Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 Queue Length Estmaton Algorthm or Sgnalzed Intersecton Usng Sectonal Travel Tme Inormaton Mnhyoung LEE Ph.D. Student Dept. o Transportaton Engneerng Unversty o Seoul 90, Jeonnong-dong, Dongdaemun-gu, Seoul 130-743 Korea Fax: +8--6490-5646 E-mal: mn63954@gmal.com Youngchan KIM Proessor Dept. o Transportaton Engneerng Unversty o Seoul 90, Jeonnong-dong, Dongdaemun-gu, Seoul 130-743 Korea Fax: +8--6490-81 E-mal: yckmm@uos.ac.kr Abstract: The purpose o ths research s to develop algorthm calculatng the trac queue length whch s man varable or eectve operaton at sgnalzed ntersecton. For the methods to calculate the trac queue length, there are queue theory and shock wave theory. And, the estmaton o trac queue length by exstng pont detecton system utlzes trac queue theory calculatng trac queue length through the number o vehcles, ths algorthm ntended to estmate more accurate length o trac queue by calculatng the length o physcal trac queue through the shock wave theory. For the stream o algorthm, the normaton o ndvdual vehcle's travel tme s gathered by ground detector n upstream detector and downstream detector, the coordnate o ndvdual vehcle on the workng drawng s estmated and the speed o shock wave creatng trac queue through the value o coordnate estmated or one cycle s calculated. The sutablty o algorthm s evaluated by Smulaton. Key Words: Queue length, Trac Flow Model, Shock wave Theory, ITS 1. INTRODUCTION The total populaton o South Korea, exceeded 50 mllon as o June 01. Socal stablty and envronmental changes ncreased the trac demand. The total length o roads across the country has acheved 105,931Km as o December 011. however, extenson o road per 1,000 populaton are stll.1km despte contnued nvestments n the road. In 01, socal overhead captal(soc), the government's budget accounted or 7% o the total budget, but declned 5.5% year-on-year. and Prorty or road-buldng socal overhead captal (SOC) s to decrease as compared to the nancal nvestment captal needs o other. Thereore as a measure to solve Trac Congeston Cost s contnuously ncreasng, t must seek the ecency measures road operaton that ncreases the unctonalty o the exstng road and mprove ecency. The development o normaton and communcaton technque s currently promotng Intellgent transport system. Also the collecton o trac normaton, processng, provdng, and has been used as the core technology underlyng the eld o control-related system. Unlke the collecton o trac normaton n accordance wth the development o normaton and communcaton and had to collect only a pont detecton system n the past. However road nrastructure and vehcle o ndvdual through communcatons wll collect path normaton between the ndvdual vehcle. Interval detecton system wll be to enhance the qualty o naccurate trac orecasts estmated rom normaton o lmted pont detecton systems o the past. Ths means that the ntersecton operatons more ecent trac management enorcement Urban servce level o the road s determned dependng on the ecency o the control sgnal at the ntersecton s enabled. In ths study, sectonal travel tme normaton s collected va DSRC, to represent the normaton o the length o the queue n the sgnalzed ntersecton. Whch s based on trac low-densty model and shockwave theory. The study objectve s amed at the development o queue estmaton algorthm or sgnalzed ntersecton usng sectonal travel tme normaton.
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013. BACKGROUND ISSUES.1 Fundamental Dagram Newell s Smpled Trac Flow Theory Newell proposed model the relatonshp between the densty and trac volume by dvdng prevous parabolc type volume-densty dagram nto uncongested and congested condton. Ths s expressed smply by assgnng uncongested state to ree low speed w1 and congested state to w. Volume-densty relatonshp s dsplayed n lnear orm by dvdng t nto areas o uncongested state and congested state There s a dculty n calculaton a prevous parabolc graph s used, but ths lnear smpled trac low theory s convenent or calculaton and the soluton can be easly derved. Shock wave Theory Fgure 1 q-k dagram o Smpled Trac Flow Theory shock wave s the propagaton movement o wave n accordance wth the change o trac densty and volume. Two derent densty o the area A, B have erased the boundares o the vertcal movng wth the speed o the trac low, the shock propagaton speed can be estmated rom the slope o a straght lne connectng two ponts o trac and densty trac densty relatonshp. Fgure Shock wave n volume-densty relatonshp
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013. Queueng Theory Denton o Queue Accordng to the Hghway Capacty Manual 000, queue s dened as a lne o vehcles, bcycles, or persons watng to be served by the system n whch the low rate rom the ront o the queue determnes the average speed wthn the queue. Slowly movng vehcles or people jonng the rear o the queue are usually 6 consdered part o the queue. such a sentence means that not only car stopped stop lne behnd the sgnal control and ncludes all the cars that are aected to the travelng speed by the vehcle queues approachng the ntersecton. Henry X. Lu(009) was dened the length o the queue o the actual sum o both parts. "Standng Queue" s that the vehcle was stopped by a sgnal control and "Movng Queue " s that a vehcle speed o the vehcle s reduced to a certan level below. There are two knds o queue. Frst, "Maxmum queue", reers to the length o queues ormed to the rear o the stop lne when the trac lght turns green equalzaton. Second, "Maxmum back o queue", the maxmum length o the stop lne to the rear end o the queue has been created wthn the same cycle. Queue Length Estmaton Fgure 3 Denton o Queue length Cumulatve arrval and departure analyss queung theory s that nvestgate the number o vehcles that passed through the stop lne o the vehcle arrved at the stop lne to determne queue length. The number o vehcles that make up the queue at any gven tme consst o the subtracton o two parts. The two parts as ollows: Frst, accumulated the vehcle arrves sequentally at eectve red. Second, departure trac volume obtaned by accumulatng the vehcle passed through the ntersecton o tme eectve green. shock wave theory s to calculate the length o the queue unlke those usng only data pont trac o cumulatve arrval and departure analyss queung theory. Frst, shock wave theory s the bass o a correlaton between trac Volume, Densty and Speed, thereore t must determne the volume-densty relatonshp o the target area. Second, t s to collect data n real tme that t s possble to explan the speed o the shock wave. Thrd, Trac volume o exstng - the process o analyzng the shock wave ancllary densty relatonshp occurs n the parabola s mathematcally mpossble. However, trac volume parabolc volume- densty relatonshp s accessble mathematcally through the Smpled Trac Flow Theory o Newell descrbed above. Type o shock wave generated by the sgnal ntersecton may be dvded nto three categores accordng to volume-densty relatonshp.
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 q m q m, k ) ( m ` Flow q a, k ) ( a V 3 ` u w V km V 1 D ensty 0, k ) ( j ` k j Fgure 4 n volume-densty relatonshp at sgnalzed ntersecton There s a derence rom the calculated queue length o the queue s calculated through cumulatve arrval and departure analyss queung theory and shockwave theory to estmate. Length s determned based on the cumulatve arrval and departure analyss queung theory, be calculated by multplyng the average length o the vehcle n an amount mathematcal vehcle stored vertcally wth respect to the tme they arrved at the stop lne. thus the error due to the length o the average car length. The length o prevously dened queue ncludes not only vehcles stopped n the queue but also vehcles that decelerated speed by the queue. As an ncrease n the number o vehcles are movng the end pont o the actual queue to upstream. Thus, end ponts o the queue are derent between cumulatve arrval and departure analyss queung theory and shockwave theory to estmate. 3. DEVELOPMENT OF QUEUE LENGTH ESTIMATION ALGORITHM 3.1 Detecton system conguraton In order to calculate sectonal travel tme o the path by sectonal detecton system, t s necessary to specy the exact endng and startng pont. At ths tme, t s necessary to select the endng and startng pont whch s regarded by consderng the actors that could aect the passage tme o the vehcle. Elements that have the greatest eect on the travel tme o the vehcle at sgnalzed ntersecton consecutve s the sgnal tme. Thereore, the detector are Installed ahead o the ntersecton. and There s a sngle ntersecton between the two detectors. Fgure 4 volume-densty relatonshp at sgnalzed ntersecton
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 3. Delay calculaton o the ndvdual vehcle measurng the tme o the pass ponts and the ID o each vehcle s possble to calculates the passage tme o ndvdual vehcles. Travel tme o ndvdual vehcles s a value that ncludes a delay tme o the sgnal n the sgnalzed ntersecton. tab tb ta (1) t A = Tme the vehcle has passed through the upstream detector t = Tme the vehcle has passed through the downstream detector t B AB =Passage tme rom A to B Delay o the ndvdual vehcle s calculated rom the derence between tme at ree low speed and actually travel tme o each vehcle. Delay L tab () v L = Dstance o the segment AB v = Free low speed Delay = Delay tme o vehcle n the segment AB 3.3 Estmatng poston o ndvdual vehcles n the shock wave There are our ponts on the trajectory through travel tme o the ndvdual vehcle. Pont 1 and Pont 4 s estmated by the value o tme and the poston o upstream and downstream detector. Fgure 5 Estmatng the coordnates o Pont 1 and Pont 4
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 Po dtme T3 w down nt1(re, ) (3) Pont 4( t, w up) (4) w down = The dstance between the stop lne and the downstream detector w = The dstance between the stop lne and the upstream detector up T 3 = Downstream detector to detect the subtracton o tme and red tme Pont and Pont3 are Ponts o the vehcle on the shock wave. Pont3 and Pont means the part o the vehcle speed s changng by acceleraton, deceleraton and stop. Pont shows a shock wave that s generated n the rear stop lne. The speed o the shock wave generated behnd the stop lne, trac densty can be expressed n relaton to the slope o the crtcal densty and the jam densty. Po dtme T1 h Fgure 6 Estmatng the coordnates o Pont and Pont 3 nt (Re, ) (5) T 1 = The derence between the tme to move ater the start o green tme h = The dstance between the vehcle and the stop lne h can be represented by the shock waves generated behnd the stop lne and the multplcaton o tme( T 1 ). h Shockwave T (6) 1 Shockwave = The speed o the shock wave generated by the rear due to the elmnaton o the queue
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 The sum o h and w down representng the wdth o the downstream ntersecton s the same as the movng dstance o the vehcle durng tme( T ). 1 h wdown tre at v ( T t ) 1 (7) t re = response tme t = Acceleraton tme requred to restore the ree speed The value o T 3 can be expressed as the sum o t1 and T. Thereore, the value o T can be calculated through the ollowng. 1 T1 Shockwave wdown tre at v ( T t ) (8) 1 Shockwave ( T3 T ) wdown tre at v ( T t ) (9) T 1 Shockwave T3 at v t t Shockwave v ( ) re (10) The coordnates o the Pont3, there s acceleraton delay derence between Pont. Pont 3(Re dtme T ( Delay AcceleratonDelay), h ) (11) 3.4 Estmate queue length 1 The speed o the shock wave s estmated usng the coordnate values or the detecton o ndvdual vehcles Pont3. Durng one cycle o the coordnate values are represented by the value o the slope o the speed o the shock wave through the method o least squares. Fnd tan mnmze n t tan d (1) 1 tan 1 Dstance ( t, d ) tan Tme
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 Fgure 7 Least-squares method or the estmaton o the speed o the shock wave. Every cycle usng the slope calculated by the least squares method to calculate the length o the queue. Queue Length = tan t (13) max t max = Tme Shockwave 1 and Shockwave meet 4.SIMULATION ANALYSIS 4.1 Descrpton o the analyss In ths study, VISSIM model s adopted to smulate the sgnal ntersecton operaton. VISSIM s a mcroscopc, behavor-based mult-purpose trac smulaton program. A pseudo network was developed as ollowngs: Roadway Characterstcs and sgnal condtons a. 500m dstance at ntersecton b. lanes per drecton c. Cycle : 100s d. Green nterval : 50s Trac/other condtons e. 100% passenger car (No truck). Capacty :,750 vehcles per hour per lane g. Jam dendty : 450 vehcles per Km h. Average ree low speed: 50 km/h 4. Development o scenaro / Assessment tools In ths study, was perormed our scenaros dependng on the saturaton o the access. Scen 1. v/c = 0.35 Scen. v/c = 0.55 Scen 3. v/c = 0.70 Scen 4. v/c = 0.90
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 Mean Absolute Percent Error(MAPE) was used n order to evaluate the t o the algorthm. A F A MAPE(%) = 100 (13) n A = Measurements F = Estmates 4.3 Smulaton result Each scenaro was perormed three tmes, accordng to the seed number. Table 1 scenaro result Scen 1 Scen Scen 3 Scen 4 Seed number 4 678 911 4 74 873 4 573 1843 6 4 109 A (m) 33.3 3.8 37.3 59.9 60.3 63.8 9.0 97.4 96.0 137.7 135. 17.8 F (m) 3.6 61.7 70.6 61.5 58.8 63.1 91.6 97.6 94.9 139.8 141.9 130. MAPE(%).6 183.7 91.3 16.8 10.3 9.8 5.6 8.6 6.6 8.1 9.8 7.1 The MAPE values decrease, ncreasng the saturaton smulaton results. The case o Scenaro 1, the value s derent or each seed. In other words, the low saturaton means that the error o the estmated speed o the shock wave. MAPE value o scenaro 3 s the best scenaro than scenaro 4 saturaton s hgh. Ths s due to long queues n Scenaro 4.In other words, the longer the length o the queue s too great error. The approach to saturaton s better the hgher the tness o the algorthm. Scenaro 1 s the derence between the value o each seed. Thus, the mnmum approach, addtonal research s needed or saturaton. 5. CONCLUSION The purpose o ths study s the development o an algorthm or estmatng the length o the queue through the sectonal travel tme normaton. Analyzed pror research on how to estmate the length o the queue and Algorthm through the nterval travel tme and the shock wave theory was developed. Fnally, evaluate the tness o the algorthm through smulaton. The hgher saturaton smulaton results showed that queue estmaton error s less. I the studes or approprate method o queue theory are contnued, ths study shows how to estmate the queue, the possblty o utlzng the sectonal travel tme normaton and t can be utlzed n advanced sgnal system. REFERENCES Adol D. May, (1990), Trac Flow Fundamentals
Proceedngs o the Eastern Asa Socety or Transportaton Studes, Vol.9, 013 Carlos F. DAGANZO (1997), Fundamentals o Transportaton and Trac Operatons Rahm F. Benekohal, Yoassry M. EL-Zohary,(001), Mult-regme Arrval rate unorm delay models or Sgnalzed ntersectons, Transportaton Research Part A. Alexander Skabardons, Nkolaos Gerolmns,(005), Real-TIme Estmaton o Travel tmes on Sgnalzed Arterals, 16th Internatonal Symposum on Transportaton and Trac Theory. Joonho Ko, Mchael Hunyer, and Randall Guensler,(006), Measurng Control Delay Usng Second-by-Second GPS Speed DATA, 86th Annual Meetng Transportaton Research Board. Ma Yng-Yng, Yang Xao-Guang, and Zhong Zhang-Jan,(008), Olne Oset Models or Coordnated Sgnal Control, 11th nternatonal IEEE Conerence on Intellgent Transportaton Systems. Henry X. Lu, Wenteng Ma, Xnka Wu, and Heng Hu,(009), Real-Tme Estmaton o Arteral Travel Tme under Congested Condton, Transportmetrca. James A. Bonneson, Mchael P. Pratt, and Mark A. Vandehey,(010), Predctng Arrval Flow Proles and Platoon Dsperson or Urban Street Segments, Transportaton Research Record, No. 173. Xnka Wu, Henry X. Lu, and Douglas Gettman,(010), Identcaton o oversaturated ntersectons usng hgh-resoluton trac sgnal data, Transportaton Research Part C, Volume 18(4). Xuegang(Je) Ban, Peng Hao, and Zhanbo Sun,(010), Real Tme Queue Length Estmaton or Sgnalzed Intersectons Usng Travel Tmes rom Moble Sensors, Transportaton Research Part C, Volume 19(6).