SMART-Signal Phase II: Arterial Offset Optimization Using Archived High-Resolution Traffic Signal Data

Transcription

1 SMART-Sgnal Phase II: Arteral Offset Optmzaton Usng Archved Hgh-Resoluton Traffc Sgnal Data Fnal Report Prepared by: Henry X. Lu Heng Hu Department of Cvl Engneerng Unversty of Mnnesota CTS 13-19

2 Techncal Report Documentaton Page 1. Report No Recpents Accesson No. CTS Ttle and Subttle 5. Report Date SMART-Sgnal Phase II: Arteral Offset Optmzaton Usng Aprl 213 Archved Hgh-Resoluton Traffc Sgnal Data Author(s) 8. Performng Organzaton Report No. Henry X. Lu and Heng Hu 9. Performng Organzaton Name and Address 1. Project/Task/Work Unt No. Department of Cvl Engneerng CTS Project #291 Unversty of Mnnesota 5 Pllsbury Drve Mnneapols, MN Contract (C) or Grant (G) No. 12. Sponsorng Organzaton Name and Address 13. Type of Report and Perod Covered Intellgent Transportaton Systems Insttute Center for Transportaton Studes Unversty of Mnnesota 2 Transportaton and Safety Buldng 511 Washngton Ave. SE Mnneapols, MN Fnal Report 14. Sponsorng Agency Code 15. Supplementary Notes Abstract (Lmt: 25 words) Tradtonally, offset optmzaton for coordnated traffc sgnals s based on average travel tmes between ntersectons and average traffc volumes at each ntersecton, wthout consderaton of the stochastc nature of feld traffc. Usng the archved hgh-resoluton traffc sgnal data, n ths project, we developed a data-drven arteral offset optmzaton model that wll address two well-known problems wth vehcle-actuated sgnal coordnaton: the early return to green problem and the uncertan ntersecton queue length problem. To account for the early return to green problem, we ntroduce the concept of condtonal dstrbuton of the green start tmes for the coordnated phase. To handle the uncertanty of ntersecton queue length, we adopt a scenaro-based approach that generates optmzaton results usng a seres of traffc-demand scenaros as the nput to the offset optmzaton model. Both the condtonal dstrbutons of the green start tmes and traffc demand scenaros can be obtaned from the archved hgh-resoluton traffc sgnal data. Under dfferent traffc condtons, queues formed by sde-street and man-street traffc are explctly consdered n the dervaton of ntersecton delay. The objectve of ths model s to mnmze total delay for the man coordnated drecton and at the same tme t consders the performance of the opposte drecton. Due to model complexty, a genetc algorthm s adopted to obtan the optmal soluton. We test the performance of the optmzed offsets not only n a smulated envronment but also n the feld. Results from both experments show that the proposed model can reduce travel delay of coordnated drecton sgnfcantly wthout compromsng the performance of the opposte approach. 17. Document Analyss/Descrptors 18. Avalablty Statement Traffc sgnals, Offsets (Traffc sgnal tmng), Optmzaton, Genetc algorthms, Archved hgh-resoluton traffc sgnal data No restrctons. Document avalable from: Natonal Techncal Informaton Servces, Alexandra, Vrgna Securty Class (ths report) 2. Securty Class (ths page) 21. No. of Pages 22. Prce Unclassfed Unclassfed 37

3 SMART-Sgnal Phase II: Arteral Offset Optmzaton Usng Archved Hgh-Resoluton Traffc Sgnal Data Fnal Report Prepared by: Henry X. Lu Heng Hu Department of Cvl Engneerng Unversty of Mnnesota Aprl 213 Publshed by: Intellgent Transportaton Systems Insttute Center for Transportaton Studes Unversty of Mnnesota 2 Transportaton and Safety Buldng 511 Washngton Avenue SE Mnneapols, Mnnesota The contents of ths report reflect the vews of the authors, who are responsble for the facts and the accuracy of the nformaton presented heren. Ths document s dssemnated under the sponsorshp of the Department of Transportaton Unversty Transportaton Centers Program, n the nterest of nformaton exchange. The U.S. Government assumes no lablty for the contents or use thereof. Ths report does not necessarly reflect the offcal vews or polces of the Unversty of Mnnesota. The authors, the Unversty of Mnnesota, and the U.S. Government do not endorse products or manufacturers. Any trade or manufacturers names that may appear heren do so solely because they are consdered essental to ths report.

4 Acknowledgments The authors wsh to acknowledge those who made ths research possble. The study was funded by the Intellgent Transportaton Systems (ITS) Insttute, a program of the Unversty of Mnnesota s Center for Transportaton Studes (CTS). Addtonal fnancal support was provded by the Unted States Department of Transportaton Research and Innovatve Technologes Admnstraton (RITA). The authors also would lke to thank Mr. Steve Msgen and hs staff from the Mnnesota Department of Transportaton for ther support on the feld mplementaton of the SMART (Systematc Montorng of Arteral Road Traffc)-Sgnal system. Dr. Henry Lu and the Unversty of Mnnesota have equty and royalty nterests n SMART- Sgnal Technologes, Inc., a Mnnesota-based prvate company whch may commercally beneft from the results of ths research. These relatonshps have been revewed and managed by the Unversty of Mnnesota n accordance wth ts Conflcts of Interests polces.

5 Table of Contents Chapter 1. Introducton... 1 Chapter 2. Hgh-Resoluton Traffc Sgnal Data Condtonal Dstrbuton of Green Start Tmes Traffc Scenaros... 6 Chapter 3. Model Formulaton Scenaro-Based Offset Optmzaton Delay Calculaton... 1 Chapter 4. Soluton Method and Optmzaton Results Chapter 5. Evaluaton Usng a Smulaton Model Chapter 6. Feld Evaluaton Chapter 7. Conclusons and Future Research References... 29

6 Lst of Fgures Fgure 2.1: Installaton of SMART-Sgnal system on TH55, Golden Valley, MN (Source: Google Maps) Fgure 2.2: Dstrbuton of green start tme of Phase 2 (Coordnated phase) n local clock, TH 55 & Boone Ave, 7: AM ~ 9: AM, 6/15/29 ~ 6/26/29 1 weekdays Fgure 2.3: Dual-rng control dagram of ntersecton TH 55 & Boone Ave durng weekday AM peaks Fgure 2.4: Dual Rng Control dagram of an example ntersecton Fgure 2.5: Phase 2 (Eastbound through) green start tme vs. assocated number of actuatons, TH 55 & Boone Ave, 6/15/29 ~ 6/26/29 1 weekdays Fgure 2.6: Condtonal dstrbutons of Phase 2 (EB) green start tme PG ( 1,2 n 1,2 ), (Left) n 1,2 =6 (Rght) n 1,2 =9, TH 55 & Boone Ave, 6/15/29 ~ 6/26/29 1 weekdays Fgure 2.7: Boundary nput volumes and turnng percentages Fgure 3.1: Queung process between two ntersectons when d Fgure 3.2: Queung process between two ntersectons when d c c g, d g <, d Fgure 4.1: GA results for each generaton Fgure 4.2: Coordnaton result for both feld and optmzed offsets Fgure 5.1: VISSIM network for test corrdor Fgure 5.2: Comparson of dstrbuton of coordnated green start between smulaton model and the feld Fgure 5.3: Smulaton result of travel delay based on dfferent offset settngs Fgure 6.1: Estmated EB queue length based on dfferent offset settngs Lst of Tables Table 4.1: Parameters for GA Table 5.1: Eastbound and Westbound average delay comparson Table 6.1: Eastbound and Westbound nput volume (7:AM~9:AM) comparson between 9/3/29 and 9/14/ Table 6.2: Sde street nput volume (7:AM~9:AM) comparson between 9/3/29 and 9/14/ Table 6.3: Eastbound and Westbound average delay comparson between 9/3/29 and 9/14/

7 Executve Summary Tradtonally, offset optmzaton for coordnated traffc sgnals s based on average travel tmes between ntersectons and average traffc volumes at each ntersecton, wthout consderaton of the stochastc nature of feld traffc. Usng the hgh-resoluton traffc sgnal data collected by the SMART (Systematc Montorng of Arteral Road Traffc)-Sgnal system, n ths project, we developed a data-drven arteral offset optmzaton model. The proposed model addresses two well-known problems wth vehcle-actuated sgnal coordnaton: the early return to green problem and the uncertan ntersecton queue length problem. To account for the early return to green problem, we ntroduce the concept of condtonal dstrbuton of the green start tmes for the coordnated phase. To handle the uncertanty of ntersecton queue length, we adopt a scenaro-based approach that generates optmzaton results usng a seres of traffc demand scenaros as the nput to the offset optmzaton model. Both the condtonal dstrbutons of the green start tmes and traffcdemand scenaros can be obtaned from the archved hgh-resoluton traffc sgnal data. Under dfferent traffc condtons, queues formed by sde-street and man-street traffc are explctly consdered n the dervaton of ntersecton delay. The objectve of ths offset optmzaton model s to mnmze total delay for the man coordnated drecton and at the same tme t consders the performance of the opposte drecton. Due to the model complexty, a genetc algorthm s adopted to obtan the optmal soluton. We took sx ntersectons along the TH55 n Mnneapols, MN as the study ste and ths corrdor has a total length of 1.83 mles wth a speed lmt of 55 MPH. Ten weekdays hgh-resoluton traffc sgnal data durng the mornng peak hours from 6/15/29 to 6/26/29 was utlzed to generate the optmal offsets. We mplemented the optmzed offset values n both VISSIM smulaton model and the feld sgnal controllers. Both test results ndcate that the model can reduce travel delay of coordnated drecton sgnfcantly wthout compromsng the performance of the opposte approach. In practce, we envson that our optmzaton program can be utlzed perodcally (for example, every few weeks) to optmze system performance usng the archved data durng that perod.

8 Chapter 1. Introducton Offset settngs are crtcal to the performance of traffc sgnal system operated n a coordnated mode. Over the years many computerzed programs have been developed for sgnal offset optmzaton, usng average traffc volume at ntersectons and average travel tmes between ntersectons. Based on the objectves of the optmzaton process, these programs can be dvded nto two groups. One group ams to maxmze the bandwdth and progresson along arterals, such as MAXBAND (Lttle et al., 1981) and PASSER II (TTI, 29), and the other group attempts to mnmze system delay and number of stops, such as TRANSYT-7F(Wallace et al., 1984) and Synchro (Traffcware, 21). In more detal, MAXBAND maxmzes weghted combnaton of bandwdths gven cycle length and splts. It allows users to nput a queue clearance tme for each approach, but the queung process s not consdered nsde the model. PASSER II maxmzes the bandwdth effcency based on pre-calculated splts. Traffc performance measures are estmated usng determnstc models. TRANSYT-7F s a macroscopc determnstc optmzaton model whch mnmzes a performance ndex, defned as a weghted combnaton of system delay and stops. It models traffc n platoons usng a platoon dsperson algorthm and consders queung process by estmatng arrval and dschargng flow second by second. MAXBAND, PASSER II and TRANSYT-7F can all be consdered as determnstc models because they only use average traffc volumes as optmzaton nputs. Traffc flow fluctuatons are not consdered n these models. As argued by Heydecker (1987), the degree of varablty of traffc flows and sgnals has a sgnfcant mpact on the outcome of sgnal optmzaton, n that usng the average flows may ncur consderable addtonal delay, compared wth the tmng obtaned by takng ths varablty nto account. In order to accommodate traffc varatons, Synchro optmzes sgnal tmng by averagng results of fve volume scenaros (1, 3, 5, 7 and 9 percentles), whch assumes the user-nput volumes are the means of random varables wth Posson dstrbuton. However, these scenaros are arbtrarly assumed and they may not be consstent wth actual traffc condtons n the feld. As ndcated by Abbas et al. (21), exstng offset optmzaton models for vehcle-actuated coordnated traffc sgnals fals to address two mportant ssues: (1) the early return to green problem because of the traffc flow varatons on non-coordnated approaches, (2) the varaton of watng queue lengths at coordnated drectons. Over the years, a number of research studes on offset optmzaton have attempted to address these two problems from dfferent perspectves. To mtgate the early-return-to-green problem, Skabardons (1996) developed several alternatve procedures to modfy controller yeld ponts and phase force-offs usng ether the average spare green tmes or the average duraton of the green tmes for the actuated phases. Shoup and Bullock (1999) developed an offlne procedure to optmze offsets, assumng the avalablty of travel tmes between ntersectons from vehcle re-dentfcaton technologes. Abbas et al. (21) developed a real-tme offset transtonng algorthm for coordnated traffc sgnals. The algorthm uses a greedy approach to search for the optmal offset by movng the green wndow to nclude more vehcles that can pass durng green tme. Gettman et al. (27) proposed a real-tme control algorthm to adjust ntersecton offsets n a coordnated traffc sgnal system, based on the sgnal phase and detector data from the last several cycles. Usng the archved sgnal status data, Yn et al. (27) presented an offlne offset refner, whch addresses the problem of uncertan green starts and ends n the determnaton of offsets. More recently, based on hgh resoluton controller data, Day et al. (21) ntroduced the Purdue Coordnaton 1

9 Dagram (PCD) to assess arteral coordnaton and Bullock et al. (211) evaluated the performance of dfferent offset optmzaton objectve functons. However, none of the prevous studes have addressed the two problems dentfed above smultaneously, whch could lead to suboptmal solutons. These two problems are ntertwned together, as traffc demand varatons wll lead to uncertan green start tmes, and uncertan green start tmes wll result n stochastc length of watng queues even wth determnstc demands. The two problems, therefore, need to be consdered smultaneously. In ths project, we propose a data-drven approach to optmze offsets for vehcle-actuated coordnated traffc sgnals, usng the massve amount of sgnal status and vehcle actuaton data collected from the feld. The proposed model s ntended to serve as an off-lne offset fne-tunng tool, whch optmzes the offsets after montorng the traffc condton n the feld for a certan perod of tme. The proposed approach, for the frst tme, addresses the two problems of vehcleactuated traffc sgnal coordnaton smultaneously. To account for the early return to green problem, for the coordnated phase, we ntroduce the concept of condtonal probablty of the green start tmes, whch can be obtaned from the archved hgh-resoluton traffc sgnal data. To handle the uncertanty of ntersecton queue length, we adopt a scenaro-based optmzaton approach, whch uses a seres of traffc demand scenaros obtaned from the archved data as the model nput. The objectve of ths model s to mnmze total delay for the man coordnated drecton and at the same tme consders the performance of the opposte drecton. We test the performance of the optmzed offsets not only n a smulated envronment but also n the feld. Results from both experments show that the proposed model can reduce travel delay of coordnated drecton wthout compromsng the performance of the opposte drecton. In practce, we envson that our optmzaton program can be utlzed perodcally (for example, every a few weeks) to optmze system performance usng the archved data durng that perod. The remander of the report s organzed as follows. In Chapter 2, we present the hgh-resoluton traffc sgnal data and ntroduce two mportant concepts: the condtonal dstrbuton of green start tmes and the traffc demand scenaros. In Chapter 3, the scenaro-based offset optmzaton model s presented. The soluton method and optmzaton results are gven n Chapter 4. The smulaton and feld tests are descrbed n Chapter 5 and Chapter 6, respectvely. Conclusons and further research drectons are ncluded n Chapter 7. 2

10 Chapter 2. Hgh-Resoluton Traffc Sgnal Data The proposed offset optmzaton model s based on the traffc data collected by the SMART (Systematc Montorng of Arteral Road Traffc)-Sgnal system (Lu and Ma, 29, Lu, et al. 29). The system s an ntegrated data collecton, storage, and analyss system whch can contnuously collect and archve hgh resoluton event-based traffc sgnal data ncludng every vehcle-detector actuaton and every sgnal phase change. Sx ntersectons along the TH55 n Mnneapols, MN were chosen as the study ste, as shown n Fgure 2.1. Ths corrdor has a total length of 1.83 mles wth a speed lmt of 55 MPH. The sx ntersectons are operated n a vehcle-actuated coordnated mode durng weekday s mornng peak (7:AM ~ 9: AM) and afternoon peak (3:3 PM ~ 5:3 PM), wth a cycle length of 18 seconds. The coordnaton favors east bound (phase 2) traffc n the mornng peak and west bound (phase 6) traffc n the afternoon. Ten weekdays data durng mornng peak hours from 6/15/29 to 6/26/29 were used n ths project. Fgure 2.1: Installaton of SMART-Sgnal system on TH55, Golden Valley, MN (Source: Google Maps). 2.1 Condtonal Dstrbuton of Green Start Tmes As mentoned above, the SMART-Sgnal system archves every sgnal change and detector actuaton at sgnalzed ntersectons. Fgure 2.2 presents an example dstrbuton of green start tmes of the coordnated phase (Phase 2) n the local controller clock at the ntersecton of TH55 & Boone Ave. Fgure 2.3 shows the correspondng dual-rng control dagram, whch has 8 phases. Based on the settngs, phase 2 and phase 6 are desgnated coordnated phases and a cycle starts at the tme when phases 3 and 8 begn. Under dfferent traffc condtons, the noncoordnated phases may be termnated due to gap-out or max-out, or at ts force-off pont. It can even be skpped f there s no vehcle actuaton for a partcular phase. Any unused green tme from the non-coordnated phases would be added to the coordnated phases (.e. phase 2 and phase 6), whch makes the coordnated green start earler,.e. the so-called early return to green problem. In ths case, the duraton tme of phase 3 and phase 4 would determne the green start tme of phase 2, as can be seen from Fgure 2.3. The mnmum splt length for phase 3 and phase 4 are 12 seconds and 16 seconds, respectvely, and ther maxmum splts are 15 seconds and 26 seconds. One pedestran phase s assocated wth phase 4, whch has a Walkng tme of 7 seconds and a Flashng Don t Walk tme of 3 seconds. Snce the assgned pedestran phase s longer than the duraton of assocated phase 4, f there s a pedestran call, t wll extend the phase 4 green beyond ts orgnal maxmum. As a result, the green start tme dstrbuton n Fgure 2.2 s clearly dvded nto three groups, as ndcated by the red numbers. In group 1, ether phase 3 or phase 4 s skpped, whch makes phase 2 green start tme smaller than the 3

11 summaton of two mnmum splt lengths ( = 28 seconds); In group 2, both phases are actve n the cycle and the total spt length vares from ts mnmum to maxmum ( = 41 seconds); In part 3, there s at least one pedestran call n the cycle whch makes coordnated phase 2 starts later than usual Probablty (%) Local cycle second Fgure 2.2: Dstrbuton of green start tme of Phase 2 (Coordnated phase) n local clock, TH 55 & Boone Ave, 7: AM ~ 9: AM, 6/15/29 ~ 6/26/29 1 weekdays. Cycle start Rng 1 P2:114 s P1:25 s P3:15 s P4:26 s Rng 2 P5:17 s P6:122 s P8:18 s P7:23 s Barrer Barrer Barrer Fgure 2.3: Dual-rng control dagram of ntersecton TH 55 & Boone Ave durng weekday AM peaks. As shown above, at vehcle-actuated ntersectons, sgnal tmngs vary from cycle to cycle under dfferent actuaton patterns and the early return to green problem of coordnated phases exst due to varous reasons. The green start tme of each coordnated phase s very much dependent on the vehcle actuatons of non-coordnated phases. To represent ths relatonshp, an assocated number of vehcle actuatons, n p, for coordnated phase p of ntersecton, s ntroduced. Wthout loss of generalty, a four-leg and 8-phase ntersecton s taken as an example. Intersecton layout and correspondng dual-rng control dagram are shown n Fgure 2.4. The numbers n the layout ndcate dfferent phases (phase 2 and phase 6 are coordnated phases here) and the red arrows ndcate dfferent movng drectons. Accordng to the dual rng control logc, dfferent rngs can only go across the barrers at the same tme. Specfcally, phase 3 and phase 8 should start at the same tme and phase 4 and phase 7 should end at the same tme. As a result, the non-coordnated phase n one rng wth less vehcle actuatons, whch s supposed to end earler, may be extended by the phases n the other rng wth more vehcle actuatons. 4

12 Cycle start Rng 1 Rng Barrer Barrer Barrer Fgure 2.4: Dual Rng Control dagram of an example ntersecton. Assume the number of actuatons for a partcular phase n each cycle s equal to the cycle nput volume of that phase, whch s usually the case for sde streets because they have stop-bar detectors n place. The calculaton of n p, can be shown n Equaton 2.1, where N p, s the cycle nput volume for phase p of ntersecton. It states that the assocated number of vehcle actuatons of phase 2 s equal to the larger values between N +,3 N and N + N,4,7,8 ; for phase 6, the assocated number of vehcle actuatons s equal to the larger values between N +,3 N and,4 N +,7 N plus the number of actuatons of phase 5 ( N,8,5 ). Note that phase 1 s not consdered when calculatng the assocated number of vehcle actuatons for phase 2, because the laggng phase after the coordnated phase usually has a fxed length of duraton. n,2 =max(n,3 +N,,4 N +N ),7,8 Equaton 2.1 n,6 =max(n,3 +N,,4 N + N ) + N,7,8,5 It s ntutve that the larger the n p, s, the later the green phase of the coordnated phase p tends to start. Takng dfferent arrval and actuaton profles of non-coordnated phases nto consderaton, the green start tme of coordnated phase p can be dfferent even f n p, s the same. Therefore, for coordnated phase p, gven ts assocated number of actuatons n p,, we can get the dstrbuton of green start tme G p,. Note that, the ntroducton of the condtonal dstrbuton P( Gp, n p, ) s specfcally desgned to accommodate the early return to green problem for the coordnated phases. Even f the nput volumes are the same, actual sgnal tmngs may stll vary and the varaton s consstent wth feld results, snce all the dstrbutons are derved from feld data. For example, Fgure 2.5 categorzes the green start tmes of coordnated phase 2 at the ntersecton TH 55 & Boone Ave accordng to the assocated number of actuatons n 1,2. The data ponts are clearly dvded nto three groups, as dscussed before. One can see that, wthn each group, as the assocated number of actuatons n 1,2 ncreases, the green start tme of phase 2 tends to be later. Therefore, dfferent values of assocated number of vehcle actuatons wll lead to dfferent dstrbutons of green start tme. The two plots n Fgure 2.6 show the condtonal 5

13 dstrbutons when n 1,2 = 6 and n 1,2 = 9 respectvely. We can see that there are two dfferent dstrbuton patterns. When n 1,2 = 6, the green start tme are almost evenly dstrbuted among 36, 39 and 42 seconds; however, when n 1,2 = 9, 6% of the tme, phase 2 green would start at 42 seconds. Smlarly, condtonal dstrbutons can be generated for phase 6 and also for other ntersectons. Fgure 2.5: Phase 2 (Eastbound through) green start tme vs. assocated number of actuatons, TH 55 & Boone Ave, 6/15/29 ~ 6/26/29 1 weekdays. Probablty (%) Green start tme (Sec) Probablty (%) Green start tme (Sec) Fgure 2.6: Condtonal dstrbutons of Phase 2 (EB) green start tme PG ( 1,2 n 1,2), (Left) n 1,2 =6 (Rght) n 1,2 =9, TH 55 & Boone Ave, 6/15/29 ~ 6/26/29 1 weekdays. 2.2 Traffc Scenaros Based on the hgh-resoluton traffc sgnal data, traffc demands at the boundary of the arteral and turnng percentages at each ntersecton can also be obtaned. As shown n Fgure 2.7, nput volume of drecton d at ntersecton s denoted by N,d ( =1,2,..., I, d = Eastbound, Westbound, Northbound or Southbound) and correspondng turnng percentages are denoted by x ϕ,d ( x = Left, Rght, Through). Wthout loss of generalty, we assume the arteral s coordnated 6

14 n the east-west drecton. To deal wth the uncertanty of traffc demand, a set of traffc scenaros S = {1,2,..., J} s ntroduced. Each scenaro j S s a vector of boundary nput volumes N, N,..., ϕ, ϕ,... T, wth a probablty of ( j) ( j) L ( j) R ( j) and turnng percentages,.e. ( 1, EB 1, SB 1, EB 1, EB ) ( j) occurrence p. In general, the more scenaros we consder, the more robust the optmzaton results wll be. But that wll nevtably ncrease the complexty of the problem. Accordng to Mulvey et al. (1995), a relatvely small number of scenaros can stll generate near-optmal results. In practce, the number of scenaros consdered n the optmzaton model s constraned by the avalablty of dataset, avalable computatonal capablty and etc, so users can choose the most sutable number of scenaros accordngly. In ths project, 1 weekdays mornng peak (7: AM ~ 9: AM) data s utlzed and every 15 mnutes nterval s consdered as one traffc scenaro. In total, there are 8 scenaros. Wthn each scenaro j S, the boundary nput volumes ( j) x ( j) Nd, and turnng percentages ϕd, are assumed to be stable and the values are set as the averages over all cycles wthn the 15-mnute nterval. N 1,SB N 2,SB N I, SB N 1,EB ϕ x 1, EB ϕ x 1, SB x x ϕ I, SB ϕ 2, SB Inter. 1 Inter. 2 Inter. I ϕ ϕ x 1, WB x 2, EB ϕ x 2, WB... ϕ x I, EB ϕ x I, WB N I, WB ϕ x 1, NB ϕ x 2, NB ϕ x I, NB N 1,NB N 2,NB N I, NB Fgure 2.7: Boundary nput volumes and turnng percentages. Gven a scenaro j S, the cycle nput volumes for ntermedate lnks can be calculated by Equaton 2.2 and Equaton 2.3. It s easy to fnd out that eastbound cycle nput volume of ntersecton +1 s the summaton of volumes of three movements at ntersecton (eastbound through, southbound left and northbound rght), as shown n Equaton 2.2. Smlarly, westbound cycle nput volume of ntersecton -1 s calculated by Equaton 2.3. By applyng Equaton 2.2 and Equaton 2.3 to each ntersecton, the cycle volume of each movement becomes known. N + = N ϕ + N ϕ + N ϕ Equaton 2.2 N = N + N + N Equaton 2.3 ( j) ( j) T ( j) ( j) L ( j) ( j) R ( j) 1, EB, EB, EB, SB, SB, NB, NB ( j) ( j) T ( j) ( j) R ( j) ( j) L ( j) 1, WB, WB ϕ, WB, SB ϕ, SB, NB ϕ, NB 7

15 8

16 Chapter 3. Model Formulaton 3.1 Scenaro-Based Offset Optmzaton To account for the stochastc nature of feld traffc, a data-drven optmzaton model s developed n ths project to generate arteral offsets. As dscussed n the prevous secton, based on the hgh-resoluton traffc sgnal data, condtonal dstrbutons of green start tme P and traffc scenaros S can be derved, whch wll be the model nputs n ths project. In general, the optmzaton model can be represented by Equaton 3.1, where the objectve s to mnmze the total travel delay D of coordnated drectons. O s the vector of ntersecton offsets (decson varables) and Ω s the feasble set of O. mn DOPS (,, ) st.. O Ω Equaton 3.1 Gven a traffc scenaro j S, snce the cycle volume for each movement can be calculated, the assocated number of vehcle actuatons, denoted by n ( j) p,, can be generated for the coordnated phases of each ntersecton. Then, gven a feasble offset O Ω, the expectaton of travel delay for coordnated phase p under scenaro j, denoted by E(D ( j) p ( O )), can be calculated by Equaton 3.2. Note that, the condtonal dstrbuton of green start tme for the coordnated phase at ntersecton s assumed to be ndependent wth that at ntersecton +1. Ths assumpton s reasonable because the green start tme of coordnated phase at each ntersecton s determned by the correspondng vehcle actuatons of non-coordnated phases and t s reasonable to assume they are ndependent. E D O E D O E D O = 1 = 1 ( ( ) I 1 1 ) ( ) I j j ( ) ( ( j ) p = p, ( ) = p, ( )) I 1 = 1 x y ( j) ( j) (, + 1,, ) ( p, p, p, ) ( + 1, p + 1, p + 1, p ) = D o o x y P G = x n = n P G = y n = n Equaton 3.2 Here O represents the offset vector [o1, o2,...,o I ] and D(.) refers to the determnstc delay calculaton model between two adjacent ntersectons gven sgnal tmngs (.e. offsets and green start tmes for coordnated phases) and traffc scenaro, whch wll be ntroduced n the next secton. The best soluton for arteral coordnaton would optmze the performance of two major drectons at the same tme. However, n most cases, the two drectons cannot acheve optmalty smultaneously and there s always a trade-off between the two. In ths project, a weghtng term α [,1] s ntroduced to represent the mportance of the mnor coordnated drecton and the ( j) ( j) weghted delay for both drectons s calculated by Equaton 3.3, where Dp ( O)and Dp' ( O) are the travel delays for major and mnor coordnated drectons respectvely. 9

17 ( p ) α ( p' ) ( j ) ( j ) ( j D O α E D O E D ) O ( ) = (1 ) ( ) + ( ) Equaton 3.3 Gven an ntersecton offset settngo, we can calculate the correspondng arteral delay seres D (1) (O), D (2) (O),..., D ( J ) (O) for dfferent scenaros. Let D (1) (O), D (O),..., D (2) ( J ) (O) be the descendng order of the seres,.e., D ( (1) O ) D (O),..., D (2) ( J ) (O). Obvously, the larger the value of D s, the worse the arteral performance wll be. In practce, motorsts and engneers may have dfferent opnons about these scenaros and therefore a trmmng factor β [,1] s ntroduced. The value of β represents the fracton of scenaros that wll not be consdered and the number of scenaros left after trmmng s J = β J(1 β) + β. If β =, there s no trmmng ( J β = J ) and all the scenaros are consdered; However, f β =1, J β =1, only the worst scenaro D (1) ( O)wll be consdered. Therefore, the measure of arteral delay gven 1 J β ntersecton offset settngo can be formulated as D ( ( k ) O ) and D J β k =1 ( k ) ( O )s the k -th largest delay value. The general form of the scenaro-based offset optmzaton model s shown n Equaton 3.4 and the determnstc delay calculaton model wll be ntroduced n the next secton. Note that, under transformed tme coordnates (.e. shfted accordng to the free flow travel tme from the frst ntersecton), ntersecton offsets vary from c /2to c /2, where c s the common cycle length. J β 1 mn D( k )( O) J β k = 1 st.. O Ω, c c Ω= [ o1, o2,..., oi]: o, 2 2 Equaton Delay Calculaton In ths project, the delays caused by man street and sde street traffc are specfcally consdered n the delay calculaton model, as wll be descrbed n ths secton. Gven ntersecton sgnal tmngs (.e. offsets and green start tmes for coordnated phases) and traffc scenaro (.e. traffc demand for each approach), the calculaton of delays for coordnated drectons becomes a determnstc problem. Snce the red tme duratons of coordnated phases have drect assocaton wth the calculaton of travel delay for coordnated drectons, green start tmes G p, are frst converted nto red tme duratons r p,.n the delay calculaton model. The calculaton for one coordnated drecton s frst consdered snce the calculaton for the opposte drecton can follow the same way. In the followng, we take the eastbound (a coordnated drecton) as an example and for smplcty purpose the subscrpt p s omtted. At each ntersecton, cycle nput volumes to the downstream ntersecton can be separated nto two parts. One s dscharged from sde streets when coordnated phase s red, denoted by W s ; the 1

18 other s dscharged from man street when coordnated phase s green, denoted by W m. For example, for eastbound traffc, W s L R m s equal to N, SB ϕ, SB + N, NB ϕ, NB and W s equal to N ϕ. Assume vehcles are unformly arrved durng red and green perod of the T, EB, EB coordnated phase and they are evenly dstrbuted at downstream lanes, the arrval flow rate per lane to downstream ntersecton n these two perods can be calculated by Equaton 3.5, where q and q (veh/sec/lane) are the arrval flow rate per lane to downstream ntersecton formed by s m sde street traffc (durng the red tme of the coordnated phase) and man street traffc (durng the green tme of the coordnated phase) respectvely, and z s number of lanes at downstream lnk. s s q = W / r / z m m q = W /( c r)/ z Equaton 3.5 In the delay calculaton model, tme coordnate of each ntersecton s shfted accordng to the free flow travel tme from the frst ntersecton. Vehcle trajectory then becomes a vertcal lne n the tme-space dagram f there s no stop or delay (see Fgure 3.1 and Fgure 3.2 ). Assume the offset reference pont s the green end (or red start) of correspondng coordnated phase. Two varables d c and d g are ntroduced to represent the tme dfference of cycle starts and green starts between ntersecton and downstream ntersecton +1 under the transformed tme coordnates. The defnton s shown n Equaton 3.6, where o s the offset value and r s the red duraton tme of coordnated phase at ntersecton. Based on the sgn of d c, the delay calculaton process s dvded nto two cases. d = o o c + 1 d = o + r o r g Equaton 3.6 1) c d In ths case the upstream red lght for the coordnated phase starts earler than that of the downstream ntersecton (See Fgure 3.1). Dependng on the start tme of the downstream green lght, vehcles dscharged from upstream sde streets wth an arrval rate q s may cause a queue at the downstream ntersecton; After the upstream ntersecton turns green, downstream ntersecton wll have arrval vehcles from upstream coordnated phase wth a rate of q m. Under dfferent values of d g and arrval flows, ths porton of vehcles may or may not cause a queue at downstream. For example, f d g, as shown n Fgure 3.1, upstream green starts earler than downstream and part of the upstream man street flow wll defntely cause a queue at downstream; f d g <, downstream green starts earler than upstream, so the queue may be cleared before the arrval of upstream man street vehcles. If t q s used to represent the porton of green at ntersecton wthn whch dscharged vehcles wll cause a queue at downstream and 11

19 q d +1 (Veh/sec) s the dschargng rate of ntersecton +1, the followng flow conservaton equaton holds. ( r d) q + tq = ( t d ) q + Equaton 3.7 c s q m q g d 1 t q can be calculated by solvng Equaton 3.7. t q = when upstream man street flow does not cause a queue at downstream. Snce t q cannot be negatve, ( r d ) q + d q = c s g d q + 1 max, d m q+ 1 q t Equaton 3.8 The frst vehcle from coordnated phase of ntersecton whch has no delay at downstream wll have the trajectory of CC ' n Fgure 3.1. Note that h represents the jammed space headway n the fgure. The area of the shadowed trangle DEF dvded by h represents the total delay (Veh.Sec) of all the vehcles dscharged from coordnated phase of ntersecton n one cycle. The delay D can be calculated by Equaton 3.9. Note that the area of the trangle may be zero f the upstream man street traffc does not cause a queue at downstream. ( r d ) q d DE FG q D = Ar( DEF)/ h = = 2h 2 c s g m q + d q t + 1 ( ) Equaton 3.9 A' C' B' c o +1 r + 1 Intersecton +1 s q h D E G d q h + 1 m q h d c F o r d g t q Intersecton A c C B c g Fgure 3.1: Queung process between two ntersectons when d, d. 2) c d < 12

20 In ths case, upstream red of the coordnated phase starts later than the downstream ntersecton. Vehcles dscharged at the end of green of upstream ntersecton wll cause a resdual queue at downstream and the queung curve s shown as HJ n Fgure 3.2. After upstream coordnated phase turns red, vehcles from upstream sde streets wll keep ncreasng the downstream queue wth an arrval rate of q s. After upstream coordnated phase turns green, downstream ntersecton wll have arrval vehcles from upstream coordnated phase wth a rate of q m (Veh/sec). If d g, as shown n Fgure 3.2, upstream man street flow wll cause a queue at downstream; f d g <, upstream man street vehcles may or may not cause a queue at downstream dependng on the arrval flow rate. Accordng to flow conservaton, Equaton 3.1 holds. d q + rq + t q = ( t d ) q + Equaton 3.1 c m s q m q g d 1 t q can be derved from Equaton 3.1 and t q = when upstream man street flow does not cause a queue at downstream. Therefore, t q can be represented by d q + rq + d q = c m s g d q + 1 max, d m q+ 1 q t Equaton 3.11 The total delay of the man street traffc ncludes two parts, trapezum HIKJ and trangle DEF, as shown n the shadowed area n Fgure 3.2. HIKJ represents the delay caused by resdual vehcles dscharged at the end of green of upstream coordnated phase and DEF s the delay caused by new arrval man street traffc. Note that the area of DEF could be zero f downstream queue s cleared before upstream man street vehcles arrve. D = Ar( HIKJ )/ h + Ar( DEF)/ h rq + ( d q ) g c m c m 2 d d [ r+ 1+ ( r + d )] [ dq ] + [ dq ] / q = s c m g q m + d tq q 1 ( ) Equaton

21 A' C' B' r + 1 o +1 c Intersecton +1 m q H h J I K s q h D m q h E G q d + 1 h Intersecton d c r A d g t q F C B o c c g Fgure 3.2: Queung process between two ntersectons when d <, d. Based on the analyss above, the travel delay for coordnated phases between each two adjacent ntersectons can be calculated accordngly gven ntersecton sgnal tmngs and traffc scenaro. Therefore, the scenaro-based offset optmzaton model s complete by takng the determnstc delay calculaton model nto Equaton

22 Chapter 4. Soluton Method and Optmzaton Results Snce the feasble regon of ntersecton offsets,.e. Ω, s a closed convex set (see Equaton 3.4) and the objectve functon s contnuous and bounded wthn ths regon, an optmal soluton to the problem must exst. Due to the complexty of the objectve functon, Genetc Algorthm (GA) s adopted to solve the problem. GA s a soluton algorthm whch mmcs natural selecton process. Frst, a populaton of solutons (chromosomes) s generated accordng to a creaton rule, typcally, n a random fashon. And then, the algorthm modfes the populaton of ndvdual solutons repeatedly. At each step, dependng on chromosome ftness, the algorthm selects chromosomes at random from the current populaton to be parents and every two parent chromosomes wll produce two new offsprng chromosomes based on a cross-over rule. The process repeats tself untl certan stoppng crtera s met, at whch tme the best soluton remans n the populaton become the fnal solutono *. In ths project, 1 weekdays (6/15/29 ~ 6/26/29) mornng peak (7:AM ~ 9: AM) data of 6 ntersectons along the TH55 were chosen to generate the optmal offsets. In the GA solvng process, snce we can take the frst ntersecton as the master ntersecton wth an offset of, each chromosome would have the length of 5, where each gene ndcates the offset value of correspondng ntersecton. For the sake of smplcty, we take β =, whch means there s no trmmng ( J β = J ) and we consder all traffc scenaros. The weghtng term α s assgned a value.1, meanng that 1 percent of weght has been assgned to the performance of mnor drecton n our objectve functon. Usng a GA toolbox n Matlab wth followng parameters shown n Table 4.1, a soluton can be acheved after about 3 generatons for the offset optmzaton of the sx ntersectons on TH55. Table 4.1: Parameters for GA. Populaton Scalng Elte Crossove Crossover Mutaton Mutaton Sze Functon Count r Fracton Functon Functon Rate 4 Rank 2.8 Two pont Unform.1 Fgure 4.1 shows the GA results at each generaton, where the star * shows the mean functon value among all ndvduals at correspondng generaton and. represents the functon value of the best-ftted ndvdual. Fnally, the program generates the offset result {, -21.4, -21, -2.9, , -21.2} for sx ntersectons from Boone Ave. to TH1 respectvely, comparng wth the feld offset settng {, -24.9, -21.6, 4.6, -2.5, -11.9} under the transformed tme coordnates. The fnal optmzed offset values appled to controllers are {, 8, 25, 47, 79, 114} and ths offset settng generates a weghted total cycle delay of 34 (Veh.Sec), comparng wth 638 (Veh.Sec) under the feld offset settng. 15

23 1 9 Best ftness Mean ftness Ftness value Generaton Fgure 4.1: GA results for each generaton. Fgure 4.2 shows the coordnaton result for both feld and optmzed offset settng n the tmespace dagram under the transformed tme coordnates. The two fgures on the left hand sde show the feld coordnaton for both phase 2 and phase 6 and the two on the rght show the optmzed result. The arrows show the traffc drecton for correspondng phases. Snce orgnal feld offsets were already optmzed by Synchro (the metropoltan dstrct of Mnnesota Department of Transportaton retmes ts traffc sgnals on all major arterals every 36 months or less), the generated offset values are very smlar wth the feld ones. Major changes happen to Glenwood (4 th ntersecton) and TH1 (6 th ntersecton) wth a 25.5 and 9.3 seconds reducton respectvely. It s hard to drectly tell the dfference from the coordnaton fgure, but as we wll demonstrate n the next secton, the optmzed offset wll further mprove the performance of the coordnated phase (eastbound of TH55) and wthout deteroraton of the performance of the opposte drecton (westbound of TH55). 16

24 Fgure 4.2: Coordnaton result for both feld and optmzed offsets. 17

25 18

26 Chapter 5. Evaluaton Usng a Smulaton Model In order to verfy the performance of the offset results generated by the proposed model, a test network was bult n VISSIM, as shown n Fgure 5.1. Dfferent traffc scenaros generated from the feld data set were coded n the network, and sgnal controller s parameters, such as mnmum green, maxmum green and vehcle extenson, were all confgured accordng to the feld settngs. The smulaton model was well calbrated n order to reveal the real traffc condton n the feld. Fgure 5.2 compares the dstrbuton of coordnated green start tme between smulaton and feld. The red columns represent the real dstrbuton from the feld whle the blue columns show the smulaton results. As one can see, smulaton results match wth feld results very well at each ntersecton. Fgure 5.1: VISSIM network for test corrdor. Probablty (%) Boone EB Local cycle second Probablty (%) Boone WB real data smulaton result Local cycle second Probablty (%) Wnnetka EB Local cycle second Probablty (%) Wnnetka WB Local cycle second 19

27 Probablty (%) Rhode EB Local cycle second Probablty (%) Rhode WB Local cycle second Probablty (%) Glenwood EB Local cycle second Probablty (%) Glenwood WB Local cycle second Probablty (%) Douglas EB Local cycle second Probablty (%) Douglas WB Local cycle second Probablty (%) TH1 EB Local cycle second Probablty (%) TH1 WB Local cycle second Fgure 5.2: Comparson of dstrbuton of coordnated green start between smulaton model and the feld. The smulaton was run for 2 tmes usng 2 dfferent random seeds. In order to compare the performance, both the offset settng n the feld and the one generated by the optmzaton model were tested n the VISSIM network and we output the average delay of vehcles traversng both eastbound and westbound. The result s shown n Fgure 5.3 and Table 5.1. As we can see, the 2

28 optmzed offset result dd mprove the performance of east bound traffc,.e. reduce travel delay by 13.9% on average. And at the same tme, t dd not make the westbound traffc worse. In order to test the statstc sgnfcance of ths mprovement of eastbound, a pared t-test has been done to the two sets of travel tmes,.e. under orgnal offsets and under optmzed offsets. The null hypothess s that the two data sets come from dstrbutons wth the equal means. It turns out that we can reject the hypothess wth a p value E-17 at the 5% sgnfcance level, whch means the travel delay mprovement s sgnfcant. Delay (Sec) Eastbound Smulaton Runs Optmzed offset Orgnal offset Delay (Sec) Westbound Smulaton Runs Optmzed offset Orgnal Offset Fgure 5.3: Smulaton result of travel delay based on dfferent offset settngs. Table 5.1: Eastbound and Westbound average delay comparson. Eastbound Average Delay (Sec) Westbound Average Delay (Sec) Orgnal Offset Optmzed Offset Change % % 21

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30 Chapter 6. Feld Evaluaton The optmzed offset values were mplemented to the 6 ntersectons n the feld for mornng peak hours (7:AM~9:AM) on 9/14/29. In order to compare the performance measures before and after the feld mplementaton, two days wth smlar volume nputs need to be chosen. After examnng 1 days before and after, 9/3/29 was selected as the baselne day wth orgnal offset settng to compare wth 9/14/29. Table 6.1 shows the comparson of Eastbound and Westbound (major drecton) nput volume durng two hours peak perod and Table 6.2 shows the comparson for sde street nput volumes. As we can see, the two major drectons nput volumes for the two days are very smlar and the day wth optmzed offset (9/14/29) carres a lttle hgher traffc. For sde streets, these dfferences of nput volumes are also wthn acceptable ranges. Table 6.1: Eastbound and Westbound nput volume (7:AM~9:AM) comparson between 9/3/29 and 9/14/29. Eastbound Input Volume Westbound Input Volume 9/3/29 (Orgnal offset) 9/14/29 (Optmzed offset) % % Change Percentage Table 6.2: Sde street nput volume (7:AM~9:AM) comparson between 9/3/29 and 9/14/29. Boone Wnnetka Rhode Glenwood Douglas TH 1 9/3/29 (Orgnal offset) 9/14/29 (Optmzed offset) Change Percentage Southbound % Northbound % Southbound % Northbound % Southbound % Northbound -* - - Southbound Northbound % Southbound % Northbound % Southbound % Northbound % *: T ntersecton, not applcable 23

31 Based on the hgh resoluton data collected by the SMART-Sgnal system, ntersecton queue length for each cycle at each of the ntersectons were estmated usng the algorthm developed by Lu, et al. (29). In order to compare the performance of the 6-ntersecton corrdor before and after the mplementaton of the optmzed offsets, arteral travel tmes for both drectons were also calculated as part of the SMART-Sgnal system based on the vrtual probe algorthm developed by Lu and Ma (29). Note the queue length estmaton algorthm and the arteral travel tme estmaton algorthms mplemented as part of the SMART-Sgnal system has been tested and evaluated n the past and t s currently n operaton on a number of ntersectons n Mnnesota and Calforna (for more nformaton on the SMART-Sgnal mplementaton, please see dotapp4.dot.state.mn.us/smartsgnal). Snce we only have 6 ntersectons, performance n between s what we are nterested n. Therefore, travel tme between stop lne of Boone and stop lne of TH1 s taken as an ndcator of corrdor performance. Table 6.3 compares the calculated travel delays of both eastbound (from stop lne of Boone to stop lne of TH1) and westbound (from stop lne of TH1 to stop lne of Boone) based on dfferent offset settngs. As we can see, both eastbound and westbound travel delays are substantally reduced after the offset adjustment. On average, the eastbound travel delay wth orgnal offset (9/3/29) s seconds and t decreases to 1.14 seconds after optmzaton (9/14/29), whch s a 15.3% reducton. For westbound, average travel delay wth orgnal offset s seconds and t decreases to 7.84 seconds after optmzaton, whch ndcates a 9.7% reducton. Consderng that the orgnal offset settng was already optmzed, the mprovement s sgnfcant. One may notce that the absolute values of eastbound and westbound average delays are dfferent wth the values from smulaton as lsted n Table 5.1, because the actual demand and actuaton profles n the feld cannot be the same wth the ones n smulaton. Fgure 6.1 also compares the estmated eastbound queue length profles durng the one hour perod at ntersectons 4 and 6 (where the major changes to offset happen) under dfferent offset settngs. One can fnd out that, n general, the optmzed offset generates shorter queue lengths than the orgnal offset. Therefore, the optmzed offset outperforms the orgnal offset not only n smulaton but also n realstc feld mplementaton. Table 6.3: Eastbound and Westbound average delay comparson between 9/3/29 and 9/14/29. Eastbound Average Delay (Sec) Westbound Average Delay (Sec) 9/3/29 (Orgnal) 9/14/29 (Optmzed) Change Percentage % % 24

32 Queue Length (ft) Intersecton 4 EB Orgnal offset Optmzed offset :22:5 7:29:17 7:36:29 7:43:41 7:5:53 7:58:5 8:5:17 Tme Queue Length (ft) 5 Intersecton 6 EB Orgnal offset 4 Optmzed offset :19:12 7:26:24 7:33:36 7:4:48 7:48: 7:55:12 8:2:24 8:9:36 8:16:48 Tme Fgure 6.1: Estmated EB queue length based on dfferent offset settngs. 25

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34 Chapter 7. Conclusons and Future Research In ths project, we propose an nnovatve approach for arteral offset optmzaton based on the large amount of hgh-resoluton feld traffc data. The model solves the two well-known problems wth actuated sgnals: (1) the early return to green problem for coordnated phases and (2) the uncertanty problem of queue szes formed at ntersectons. To account for the two problems, we ntroduce the concepts of condtonal dstrbuton of the green start tmes and traffc demand scenaros, both of whch can be obtaned from the hgh-resoluton traffc dataset. We explctly consder the queues formed by sde-street and man-street traffc under dfferent stuatons. The objectve of ths model s to mnmze total delay for one coordnated drecton and at the same tme take the performance of the other drecton nto consderaton. Because of the complexty of the objectve functon, the problem s solved by the Genetc Algorthm. We mplemented our optmzed offset values to both VISSIM smulaton model and the feld sgnal controllers. Both test results ndcate that the model successfully optmzes the offsets along the sgnalzed arterals. It mproves the performance of the corrdor sgnfcantly. Lookng forward, we envson that our optmzaton program can be utlzed perodcally (for example, every a few weeks) to optmze system performance usng the archved data durng that perod. In the state-of-the-art practce, for most of the traffc management agences, sgnal retmng s only conducted once every 3 to 5 years because t nvolves largely manual processes. But t s commonly understood that traffc delay ncreases 3-5% per year smply due to the fact that the tmng plans are not kept up to date. For many resource-lmted agences, t would be desrable to replace the labor-ntensve sgnal re-tmng process wth algorthms for automated or sem-automated updatng of the sgnal parameter settngs. The avalablty of the massve amount of hgh-resoluton traffc sgnal data has made ths possble. Although our offset optmzaton s movng one step further along ths drecton, t should be extended to nclude other sgnal control parameters such as green splts. We leave these topcs for future studes. 27