n whch the model provdes farly acceptable results. Ths s ndcated n the fgures that show that the two models agree farly over a range of condtons, although there could be sgnfcant dfferences under certan condtons. 7. LEVEL OF SERVICE The Hghway Capacty Manual currently uses percent tme spent followng and speed as measures of effectveness for establshng the level-of-servce provded by a two-lane hghway. Percent tme spent followng s defned by the manual as the "average percentage of travel tme that vehcles must travel n platoons behnd slower vehcles due to the nablty to pass". In prevous versons of the Hghway Capacty Manual, t was called percent tme delay, but was renamed n response to confuson regardng the meanng of the term (Harwood et al 1999). The new defnton, however, s stll not totally clear snce t can be nterpreted as ether the "average percentage" or as the "percentage of average travel tme". It appears f the manual uses the frst nterpretaton, but ths could not be clarfed durng the study. A problem wth percent tme spent followng s that t s dffcult to measure n the feld. The Hghway Capacty Manual therefore allows the use of percentage followers as a surrogate measure for percent tme spent followng. Due to the complextes nvolved n measurng (and modellng) percent tme spent followng, t was decded to rather use percentage followers as the measure of effectveness. A further mportant ssue that was dentfed wth the use of many of the measures of effectveness used by the Hghway Capacty Manual s that they provde an ndcaton of the level of servce experenced by ndvdual road users and not the total servce provded to all road users. The

10 problem wth ths approach s that level of servce could be poor but the volume of traffc would be too low to warrant mprovements. A norm based on the total measure of effectveness establshed for all users would provde a better ndcaton of when upgradng of a faclty s warranted. An example of the above ssue can be found n the evaluaton of traffc sgnal controlled ntersecton. The HCM uses average delay per vehcle as the measure of effectveness n the evaluaton of such ntersectons. Ths norm s then often used as the crteron for ntersecton upgradng. The new Volume 3 (Traffc Sgnal Desgn) of the South Afrcan Road Traffc Sgns Manual (NDOT, 2001), however, uses average queue length as the warrant for the nstallaton of traffc sgnals. Ths average queue length s drectly related to "total delay" (n unts of vehcle-hours per hour) rather than "average delay". A poor average level of servce may be experenced at an ntersecton, but traffc sgnals would not be warranted when traffc volumes are low. An nterestng aspect of the HCM s that t uses traffc densty as a measure of effectveness n the evaluaton of freeways. Traffc densty s defned n terms of vehcles per klometre of road (per lane), but s also drectly related to "total travel tme" (n unts of vehcle-hours) per klometre of road rather than "average travel tme". Traffc densty s therefore senstve to the volume of traffc on a road. An alternatve measure of effectveness was therefore developed durng the study, namely "follower densty". Ths measure s defned as the number of followers per klometre per lane. The measure can relatvely smply be calculated by means of the followng equaton: n whch: K F = P F Q N U K F P F Q N U = Follower densty (followers per klometre per lane) = Percentage followers = Traffc flow n drecton of travel = Number of lanes n drecton of travel = Average (macroscopc) speed Experence wth the above measure of effectveness ndcates that t provdes a relatvely good ndcaton of when capacty upgradng s warranted. It wll only ndcate a need for such upgradng when both a poor level of servce s experenced and traffc volumes are hgh. 8. CONCLUSIONS AND RECOMMENDATIONS The ntal am of the study was to evaluate alternatve traffc models for two-lane hghways. Durng the study, however, t was found that all avalable models had varous shortcomngs. A new model based on macroscopc smulaton was therefore developed. No serous flaws have yet been dentfed wth the model, although addtonal calbraton of some of the model parameters would be requred. Durng the study t was found that percent tme spent followng or percentage followers only provde an ndcaton of the level of servce experenced by an ndvdual road user, but that these measures cannot be used for purposes of warrantng capacty upgrades of a road. An alternatve measure of effectveness, namely follower densty was therefore developed whch takes traffc volume nto account. Ths measure provdes a better ndcaton of when capacty upgradng s warranted.

11 It s recommended that rural road authortes should start applyng the model to all new desgns as well as on exstng roads on whch traffc problems are beng experenced. The model can even be useful n evaluatng the desgn of roads that do not carry large volumes of traffc snce t contans a module that checks the "desgn consstency" of a road. The model s relatvely smple to apply and requres data that are normally avalable when a road s desgned. At the tme of the wrtng of ths paper, the model has only been mplemented n MS-DOS, but the plan s to extend the model to the Wndows envronment. 9. ACKNOWLEDGEMENTS The paper s based on a research project of the South Afrcan Natonal Road Agency Lmted. Permsson to use the materal contaned n the paper s gratefully acknowledged. The opnons expressed, however, are those of the authors and do not necessarly represent the polcy or practce of the Agency. 10. REFERENCES [1] Federal Hghway Admnstraton (FHWA), 2003, Interactve Hghway Safety Desgn Model (IHSDM) Program manual, Turner-Farbank Hghway Research Center (TFHRC), McLean. [2] Harwood, D.W., A.D. May, I.B. Anderson, and L. Leman, 1999, Capacty and qualty of servce of two-lane hghways, Natonal Cooperatve Hghway Research Program, Transportaton Research Board, Natonal Research Councl. [3] Hoban, C.J., G.J. Fawcett and G.K. Robnson, 1991, A model for smulatng traffc on two-lane rural roads, User gude and manual for TRARR Verson 3.2, Techncal Manual ATM 10B, Australan Road Research Board, Vctora, Australa. [4] Leman, L., and A. D. May, 1996, UCBRURAL: A User-frendly Interface for Rural Hghway Computer Smulaton Model wth Emphass on the Incorporaton of the TWOPAS Model, Report No. FHWA/CA/TO-96/25, Calforna Department of Transportaton. [5] McLean, J, 2003, Personal correspondence receved. Project leader - TRARR development. [6] Mller A.J., 1960, A mathematcal model for the study of road traffc flow. PhD thess, Manchester. [7] Mller A.J., 1961, A queung model for road traffc flow, J. Royal Stat. Soc., 23B(1), [8] Mller A.J., 1963, Analyss of bunchng n rural two-lane traffc, Op. Res., 11, [9] Mller A.J., 1965, Queung n rural traffc, Proc. Thrd Internatonal Symposum on the Theory of Traffc Flow, [10] Natonal Department of Transport, 2001, Volume 3: Traffc sgnal desgn, South Afrcan Road Traffc Sgns Manual, Pretora. [11] Normann O.K., 1942, Results of hghway capacty studes, Publc Roads, 23(4), pp [12] St. John, A.D. and D.W. Harwood, 1986, TWOPAS Programmer's Gude, Federal Hghway Admnstraton. [13] Transportaton Research Board (TRB), 2000, Hghway capacty manual (Metrc unts), Natonal Research Councl, Washngton, D.C. [14] Wardrop J.G., 1952, Some theoretcal aspects of road traffc research, Proc. Instn. Cv. Engnrs., 2,

12 THE OPERATIONAL ANALYSIS OF TWO-LANE RURAL HIGHWAYS van As, C. 1 and van Nekerk, A. 2 1 Traffc Engneer. 2 South Afrcan Natonal Road Agency Lmted. BIOGRAPHY Alex van Nekerk has a postgraduate qualfcaton n Transportaton Engneerng. He s employed by the South Afrcan Natonal Roads Agency (Ltd) (North) where he s Dvsonal Head for Toll and Traffc. He s responsble for toll feasblty studes, toll operatons, traffc engneerng and geometrc engneerng. He serves as commttee member on the PIARC C1.4 commttee for Network Operatons and s a board member of the South Afrcan Socety for ITS (SASITS).