Iterative Tuning Strategy for Setting Phase Splits in Traffic Signal Control

Transcription

1 24 IEEE 7th Internatonal Conference on Intellgent Transportaton Systems (ITSC) October 8-, 24. Qngdao, Chna Iteratve Tunng Strategy for Settng Phase Splts n Traffc Sgnal Control Yu Wang, Danwe Wang, Nan Xao, Ytong L and Emlo Frazzol Abstract Ths paper ntroduces Iteratve Tunng (IT) strategy for urban traffc sgnal control. Ths strategy s motvated by people s daly repettve travel patterns between homes and workng places. Statstcal analyss of a real traffc network shows that traffc flows of junctons are repettve wth small varatons on a weekly bass. The man dea of IT s that, daly traffc sgnal schedules are tuned wth antcpaton of traffc demands. In ths paper, only phase splt s tuned teratvely to balance the traffc demands from all drectons n a juncton. Each juncton has ts own controller and these controllers can work cooperatvely to mprove the network performance after several teratons. Therefore IT strategy s scalable for arbtrary large urban networks. Marna Bay and Clement areas n Sngapore based on real traffc data are smulated and smulaton results show that IT strategy can mprove the performance consderably comparng wth fxed-tme strategy. I. INTRODUCTION Traffc sgnal control strateges have gone through varous development from fxed-tme to adaptve strateges, from sngle juncton to coordnated mult-junctons. The fxed-tme algorthm was developed by Webster [] to optmze splts and cycle length wth delay estmated model. MAXBAND, developed by Lttle [2], consders the synchronzaton of traffc sgnals so that a car, startng at a man artery and travelng wth free speed, can go through several junctons wthout stop for a red lght. TRANSYT (TRAffc Network StudY Tool), developed by Robertson [3], s the most well-known and frequently appled fxed-tme traffc sgnal strategy. It s the benchmark to test the performance mproved by adaptve traffc-responsve strateges. SCATS and SCOOT are the most popular adaptve coordnated traffc strateges. SCATS (Sydney Coordnated Adaptve Traffc System) [4], s a model-free dstrbuted strateges wth predefned sgnal plans. SCOOT (Splt Cycle Offset Optmsaton Technque) [5], s almost lke adaptve TRANSYT strategy wth three knds of optmzer: Splt Optmzer, Offset Optmzer and Cycle length Optmzer. OPAC (Optmzed Polces for Adaptve Control) [6] strategy s a real-tme dstrbuted sgnal optmzaton algorthm wth three control layers to optmze cycle, splt, offset and phase sequences. RHODES (Real-tme Herarchcal Optmzng Dstrbuted Effectve System) s an adaptve traffc control Y. Wang and D. Wang s wth EXQUISITUS Centre for E- Cty, School of Electrcal and Electronc Engneerng, Nanyang Technologcal Unversty, Sngapore wang676@e.ntu.edu.sg; edwwang@ntu.edu.sg N. Xao and Y. L are wth the Sngapore-MIT Allance for Research and Technology Centre, Sngapore 3862, Sngapore xaonan@smart.mt.edu; ytong@smart.mt.edu E. Frazzol s wth the Massachusetts Insttute of Technology, Cambrdge MA 239, USA FRAZZOLI@mt.edu systems developed by P. Mrchandan et al [7] by usng conservaton model to predct traffc dynamcs. Dynamc programmng s employed for OPAC and RHODES to make them not real-tme feasble for large-scale traffc networks. Back Pressure (BP) was proposed [8] n traffc sgnal control and t leads to maxmum network throughput wth global optmalty. Pressure releasng polcy [9] extended t wth fnte queue capactes. Store-and-forward model of traffc dynamcs was frst suggested by Gazs and Potts [], and extended by Dynamcs Systems and Smulaton Laboratory (DSSL) []. Optmzaton process s carred out wth lnear quadratc regulator (LQR) based on lnear traffc model. After that, de Olvera [2] reported that consderable mprovements mght be made by replacng LQR procedures wth Centralzed Model Predctve Control (CMPC) snce MPC takes constrants of phases and lnks maxmum volumes nto account. Facng large-scale dynamc systems, Lucas Barcelos et al. [3] proposed mult-agent model predctve control to decompose a centralzed model predctve control system nto decoupled subsystems. However n the analytc model, the topology of network, lke turnng ratos, s assumed to be constant, whch s not correct n realty. As tme spreadng, analytc model wll accumulate errors whch leads to suboptmal traffc sgnal settngs. Wang et al. [4] proposed FRIDE to descrbe traffc dynamcs to mprove the accuracy of shortterm predcton. In ths paper, Iteratve Tunng (IT) strategy s motvated by repettve actvtes on workng days. In urban traffc control system, people travel from homes to workspaces n the mornng and return n the evenng on workng days. Festn [5] studed the general daly traffc profles n the Unted States and fve areas for the perod Results show that daly traffc profles are repettve on a weekly bass. Roess et al. [6] showed that typcal varatons of daly traffc patterns were around 3% and 6% on weekdays and weekends, respectvely. IT strategy s adapted from Iteratve Learnng Control (ILC). ILC approach had been appled for densty control of freeway traffc flow and acheved robust performance [7]. Huang [8] proposed an teratve learnng approach for sgnal control n urban traffc networks. It uses traffc assgnment model to fnd the global optmal sgnal control and flow patterns. In control process, traffc sgnal s controlled to drve the traffc pattern approachng the desred flow pattern. Ths paper proposes IT strategy to tune phase splts based on repettve traffc flows. Dfferent from tradtonal ILC theory, there s no desred trajectory snce t s dffcult to /4/$3. 24 IEEE 2453

2 fnd the accurate traffc flow patterns based on any analytc model. The rest of ths paper s organzed as follows: Secton II shows that hstorcal traffc flow patterns are repettve. Secton III descrbes objectves and tunng processes of IT strategy. Secton IV presents two case studes and ther smulatons. Secton V analyzes the smulaton results. Secton VI concludes ths paper and suggests some topcs for further research. II. REPETITIVE TRAFFIC FLOW PATTERNS For urban traffc system, the most frequently used methodology to descrbe sgnalzed junctons n Unted States s ntroduced n Hghway Capacty Manual(HCM) [9]. Before IT strategy s ntroduced, conceptual frameworks concernng hstorcal traffc flows and IT strategy are summarzed. ) Daly Traffc Pattern (DTP): DTP s the profle of traffc flows along 24 hours a day. From the analyss of Chrobok et al. [2], DTPs of workng days are qute smlar snce actvtes are almost the same except workng days before holdays or weekends, n partcular the afternoon s traffc flows may dffer. Therefore, workng days are categorzed nto two classes: Normal Workng Days: workng days except days before holdays. Last Workng Days: workng days before holdays. 2) Daly Traffc Sgnal Schedules (DTSS): DTSS are phase duratons for a juncton from : to 24 :. For a juncton, f DTPs of phases are repettve, traffc demands n all phases are repettve and repettve phase duratons can be appled. Therefore, DTSS wll be dentcal for the dates wth repettve DTPs of phases. The bass for IT strategy s the repeatablty of DTP. There s an assumpton made here: urban nfrastructures nclude road, resdences, workplaces etc, changes slowly. To verfy ths assumpton, hstorcal traffc data of Marna Bay Area, located at Central Busness Dstrct n Sngapore, are analyzed. Fg. shows the network dagram. approachng one juncton that have the same green phase. For every day, there exsts one set of traffc flows x w j, (τ), where w s the ndex of workng days; and ω W where W s the set of workng days. Mean M n Eq. (), Standard Devaton S n Eq. (2) and Coeffcent of Varaton V n Eq. (3) are utlzed to analyze the varatons. M = n w S = ω W n w x w j, (τ) () ( x w j, (τ) M ) 2 ω W V = S (3) M where n w s number of workng days. In statstc, Coeffcent of varaton(cv) expressed n percentage, shows the extent of varablty relatve to mean value. If CV of traffc flows wthn certan tme nterval s very small, traffc flows are almost the same and DTP s repettve. In ths paper, CV s used to ndcate the repetton of DTPs for every tme nterval. There are 4 junctons ncluded and Juncton 2, 5 and 9 are elmnated due to most data errors of loop counts. Daly traffc patterns of class of Normal Workng Days for other junctons are analyzed. Tme nterval T s 5 mnutes. Shown n Fg. 2, dfferent junctons have dfferent daly traffc patterns. A day s categorzed nto Lght Traffc Perod (: to 7:) and Heavy Traffc Perod (7: to 24:). Traffc sgnal control system manly focuses on Heavy Traffc Perod. As ndcated n Fg. 3, CVs of junctons are lower than 5% durng Heavy Traffc Perod. Means Normal Workng Days (T = 5 mnutes) Tme (h) Coeffcents of Varatons Normal Workng Days (T = 5 mnutes) Tme (h) (2) Mean values for Junc- Fg. 2. tons Fg. 3. Coeffcents of varatons for Junctons Fg.. Marna Bay Area n Sngapore For juncton j and j J, where J s the set of junctons n the network, traffc flows x j, (τ) are collected, where s the ndex of lane groups; τ s the ndex of tme ntervals. Referrng to [6], lane group s defned for one or more lanes III. ITERATIVE TUNING STRATEGY FOR PHASE SPLITS In IT strategy, daly traffc sgnal schedules are obtaned based on daly traffc patterns correspondngly. Each class of daly traffc patterns has ts own daly traffc sgnal schedules. IT strategy has the followng features: It requres lttle system knowledge and analytc model of system s not requred. Therefore errors from model descrptons are not crtcal. It s an off-lne tunng methodology and thus the onlne computaton tme s not an ssue. Repettve dsturbances can be rejected and repettve errors can be compensated. It adapts to the changes of traffc patterns teratvely. The flow chart of IT strategy s shown n Fg

3 Fg. 4. A. Data Analyss and Processng Flow Chart of Iteratve Tunng Strategy For each juncton, hstorcal traffc flow patterns X h of the entre day are memorzed. For juncton j J, x j, (k) X, F j s collected durng the entre day, where X represents new-collected traffc flows; F j s the set of lane groups of juncton j; where k s the ndex of cycles. If there s a specal event on one day, traffc flows may be dfferent. Therefore, Pattern Checkng Algorthm s presented to check whether new-collected traffc flows X are repettve wth any class of hstorcal traffc flow patterns X h or not. ) Pattern Checkng Algorthm: Pearson product-moment correlaton coeffcent γ s calculated to measure the lnear correlaton between X and X h. γ th s set as the threshold Pearson coeffcent. If γ γ th, traffc patterns X are repettve wth hstorcal traffc flow patterns X h. If γ < γ th, traffc patterns X are non-repettve. 2) Pattern Updatng Algorthm: For both classes of workng days, hstorcal traffc flows are updated n Eq. (4) to adapt to the slowly changng traffc condtons. { αxh +βx, f γ γ th ; X h = X h, f γ < γ th (4). where α andβ are weghtng coeffcents and satsfy α+β =, whch control the updatng speed and do not affect the performance of IT strategy. The updated traffc flows X h are stored n the database to be hstorcal traffc flow patterns X h, whch are also the nputs of IT strategy. B. Iteratve Tunng Based on HCM 2 methodology [9], the least delay tme for a sngle juncton s obtaned when phase occupances are balanced. The objectve of IT strategy s to mnmze the delay tme. IT strategy s a decentralzed methodology and each juncton has ts own IT controller. The controllers tune phase splts teratvely untl phase occupances are balanced. Least delay tme for every juncton s mnmzed, and delay tme of network s reduced. For juncton j J, based on updated traffc flows X h, traffc flows X j (k) for all lane groups are retreved. For a phase p P j wth phase duraton u j,p (k), where P j s the set of phases of juncton j, there are one or more correspondng lane groups x j, (k) havng the rght of way, where x j, (k) X j (k) wth F j,p, and F j,p s the set of lane groups of juncton j whch have the rght of way durng phase p. Maxmum phase occupancy o j,p (k) s calculated as the maxmum rato of traffc flows per lane xj,(k) and road n lg capactes su j,p (k), whch s expressed n Eq. (5), o j,p (k) = { xj,(k) max Fj,p n lg su j,p (k) }, p P j, j J, k (5) where n lg s number of lanes n the lane group ; s s the saturaton flow per lane and t s assumed to be fxed. After that, phase occupancyo j,p (k) s converted nto phase occupancy error e j,p (k) n Eq. (6). As n Eq. (7), f e j,p (k) E j (k), p P j approaches, phase occupances for ths juncton are balanced and delay tme s almost mnmzed. E j (k) s the vector to represent phase occupancy errors of juncton j. p P e j,p (k) = o j,p (k) j o j,p (k) n p (6) e j,p (k), p P j, j J, k (7) where n p s the number of phases for the juncton. AssumngE j (k) s obtaned by Eq. (5) and Eq. (6). hstorcal sgnal duraton U j,h (k) s retreved from the database of traffc sgnal schedules U h. The tunng procedure for phase splts s constructed below n Eq. (8): Û j (k) = U j,h (k)+le j (k +) } U j (k) = C{Ûj (k), j J, k where L s defned as the tunng functon and L = λi; I s the dentty matrx wth approprate dmenson; λ can be determned by tral-and-error method, whch may not affect the performance; C{} s the functon to take constrants nto account. For phase u j,p (k) = C{û j,p (k)}, wth u j,p (k) U j (k), p P j, constrants are consdered. As shown n Eq. (9), functon C{} takes phase constrants nto consderaton. For the concern of safety, maxmum phase tme u max and mnmum phase tmeu mn for each phase are predefned. (8) u mn < u j,p (k) < u max, p P j, j J, k (9) Equaton Eq. (9) can be realzed by: û j,p (k), f u mn < û j,p (k) < u max ; C{û j,p (k)} = u max, f û j,p (k) u max ; u mn, f û j,p (k) u mn. () Functon C{} also consders the constrant of cycle length n Eq. (). u j,p (k)+t L = C, j J, k () p P j 2455

4 Where C s the cycle length; t L s the total lost tme wthn a cycle. Ths constrant n equaton Eq. () s satsfed by C{û j,p (k)} = û j,p (k) p P j û j,p (k) (C t L) (2) Equatons Eq. () and Eq. (2) are calculated alternately untl the constrants Eq. (9) and Eq. () are satsfed smultaneously. Besdes, phase duratons are set to be accurate to the resoluton of controllers. As phase duratons U j (k) U, j J, k are obtaned fnally, where U s the vector of phase duratons for the entre day, they wll be appled for the next date wth repettve traffc flows, whch s stored n the database as traffc sgnal schedules U h. IV. CASE STUDIES In ths secton, two case studes are ntroduced. Real traffc flows are smulated based on average values of one month s raw data. A. Smulaton Platforms Vssm [2], a mcroscopc smulator (Developed by PTV Planung Transport Verkehr AG n Karlsruhe, Germany), s used to construct traffc dynamcs. In order to program traffc control algorthms easly and effcently, Vssm s cosmulated wth Matlab by COM Interface [22]. Matlab s the man software to collect traffc flows step by step, and to recall control algorthms based on the current states. After tme settngs for the next cycle are evaluated, they are sent back to Vssm smultaneously. The smulaton results are logged n Excel fles by Vssm. Two cases are setup n Vssm, ) Case I: Marna Bay Area (MBA) s a closed road network locatng n Central Busness Dstrct (CBD) of Sngapore (Fg. ). There are 4 junctons n total and 2-4 phases specfed for each juncton. The smulatng perod s one hour from 8 : am to 9 : am, snce traffc flows durng ths perod are largest durng a day. In ths case, the vehcle nputs are dentcal and varatons of traffc flows are not consdered. 2) Case II: Clement s a open road network, whch has qute large traffc demands. There are only 5 junctons n Clement and one arteral road consdered (Fg. 5). The smulatng perod s 5 hours from 7 : am to : pm, whch ncludes most of heavy traffc perod. Fg. 5. Clement n Sngapore In ths case, varatons of traffc flows are consdered to verfy the robustness of IT strategy. There are scenaros wth varaton of around 5% smulated one by one sequentally. B. Crtera of Comparson For these two cases, fxed-tme algorthm, SCATS-lke strategy, and IT strategy are appled for comparsons. Fxedtme algorthm s obtaned based on Webster algorthm [], whch s also the ntal settngs of IT strategy. SCATS s used n Sngapore, but not released n publc. A so-called SCATS-lke algorthm s used here [23]. Crtera of Comparson n ths paper nclude Total Number of Vehcle (TNV) and Average Delay Tme (ADT). Delay tme s the subtracton between total travel tme of all vehcles and total free-flow travel tme (travel tme when vehcles are runnng n free-flow speed). TVN stands for the total number of vehcles whch have left the network. ADT means the delay tme per vehcle. C. Orgn-Destnaton Pars Orgn-Destnaton (OD) pars [24] are manly desgned to construct traffc flows close to the real stuatons on workng days snce every vehcle has ts own orgn and destnaton. In smulaton areas, orgn and destnaton ponts are located at the margns and parkng lots nsde the networks. LSQR s carred out to fnd OD matrces wth the objectve that estmated traffc flows X are close to real data X. Root Mean Square Error (RMSE) n Eq. (3) s calculated to quantfy the total percentage error of OD estmate. In Vssm, fles.weg and.bew store the paths, volumes and costs between orgns and destnatons, whch are created under fxed-tme algorthm. These fles guarantee that traffc condtons are completely dentcal for all algorthms. RMSE = NM NM τ (x (τ) x (τ)) 2 τ x (τ) % (3) where s the ndex of lane groups, τ s the ndex of tme ntervals; N s total number of lane groups; M s total number of tme ntervals. ) Case I: In MBA, there are 3 orgns and 2 destnatons ncluded. Tme nterval s set to be mnutes. OD matrces are estmated based on average traffc flows wthn month s workng days. RM SE of OD estmaton s 7.83%. 2) Case II: In clement, n order to estmate traffc flows more accuracy, each pont gong n or out of the network are modeled as orgn or destnaton. Therefore 4 orgns and 5 destnatons are ncluded. RM SE of OD estmaton s 5.38%. The same to the procedures of Case I, ntal OD matrces OD are obtaned. Then ten sets of OD matrces OD v wth varatons are calculated n Eq. (4). For each tme nterval, OD v (τ) = ϕ OD(τ) rand+od(τ) (4) where ϕ s the amplfer factor; rand s matrx of random number wth proper dmenson, and each tem n rand [,]; s nner product. 2456

5 V. SIMULATION RESULTS In ths secton, smulaton results are summarzed. Some parameters are descrbed frst. As descrbed n Eq. (4), α and β are set to be.8 and.2, respectvely. Total Phase Dfference θ, as shown n Eq. (5), s used to ndcate the convergence of phase tme for every teraton. θ = u j,p (k) u j,p,h (k) (5) k j J p P j where u j,p,h (k) s hstorcal phase duraton. Average delay tme reducton I ADT for the whole network s calculated as Eq. (6): I ADT = ADT FT ADT ADT FT %; (6) where ADT FT s the ADT under fxed-tme strategy; ADT s ADT under all strateges. A. Case I Iteratve tunng (IT) s appled n the smulatons. For each teraton, one set of OD matrces are smulated and traffc dynamcs are completely dentcal. In the frst teraton, hstorcal phase tme U h and hstorcal traffc flows X h are obtaned from fxed-tme strategy. Based on Eq. (8), phase tme U s tuned teratvely. In the frst few teratons, θ s gong up snce traffc flow are tuned. When traffc flows are tuned well, θ s approachng gradually (Fg. 6), whch ndcates tuned phase tmes wll approach steady states gradually. Total Phase Dfference (s) Fg. 6. Total Phase Dfference Average Delay Tme (s/veh) Fg. 7. Average Delay Tme As smulatons are carred on teratvely, average delay tme decreases untl steady states. The delay tme versus number of teratons are shown n Fg. 7. The red lne n the graphs ndcates that fnal steady state of ADT s 5.29 seconds. The trajectores show that after around 3 teratons, the delay tme s reduced to the optmum pont and goes to steady states after 6 teratons. Smulaton results under fxed-tme Strategy, SCATS-lke and IT are summarzed n Table I. At the end of smulaton, there s no traffc congeston, TNV under all strateges are smlar. From data of ADT, IT strategy can obtan much better performance over other strateges. Comparng wth SCATS, IT strategy can outperform n average delay tme reducton by 7.34%. From traffc raw data analyss, juncton 6 s crtcal juncton n Marna Bay Area. Traffc congeston s formed around TABLE I PERFORMANCE OF CASE I Algorthm TNV (veh) ADT (s/veh) Fxed-Tme SCATS-lke (5.59%) IT (22.93%) Juncton 6 due to hgh traffc demands. Maxmum queue lengths wthn a cycle and correspondng phase duratons are depcted n Fg. 8 for juncton 6, respectvely. The horzontal axs represents the number of cycles. In one hour smulaton, there are 45 cycles n total. For juncton 6 (Fg. 8), under fxed-tme strategy queue s accumulated from 25 th cycle to 35 th cycle durng Phase I. Correspondngly under IT strategy, more green tme s allocated to Phase I and queue s rapdly dscharged. Meanwhle, the green tme of Phase III s reduced and a small queue s formed. The comparson shows that IT strategy tunes phase splts based on prevalng traffc demands. Queue length and queue accumulatng perod are largely reduced. Tme Duratons Queue Length (m) Juncton 6 under Fxed tme Strategy 6 Phase I Phase II 4 Phase III Juncton 6 under Fxed tme Strategy B. Case II Queue of Phase I Queue of Phase II Queue of Phase III Tme Duratons Queue Length (m) Juncton 6 under IT strategy Phase I Phase II Phase III Juncton 6 under IT Strategy Queue of Phase I Queue of Phase II Queue of Phase III Fg. 8. Comparsons of Juncton 6 In the smulaton of Clement, varatons of traffc flows are consdered. There are scenaros desgned for smulatons. Under fxed-tme strategy, average coeffcent of varaton of traffc flows s 8.3%. Iteratve Tunng strategy s appled to these scenaros one by one sequentally. Total phase dfference s shown n Fg. 9. In the frst teraton, traffc sgnal schedules and traffc flows are obtaned from fxed-tme strategy and average hstorcal data, respectvely. In total there are 2 teratons and 2 batches of teratons for these ten scenaros. Lke the results n Case I, θ s gong up and falls down wth small oscllatons eventually. Meanwhle, as shown n Fg., average delay tme s reduced gradually untl steady states. Ten scenaros n the last batch of teratons under IT strategy are compared wth fxed-tme strategy (Fg. ). For all scenaros, IT strategy outperforms fxed-tme consderably. For most of scenaros, delay tmes under IT strategy are also lower than that under SCATS-lke strategy. 2457

6 Total Phase Dfference (s) Fg. 9. Total Phase Dfference Average Delay Tme (s/veh) Average Delay Tme (s/veh) Fg Ten Scenaros Fg.. Comparsons Performance of Case III Fxed Tme SCATS lke IT Average delay tme for all strateges are summarzed n Table II. Snce after pm, traffc demand s qute small and there s no congeston everywhere, TNV s very smlar. Durng entre smulaton perod, IT strategy can reduce the delay tme by 8.38%. Due to varatons of traffc flows, IT strategy can not response to the dsturbances and the performance s affected slghtly. However, the performance s stll better than that of SCATS by around 3.26%, whch proves that IT strategy can work very well on workng days. TABLE II PERFORMANCE OF CASE II Algorthm TNV (veh) ADT (s/veh) Fxed-Tme SCATS-lke (5.2%) IT (8.38%) VI. CONCLUSIONS Ths paper ntroduces Iteratve Tunng (IT) strategy wth phase splts by usng hstorcal traffc flows. The analyss of hstorcal raw data shows that traffc flow patterns on weekdays are repettve on a weekly bass wth small varatons. Wth antcpaton of traffc flows, IT controllers of all junctons tune daly traffc sgnal schedules teratvely to reduce delay tme of traffc network. The smulaton results of Marna Bay Area show that IT strategy can reduce the delay tme of the network consderably. Although IT strategy can not response to the non-repettve dsturbances, from the smulatons of Clement wth non-repettve dsturbances, t stll works well for workng days as varatons of traffc flows are qute small. The future work wll focus on Iteratve Tunng Strategy wth cycle tme, offset and splts, whch can work cooperatvely to approach the sutable traffc sgnal schedules. ACKNOWLEDGEMENT The work s supported by the Sngapore-MIT Allance for Research and Technology (SMART) Center for Future Urban Moblty (FM). REFERENCES [] F. V. 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