Available online a www.sciencedirec.co ScienceDirec Procedia - Social and Behavioral Scien ce s 96 ( 2013 ) 1745 1754 13h COA Inernaional Conference of ransporaion Professionals (CICP 2013) Capaciy Model for Signalized Inersecion under he Ipac of Upsrea Shor Lane Jing ZHAO a, Meiping YUN b *, Xiaoguang YANG c a,b,c he Key Laboraory of Road and raffic Engineering, Minisry of Educaion, 201804, P.R.China Absrac In Highway Capaciy Manual (HCM) 2010, various facors were considered o adjus he base sauraion flow rae for capaciy analysis of signalized inersecions. However, ipacs of shor lane were only addressed by he adjusen for lane uilizaion based on deerinisic analysis. Such analysis does no consider poenial queue overflow and blockage resuled fro shor lane. his paper presened a heoreical odel for esiaing lane group capaciy a signalized inersecions wih consideraion of upsrea shor lane effecs based on probabiliy heory. hree scenarios of signal phase sequences were aken ino accoun, reflecing he relaionship beween oveen ha ay cause blockage and oveen ha ay be blocked. he proposed odel was validaed by VISSIM siulaion. Resuls of exensive analysis showed ha he upsrea shor lane ay have a subsanial ipac on capaciy: he capaciy is posiively correlaed wih effecive green ie lengh and negaively correlaed wih shor lane lengh. Aong he hree scenarios of phase sequence plans, he wors one causing he larges decrease in lane group capaciy is phase sequence case 2 (he oveen ha ay cause blockage follows he oveen ha ay be blocked). I is shown ha here is an opial cycle lengh o obain axiu capaciy when upsrea shor lane exiss. 2013 he Auhors. Published by Elsevier by Elsevier Ld. Open B.V. access under CC BY-NC-ND license. Selecion and/or peer-review peer-review under under responsibiliy responsibiliy of Chinese of Overseas Chinese ransporaion Overseas ransporaion Associaion (COA). Associaion (COA). Keywords: signalized inersecion; capaciy; shor lane; probabilisic analysis 1. Inroducion Shor lane is he lane wih liied lengh which canno be regarded as an independen lane as a full lane, exclusive lane or unliied lengh lane. I widely exis in road widening inersecions. Alhough increasing he nuber of lanes a an approach can increase capaciy of signalized inersecion, hese addiional shor lanes ay no funcion as full lanes. Due o he liied lengh of shor lane, i is poenial o generae queue blockages for * Corresponding auhor. el.: 13916850501. E-ail address: yunp@ongji.edu.cn 1877-0428 2013 he Auhors. Published by Elsevier Ld. Open access under CC BY-NC-ND license. Selecion and peer-review under responsibiliy of Chinese Overseas ransporaion Associaion (COA). doi: 10.1016/j.sbspro.2013.08.199
1746 Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 road widening inersecions. herefore, he inial lengh of shor lane is saed in any design anuals (JSCE, 1989; AC, 1999; Yang, 2003; FGSV, 2006; AASHO, 2011). Bu wih increasing deand of raffic flow, he phenoenon ha called shor lane doino effec becoes ore coon. I is essenial o esiae he ipac of shor lane on capaciy. In HCM2010 (2010) and CCG (2008), any works have been done o esablish he adjusen facors of signalized inersecion capaciy, which include lane widh, heavy vehicles, grade, parking condiions, local bus blockage, ype of area, lane uilizaion, righ urns, lef urns and pedesrian-bicycle blockage. However, he guidance on how o accoun for ipacs of shor lane adds or drops was only addressed by he adjusen for lane uilizaion. he negaive effecs of he poenial queue overflow and blockage resuled fro shor lane is ignored. As a resul, adoping HCM2010 odel o esiae capaciy of inersecions wih shor lanes, he resul will be higher han he acual capaciy. Differen fro HCM2010, soe researches adjused shor lane ipacs by fixed values based on deerinisic analysis, such as Guell (1983), Ausralia (1988), Wu (2005) and Jiang (2007). However, he shor lane doino effec is no ineviable. I is a synheic effec of geoeric condiions, raffic condiions and signalizaion condiions. Alhough he blockage caused by he shor lane is aken ino consideraion in hese ehods, he probabiliy of he queue overflow blockage were ignored. In recen years, soe probabiliy analysis odels for shor lanes were proposed (Cheng, 2002; ian & Wu, 2006; Wu, 2007). In hese odels, he relaionship beween he lengh of he shor lane and he possibiliy of queue overflows has been aken ino consideraion. However, hese ehods also have soe disadvanages, such as: (a) ignoring he effec of he phase sequence plan: differen probabiliy and occurring ie of queue blockages due o he shor lane will be resuled fro various phase sequence plan, which is ignored in any sudies before; (b) ignoring he ineracion aong oveens a he approach: i is assued ha he exclusive lef or righ urn shor lane would be blocked by he hrough oveen vehicles, bu acually, he sauraion flow rae of hrough oveen would also be effeced by he lef urn queue overflow which depends on he volues and phase sequence plan of he wo oveens; (c) ignoring he effec of vehicle arrival disribuion: since he probabiliy heory is used in hese sudies, he vehicle arrival disribuion ay ipose he shor lane effec. In order o esiae he effec of upsrea shor lane on he capaciy of signalized inersecion, he auhors proposed a heoreical odel considering all of he hree cases of signal phase sequence, which reflecs he relaionship beween he oveen ha ay cause he blockage and he oveen ha ay be blocked. In addiion, several kinds of vehicle arrival disribuion were aken ino accoun. he res of he paper is organized as follows. In Secion 2, qualiaive analysis of shor lane effec on signalized inersecion capaciy and he noaion adoped in his paper is firsly described. he forulaion of he lane group capaciy wih he effec of upsrea shor lane is proposed in Secion 3. Secion 4 is validaion of he forulaion VISSIM siulaion in. Sensiiviy analysis of shor lane lengh, effecive green ie, phase sequence plans and cycle lengh on he capaciy of signalized inersecion is discussed in Secion 5. Conclusions and recoendaions are given a he end of he paper. 2. Qualiaive analysis and general noaion he ipac of upsrea shor lane on capaciy of signalized inersecion includes following wo aspecs: (1) he shor lane resuls in flucuaion of he sauraion flow rae of approaches. Afer he clearance of he axiu queue lengh of he shor lane wih sauraion flow rae a he sop-line, he raffic flow has o pass wih he axiu arrival rae of he road non-widened secion. hese wo sauraion differen flow raes resul in a non-unifor raffic flow. (2) he shor lane resuls in he queue blockage. he effec of raffic blockage a he shor lane on he capaciy varies fro differen ypes of phase sequence plans, which can be concluded as hree cases, as able 1 illusraed.
Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 1747 able 1. Qualiaive analysis of he ipac of shor lane on capaciy under differen phase sequence plans Phase sequence plans Case 1: oveen B follows oveen A Case 2: oveen A follows oveen B Case 3: boh oveens fully overlap ie blockage ay occur A he iddle or end of he green ie of oveen B During all he green ie of raffic flow B A he iddle or end of he red ie of oveen A Noe: oveen A and B are defined as he oveen ha ay cause he blockage and he oveen ha ay be blocked respecively. he sybols and paraeers used in he odel are lised in able 2. able 2. Sybols and paraeers c c 1 c 2 C g e g Ae g Be h d L N P P (x =i) q A q M s 1 s 2 s 3 v x y capaciy of lane group wih he consideraion of shor lane (veh/h) capaciy of lane group wihou he consideraion of queue overflow caused by shor lane (veh/h) capaciy of lane group when he blockage occurs (veh/h) cycle lengh (s) effecive green ie for he lane group (s) effecive green ie for oveen A (s) effecive green ie for oveen B (s) space headway for queuing vehicles () lengh of he shor lane () nuber of queuing vehicle he shor lane could accoodae probabiliy of queue blockage probabiliy of he nuber of vehicles arrived equals o i a he ie arrival rae of he oveen ha ay cause he blockage (veh/s) arrival rae of he approach (veh/s) duraion of he ie fro he sar of he red for oveen A o he sar of he green for oveen B (s) sauraion flow rae for subjec lane group wihou he consideraion of shor lane (veh/h) axiu arrival rae of he road non-widened secion (veh/h) sauraion flow rae when he blockage occurs (veh/h) he ie blockage occurs (s) axiu queue clearance ie (s) desired speed (/s) nuber of vehicles arrived for he oveen ha ay cause he blockage a he ie he raio of arrival rae of he oveen ha ay cause he blockage over he arrival rae of he approach
1748 Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 3. Ipac of upsrea shor lane on capaciy 3.1. Capaciy odel wihou consideraion of queue blockage As Fig. 1 shown, wihou consideraion of queue overflow, he upsrea shor lane would only cause a flucuaion of he sauraion flow rae of approaches. Fig. 1. Sauraion flow rae wihou he consideraion of queue blockage When he effecive green ie is shorer han he axiu queue clearance ie, he flow rae of he lane group is equal o he sauraion flow rae, s 1, during all effecive green ie and he upsrea shor lane has no effec on he lane group capaciy. he capaciy of a given lane group ay be saed as shown in Equaion (1). Since any works have been done o esiae he sauraion flow rae for subjec lane group wihou consideraion of upsrea shor lane, s 1, insead of discussed in deail, i is assued o be an inpu paraeer of he odel. ge c1 s1, ge C When he effecive green ie is longer han he axiu queue clearance ie, he flow rae of he lane group is equal o he sauraion flow rae s 1 during he axiu queue clearance ie, and i is equal o he axiu arrival rae of he road non-widened secion s 2 during he res of he effecive green ie. he capaciy of a given lane group ay be saed as shown in Equaion (2). ge c2 s1 s2, ge C C he axiu queue clearance ie is equal o he ie for clearing he sopped vehicles in he shor lane, which could be copued using Equaion (3). 3600L sh 1 3.2. Probabiliy of queue blockage d he probabiliy of blockage a he ie equals o he probabiliy ha he nuber of vehicles arrived a he ie is ore han he axiu nuber of queuing vehicle he shor lane could accoodae, which could be copued using Equaion (4). Fig. 2 shows he relaionship beween he probabiliy of queue blockage and he (1) (2) (3)
Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 1749 vehicle arrival rae under hree ypes of vehicle arrival disribuing which includes he poisson disribuion, binoial and negaive binoial disribuion. i j j i j P P'( x i) C y (1 y ) (4) y q q i N A M j N i (5) Fig. 2. Probabiliy of queue blockage 3.3. Capaciy odel wih consideraion of queue blockage As Fig. 3 shows, when he blockage occurs, fewer lanes could be used and hen he sauraed flow rae of oveen B (he blocked oveen) will be decreased. he influence exen is relaed o he effecive green ie g e, he axiu queue clearance ie, and he ypes of phase sequence plans. he following is he capaciy calculaion odel analysis for oveen B (he blocked oveen) under he hree cases of phase sequence plans lised in able 1. Fig. 3. Sauraion flow rae wihou consideraion of queue overflow
1750 Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 1) Case 1: oveen B follows oveen A Moveen A Moveen B Sauraion flow rae of oveen B L/v / s 1 s 2 s 3 / effecive green ie effecive red ie Fig. 4. Sauraion flow rae during differen periods of a signal cycle wih he consideraion of queue blockage (Case 1) s1, C c2 L L in, ax,0 v v s1 s2 s3, C C C Case 2: oveen A follows oveen B Moveen A Moveen B Sauraion flow rae of oveen B L/v s 1 s 2 s 3 / effecive green ie r effecive red ie (6) Fig. 5. Sauraion flow rae during differen periods of a signal cycle wih he consideraion of queue blockage (Case 2) s1, C c2 s1 s3,, r C C L L in r, ax r,0 v v s1 s2 s3,, r C C C (7)
Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 1751 Case 3: boh oveens fully overlap Moveen A Moveen B Sauraion flow rae of oveen B s 1 s 2 s 3 / L/v effecive green ie effecive red ie Fig. 6. Sauraion flow rae during differen periods of a signal cycle wih he consideraion of queue blockage (Case 3) s1, C c2 L L gae gae v v 1 2 3 ax(,0) ax(,0) s s s C C C (8) 3.4. Capaciy odel wih consideraion of he shor lane According o wha has been discussed, he capaciy of he lane group wih he consideraion of he shor lane should equal o he su of he producs of he capaciy when blockage doesn occur and he inverse probabiliy of queue blockage and he capaciy when blockage occurs and he probabiliy of queue blockage, which can hen be obained by equaion (9). c P c1 P c 2 (9) 4. Model validaion he influence of he shor lane on he capaciy of signal inersecion is coposed wih hree sub-odels: (1) he capaciy wihou he consideraion of queue blockage; (2) probabiliy of blockage; (3) he capaciy wih he consideraion of queue blockage. he siulaion package VISSIM was used o siulae he sochasic variaion of raffic flow and validae he accuracy of he proposed odels. able 3 suarized he daa inpus. able 3. Inpu daa Inpu daa cycle lengh (C) 60 (s), 90 (s), 120 (s) effecive green ie (g e) 0-40 (s) sauraion flow rae for subjec lane group wihou he consideraion of shor lane (s 1) 3600 (veh/h) axiu arrival rae of he road non-widened secion (s 2) 1800 (veh/h) sauraion flow rae when he blockage occurs (s 3) 0 (veh/h) he lengh of shor lane (L) 60 () vehicle arrival disribuion Poisson disribuion he raio of arrival rae of he oveen ha ay cause he blockage over he arrival rae of he approach (y) 60% Value
1752 Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 he desired speed (v) space headway for queuing vehicles (h d) vehicle ype Inpu daa Value 12.5 (/s) 7 () personal car Fig. 7, 8 and 9 shows he validaion resuls of he sub-odel (1), (2) and (3) respecively. Copared wih he proposed odel calculaion resuls and siulaion resuls, i can be calculaed ha he average error is 2.3%, 5.6% and 3.4% respecively. Fig. 7. Validaion of odel (1) 5. Sensiiviy analysis Fig. 8. Validaion of odel (2) Fig. 9. Validaion of odel (3) In his secion, he effec of upsrea shor lane on he capaciy of he lane group is evaluaed based on nuerical analysis. Excep for furher descripion, he cycle lengh is se o 120 (s); he effecive green ies for oveen A and oveen B are se o 40 (s); he arrival rae of he approach is se o 1000 (veh/s); he raio of arrival rae of he oveen ha ay cause he blockage over he arrival rae of he approach is se o 0.6; sauraion flow rae for subjec lane group wihou he consideraion of shor lane is se o 3600 (veh/h); axiu arrival rae of he road non-widened secion is se o 2160 (veh/h); sauraion flow rae when he blockage occurs is se o 1600 (veh/h); and he space headway for queuing vehicles is se o 7 ()
Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 1753 Fig. 10(a) shows he relaionship beween capaciy and he arrival rae of vehicles under he hree cases of phase sequence plan lised in able 2. I is illusraed when he phase sequence plan is case 1 or case 3, here is a sligh decrease in capaciy wih he increase of vehicle arrival rae. When he phase sequence plan is case 2, here is a significan decrease wih he increase of vehicle arrival rae. So, for phase sequence plan case 2, he arrival rae of vehicles is a crucial facor o capaciy. Fig. 10(b) shows he relaionship beween he capaciy and shor lane lengh. I is illusraed ha wih he increase in he shor lane lengh, here is an upward rend in capaciy. So, he effec of upsrea shor lane on capaciy has an inverse correlaion wih he shor lane lengh. Moreover, when he lengh of he shor lane is shor, here is a grea difference in capaciy under hree cases of phase sequence plan. he phase sequence plan case 2 would cause a ore significan effec on lane group capaciy. When he lengh of a shor lane reaches a cerain value (abou 100), capaciy in hree cases of phase sequence plan is nearly sae. Fig. 10(c) shows he relaionship beween he capaciy and he effecive green ie. I is illusraed ha wih he increase in effecive green ie, he upward rend in capaciy becoes slower. So, he effec of upsrea shor lane on capaciy has a correlaion wih he effecive green ie. Fig. 10(d) shows he relaionship beween he capaciy and he cycle lengh. Wih he consideraion of he exisence of shor lane, he capaciy does no always go up wih cycle lengh as i usual does. here is an opial cycle lengh for he capaciy (a) Ipac of arrival rae on capaciy (b) Ipac of he lengh of shor lane on capaciy (c) Ipac of effecive green ie on capaciy (d) Ipac of cycle lengh on capaciy Fig. 10. Sensiiviy analysis resuls
1754 Jing Zhao e al. / Procedia - Social and Behavioral Sciences 96 ( 2013 ) 1745 1754 6. Conclusions his paper presened a heoreical odel for esiaing lane group capaciy considering he ipac of shor lane based on he analysis of probabiliy of queue blockage under hree phase sequence plan cases. Exensive nuerical analysis was conduced o evaluae ipac of several criical facors, such as arrival rae, shor lane lengh, effecive green ie, and cycle lengh. his research leads o he following conclusions. 1) he upsrea shor lane ay have a subsanial ipac on capaciy, which posiively relaed wih effecive green ie and negaively relaed wih he shor lane lengh. For good operaion purpose, he shor lane lengh should generally be no less han 100. 2) he ipac of shor lane on capaciy is sensiive o phase sequence plan. Aong he hree cases of phase sequence plans, case 2 (he oveen causing he blockage follows he oveen ha ay be blocked) would cause a ore significan ipac on lane group capaciy. 3) Wih consideraion of shor lane, here ay exis an opial cycle lengh for axiu capaciy. Soe facors in he odel are closely relaed wih driver behavior and local raffic condiion, such as basic sauraion flow rae, space headway for queuing vehicles, vehicle arrival disribuion, and so forh. However, hey were no discussed in he odel. For applicaion in he pracice, hey should be calibraed for local raffic condiion. Acknowledgeens he research is suppored by he Naional Naural Science Foundaion of China (Gran No. 51178344), and he Shanghai Coiee of Science and echnology, China (Gran No. 12231201500). References Japan Sociey of Civil Engineers (JSCE). (1989). Handbook of Civil Engineering (4h ed.). okyo: Gihodo Shuppan. (in Japanese) AC. (1999). Geoeric design guide for Canadian roads. Oawa: ransporaion Associaion of Canada. Yang, X.G. (2003). Manual of urban raffic design. Beijing: China Counicaion press. Road and ransporaion Research Associaion (FGSV). (2006). Guidelines for raffic signals (RiLSA) (Li, K.P. ranslae). Beijing: China Archiecure & Building Press. (in Chinese) AASHO. (2011). A policy on geoeric design of highways and srees (6h ed.). Washingon, D.C.: Aerican Associaion of Sae Highway and ransporaion Officials (AASHO). ransporaion Research Board. (2010). HCM2010 Highway Capaciy Manual. Washingon, D.C.: ransporaion Research Board. eply S., Allingha D.I., Richardson D.B., & Sephenson B.W. (2008). Canadian capaciy guide for signalized inersecions. Disric 7, Canada: Insiue of ransporaion Engineers. Guell, D.L. (1983). Addiional hrough lanes a signalized inersecions. Journal of ransporaion Engineering, 109(4), 499-505. Naional Associaion of Ausralian Sae Road Auhoriies. (1988). Guide o raffic engineering pracice, par 2-capaciy. Sydney: Associaion of Ausralian Sae Road and ranspor Auhoriies. Wu, B., & Li, Y. (2005) raffic anageen and conrol (3rd ed.). Beijing: China Counicaion Press. Jiang, J.Y. (2007). Research on he iproveen of raffic organizaion and signal iing for isolaed inersecions and arerial roads. Shanghai: ongji Universiy. Cheng, G.Z. (2002). Research on he capaciy of widened signalized inersecion. Harbin: Harbin Insiue of echnology. ian, Z.Z., & Wu, N. (2006). Probabilisic odel for signalized inersecion capaciy wih a shor righ-urn lane. Journal of ransporaion Engineering, 132(3): 205-212. Wu, N. (2007). oal approach capaciy a signalized inersecions wih shared-shor lanes - a generalized odel based on siulaion sudy. ransporaion Research Record: Journal of he ransporaion Research Board, 2027, 19-26.