Determination of storage lengths of right-turn lanes at signalized. intersections

Transcription

1 Detemination of toage length of ight-tun lane at ignalized inteection By Jinghui Wang Lei Yu Hui Xu ABSTRACT Thi pape develop an analytical method of detemining toage length of ight-tun lane at ignalized inteection baed on Queuing Theoy Pinciple. The model of the toage length fo two cae (Right-Tun-On-Red (RTOR) and o RTOR) ae epectively developed, conideing two ituation: a. oveflow: the ight-tun vehicle oveflow the lane and block the movement of the though-vehicle; and b. blockage: the queued though vehicle block the entance of ight-tun vehicle. The tudy invetigate the effect of atuation atio on the toage length to exploe the influence of atuation atio on ight-tun length, and alo povide the citical taffic volume fo detemination of the toage length. The impact of atuation atio and confidence level (the confidence pobability of no-oveflow o no-blockage) ae alo taken into account in thi tudy, which ha little conideed in the exiting efeence. Finally, the ecommended toage length ae obtained by modeling olution and veified though Viim imulation. It i demontated that the obtained eult ae eaonable. 1. ITRODUCTIO The ight-tun lane i an impotant deign element at a ignalized inteection. It help to inceae the capacity of inteection by epaating ight-tun movement fom though movement and alo by poviding an additional channel of flow. The length of ight-tun lane i one of the mot impotant facto which affect the efficiency of the inteection. Theefoe, the exploation of the length of the ight-tun lane become a vey ignificant iue and i intenively tudied in thi pape. Geneally, a hown in Figue 1, the length hould be long enough to toe all the Vehicle (thoughand ight-tun vehicle, epaately) that aive duing the ed phae, into individual lane. Howeve, the guideline about the length of the ight-tun lane vay in the liteatue. Thi pape eview the cuent guideline and pactice, dicue the poible facto which affect the length of ight-tun lane, develop two model of computing the length, and the eult can be ued fo deign efeence. The analyi i pefomed fo two cae, when ight-tun-on-ed (RTOR) i pemitted and not pemitted, and alo involve the effect of atuation atio and confidence level (confidence level efe to the confidence pobability of no-oveflow o no-blockage fo ight-tun lane) on the length. The emainde of thi pape i oganized a follow: the fit ection put fowad the pupoe of thi tudy; the econd ection eview the exiting efeence; and the thid ection develop two model of detemining the length of ight-tun lane baed on Queuing Theoy Pinciple; the fouth ection dicue the ecommended length of ight-tun lane baed on the developed model conideing the effect of atuation atio and cot; and the lat ection doe the compaative analyi of the length of ight-tun lane between the RTOR cae and with O-RTOR cae, and alo veifie the eult of the ecommended length obtained by model uing VISSIM imulation. Jinghui Wang, Gaduate Student Dept. of Tanpotation Studie Texa Southen Univeity, 3100 Clebune Steet, Houton, TX77004, Tel: , wjhtongji@hotmail.com; Lei Yu, Pofeo and Dean, Dept. of Tanpotation Studie, Texa Southen Univeity, 3100 Clebune Steet, Houton, TX77004, Tel: , yu_lx@tu.edu. Hui Xu, Enginee, Municipal engineeing deign intitute in Suzhou.

2 Figue 1 the two cae fo dicuion 2. STUDY PRPOSE Mot of the exiting guideline o pactice fo detemining the length of ight-tun lane ae limited and lack pecificity. Fo example, only few liteatue take atuation atio and confidence level into conideation when detemining the length of ight-tun lane which alo affect the length. The pupoe of thi tudy i to develop an analytical poce to detemine the length of ight-tun lane though Queue Theoy Pinciple, conideing both of thee two facto. The poce of detemining the length i vey complicated becaue of a vaiety of facto which have an effect on the detemining poce. The facto that affect the length of ight-tun lane (1) Aival ate of vehicle: though, ight-tun, and co-taffic, and the vehicle type; Aival equence of the two type of vehicle (though, and ight-tun vehicle); Signal phae, cycle time, and timing fo each phae (geen time/ cycle time atio); Geomety of the inteection including hoizontal and vetical alignment; Sight ditance (paticulaly when ight-tun-on-ed (RTOR) i allowed) and gap Acceptance; Pedetian and bicycle activitie; Right-tun-on-ed (RTOR) pemitted o not; Appoach peed; Peence of tanit vehicle and bu top location; The atuation atio of appoach diveway (ight-tun lane and though lane); Confidence level; Among thee, the vehicle aival ate, aival equence of the two type of vehicle, ignal phae, RTOR pemitted o not, the atuation atio and confidence level ae the mot elevant facto which affect the length of the ight-tun lane. All of thee mot elevant facto ae conideed when developing the model of the length of the ight-tun lane and dicuing the ecommended length accoding to the model. Othe ae not taken into conideation in thi tudy. 3. LITERATURE REVIEW The liteatue eview include two ection: the fit ection i the eeach about RTOR, and the econd one i detemining the length of ight-tun lane at ignalized inteection.

3 3.1 The liteatue eview about RTOR Mot of exiting eeache about RTOR ae focuing on the capacity of inteection and few go deep in the tudy of the length of ight-tun lane. Shinya Kikuchi (1), at Viginia Tech, develop the pobability model of detemining the length and ugget the ecommended length accoding to the model when RTOR i pemitted. Howeve, the model in thi pape ae vey complicated and not eaily olved becaue of it infinite eie, which alo don t take the cot into conideation. Feng-Bo Lin (2) tated that RTOR could effectively educe ight-tun delay, if the atuation atio of the co flow i le than 0.6, and the ight-tun delay without RTOR exceed 30 ec pe vehicle. Lin wa the fit peon to point out that the need to examine the poibility of the though-vehicle blocking the tun lane; howeve, hi equationtion lacked conideation of vehicle aival equence. Tian and Wu (3) developed an analytical method of modeling the elationhip between the length of a ight-tun lane and it capacity. They uggeted that it i vey impotant to conide vehicle aival equence when dicuing the length of a ight-tun lane. Tako (4) alo ecognized the impotance of vehicle aival equence and the poibility of blockage of the ight-tun vehicle, but jut focued on the eeach of capacity and did not go deep in the analyi of the length. ITE Handbook (5), in which K equal to 1.5, popoed the ecommended length when RTOR i pemitted, without giving any explanation about the length but that K i a andom aival facto. (1) whee toage length in feet; volume in vehicle pe hou; and g/c: geen time cycle length atio. 3.2 The detemination of the length fo ight-tun movement at ignalized inteection Shinya Kikuchi (1), at Viginia Tech, develop the pobability model of detemining the length and ugget the ecommended length accoding to the model when RTOR i pemitted and not, coniting of a combination of input vaiable, like aival ate and equence, geen-to-cycle atio. Howeve, the model in thi pape i vey complicated and not eaily olved becaue of it infinite eie. Beide, thi pape ha not taken the atuation atio into conideation when detemining the length and the model cannot be widepead ued. FHWA Signalized Inteection: Infomational Guide (6, p.329) ugget that the toage length hould be long enough to accommodate the maximum vehicle queue fo both ight tun- and though lane unde deign yea condition. The AASHTO Geen Book (7, p.719) ugget, the length of the ight-tun (o left-tun lane) hould uually be baed on one-half to two time the aveage numbe of vehicle queue pe cycle. Tanpotation and Land Development, publihed by ITE (8), peent a look-up chat baed on the AASHTO Geen Book. Delawae (9) ugget that the toage length hould be ufficient to accommodate the maximum vehicle queue mot commonly expeienced fo both ight-tun and left-tun lane. The ecommended length of eithe left tun o ight-tun i 100 ft (30 m) fo heavy though taffic and 50 ft (15 m) fo light though taffic. Califonia (10) and Minneota (11): The analytical method of detemining toage length fo ight-tun movement i in the ame way a fo left-tun movement. The toage length hould be baed on

4 one-half to two time the aveage numbe of vehicle pe cycle, a i uggeted by AASHTO Geen Book (7). Othe tate, like Floida (12), Wahington (13), and Tenneee (14), alo tate that the method of detemining the length of a ight-tun lane i in the ame manne a the one fo the left-tun movement, and the length hould atify the maximum vehicle queue expected commonly Jingyuan Wang and Wei Wang (15) in China ugget the eaonable length fo left-tun lane at ignalized inteection with no RTOR and put fowad the conception of citical taffic volume which affect the detemination of the length, without conideing the RTOR cae. Howeve, the analytical poce can alo be ued to detemine the length of ight-tun lane. Feng-Bo Lin (2) alo develop the model of detemining the length though pobability theoy pinciple and ugget the ecommended length fo ight-tun movement, conideing the taight-though and ight-tun volume; howeve, othe facto affecting the length haven t been conideed in the model, o have the ituation with RTOR. Gatti (16) eview the equiement of the length fo both ight tun- and left-tun lane, teating left-tun and ight-tun equally. Alo it i not convictive to make a ditinction between RTOR and O-RTOR cae jut by giving a andom facto K, like ITE Handbook (5) doe. 3.3 Concluion In concluion, the available liteatue can be ummaized a follow: (a) the length of ight-tun lane when RTOR i pemitted ha been little tudied in detail; and (b) atuation atio and confidence level have not been tudied deeply in the exiting efeence; and (c) ome elatively eaonable analytical method ae too complicated to be put in wide ue. Fo thee pupoe, it i impotant to develop a imple and ueful analytical method fo detemining the length of ight-tun lane in the two cae (RTOR and O RTOR), alo conideing atuation atio and confidence level. 4. MODEL DEVELOPMET A mentioned befoe, both RTOR and O-RTOR cae hould be tudied when dicuing the length of ight-tun lane. Fo each cae, the two ituation (oveflow and blockage) ae conideed when developing model. In thi ection, RTOR and O-RTOR will be developed epectively though queuing theoy unde the following aumption: 1. The aival patten confom to Poion Ditibution, and the headway confom to negative exponential ditibution; 2. The ecommended length in the model ae indicated by the numbe of vehicle queuing in though and ight-tun lane; 3. The appoach with only one though lane and one ight-tun lane will be the object of thi tudy, othe kind of appoache with multiple lane ae not tudied in thi pape; 4. The effect of vehicle type i not conideed when developing model; 5. The queuing vehicle duing the ed phae depat paking line by atuation ate; 6. The ight-tun and though movement hae the ame geen phae. 4.1 Paamete otation The following notation i ued in thi pape: P n =the pobability of n vehicle lining up in the ight-tun lane;

5 P( n ) =the pobability of no-oveflowing (confidence level); P n =the pobability of n vehicle lining up in the though lane; P( n ) =the pobability of no blockage (confidence level); n =the numbe of queuing vehicle; =the numbe of ight-tun vehicle aiving pe cycle; u =the numbe of depatue ight-tun vehicle duing the geen phae without RTOR, o = u atuation atio of ight-tun lane; u =the numbe of depatue ight-tun vehicle pe cycle with RTOR; =the numbe of taight-though vehicle aiving pe cycle; u =the numbe of depatue though vehicle duing the geen phae, o epeent atuation atio u of though lane; C =Cycle length; g =the duation of geen phae fo both ight-tun and though movement; q =the aival ate of ight-tun vehicle; q =the aival ate of though vehicle; q c =the aival ate of co taffic; S =the atuation flow of ight-tun lane, HCM2000 aume S 1550 vph / h ; S =the atuation flow of though lane, HCM2000 aume S 1650 vph / h ; x and x =the atuation atio of ight-tun lane; =the maximum queue length of ight-tun lane without RTOR; =the maximum queue length of ight-tun lane with RTOR; =the maximum queue length of though lane; =the ecommended length of ight-tun lane without RTOR; =the ecommended length of ight-tun lane with RTOR; c =the numbe of vehicle that can potentially make a ight tun duing the ed phae;

6 =the citical gap fo making ight tun (), aumed =follow-up time (), ; 4.2 Modeling tep Fo RTOR and O-RTOR, the modeling poce i divided into two tep: 1. Develop the model fo o-rtor; 2. Geneate the model fo RTOR though modifying the model of o-rtor. Step 1 Develop the model fo o-rtor Accoding to the Queuing Theoy: the pobability of n vehicle lining up in the ight-tun lane and though lane i epectively ignified a follow: P n (1 )( ) n u u (2) P n (1 )( ) n u u When P value i detemined, thee mut be an value coeponding to it, which epeent the maximum queuing length, Baed on the alteation of equation (2) and (3), the pobabilitie of no-oveflow and no-blockage have been obtained a follow: 2 (1 ) (1 )( ) (1 )( )... (1 )( ) 1 (3) P( n ) P( n 0) P( n 1)... P( n ) u u u u u u u 1 ( ) u P( n ) P( n 0) P( n 1)... P( n ) u u u u u u u 2 (1 ) (1 )( ) (1 )( )... (1 )( ) 1 ( ) u 1 Though logaithm calculation of equation (4) & (5), we can get the expeion of the maximum queuing length (in numbe of vehicle pace) fo ight-tun lane and though lane: ln(1 P( n )) 1, 1.0 ln( ) u u ln(1 P( n )) 1, 1.0 ln( ) u u Conideing a combination of the equation a follow, the ultimate model of the maximum length ae hown below: (6) (7) (4) (5)

7 qc Sg qc Sg u u 3600, 3600, 3600, 3600 ln(1 P( n )) 1 qc ln( ) Sg (8) ln(1 P( n )) 1 qc ln( ) Sg In geneal, the length of a ight-tun lane need to atify not only the line-up demand of ight-tun vehicle (no-oveflow), but alo the demand of though vehicle (no-blockage). In thi way, it i neceay to elect the lage value between the two maximum queuing length a the ecommended toage length: max(, ) Step 2 Geneate the model fo RTOR The theoy pinciple and analytical method in thi ection ae the ame a o-rtor; howeve, thee i omething diffeent duing the ed phae. o vehicle can go though the top line duing the ed phae when RTOR i not pemitted. In thi way, the maximum ight-tun queue length (in numbe of vehicle) when RTOR i pemitted may be le than the one when RTOR i not pemitted, but the length of the though lane will not be affected. That i to ay, the ight-tun lane can toe not only the vehicle in the phyical length, but alo the one that potentially can make a ight tun duing the ed phae. The numbe of vehicle that potentially can make ight tun duing the ed phae depend on the co taffic, gap acceptance, follow-up time and the geen phae of co taffic. It i obtained by modifying the model in HCM RTOR capacity. (10) (9) c qg c e * qc /3600 qc 0 /3600 e (11) Baed on the equation (11), the atuation atio i modified a equation (12) conideing the change of the numbe of ight-tun vehicle depating pe cycle. x qc 3600 qc u S g 3600 Sg c 3600 c (12) Due to the modification of atuation atio, the maximum queue length of the ight-tun lane can be modified a follow: ln(1 P( n )) qc 1 ln( ) S g 3600 With the ame pinciple, the lage value between the two maximum queuing length would be elected c (13)

8 a the ecommended length of ight-tun lane: max(, ) (14) 5. RECOMMEDED LEGTHS In thi ection, the ecommended length will be epaately given out fo both cae: RTOR and o-rtor. Alo, to pobe the effect of vaiou facto on ecommended length unde diffeent condition, compaative analyi will be pefomed between the two cae. 5.1 The effect of Satuation atio on Maximum Queue Length Satuation atio i impotant and need to be valued befoe detemining the ecommended length. It ha tong elationhip between the maximum queue length and atuation atio. Accoding to the model in the pio ection, the equation of atuation atio unde the condition of o-rtor can be indicated a follow: Satuation atio of the ight-tun lane: x qc gs (15) Satuation atio of the though lane: x qc gs (16) Equa (12) i the expeion of atuation atio fo RTOR. Accoding to model (8), (9), (12), (13), (15) and (16), the elationhip between maximum queue length and atuation atio would neve change unle P value (confidence level) alte. Theefoe, the tend of the maximum queue length changing with atuation atio will not be alteed with the alteation of ignal timing, volume and RTOR o O-RTOR. In thi way, it i ufficient and convictive unde jut only one cae to tudy the elationhip between the maximum queue length and atuation atio. The pobability (P) i aumed to be 95% which i the value mot often quoted in the liteatue. The cuve eflecting the tend ha been geneated a follow (accoding to eq. (15), aumed that: C=90, g=45, RTOR i not pemitted): Figue 2 the tend of the maximum queuing length changing with atuation atio The maximum queue length inceae a atuation atio acend fo both ight tun- and though lane, epecially when x Little inceae of atuation atio will caue apid acend fo the length when x 0.85, which i bound to geatly inceae the atuation atio. Pactically, it i uneaonable

9 and uneconomical to geatly inceae the ecommended length jut fo atifying the little gow-up taffic volume. Conequently, it i neceay to make the taffic volume go back to an acceptable level befoe detemining the ecommended length when x In thi way, the exploation of citical taffic volume ha it ignificant ene and x 0.85 become the citical point which i ued to be the citeia fo detemining the citical taffic volume. Table 1 how the eult of citical ight-tun volume fo detemining the length of ight-tun lane in O-RTOR cae: Table 1 citical taffic volume Right-tun lane Geen Cycle Length Time Inteval Appaently, the le geen-to-cycle atio i, the malle the value of citical volume will be. That becaue the atuation atio will inceae with the deceaing of geen-to-cycle atio when taffic volume i a contant. In thi way, the volume (the citical volume) when x 0.85 will deceae with the eduction of geen-to-cycle atio. In the ame way, the citical volume in RTOR cae can alo be obtained with the ame analytical method, and the eult how that x 0.85 i till the citical point. Theefoe, the tudy of detemining the length of ight-tun lane cannot be diectly pefomed unle the actual volume i not geate than the citical volume. 5.2 Detemining the ecommended Length Conideing a combination of vaiable: ight-tun flow (50, 100, 150,, 650), taight-though flow (50, 100, 150,, 650), RTOR and O RTOR, co taffic (400, 800, 1200), geen-to-cycle atio (0.75, 0.5, 0.375), the ecommended length can be obtained though model-olving. 1. Geneal analyi Geneally, the tend of ecommended toage length changing with taffic volume ae in the imila way, hown in appendix. That i, when taffic volume gow up, the ecommended length will inceae a well. In ome cae, howeve, the ecommended length ae contant when the ight-tun volume o though volume gow up. Why doe thi happen? Appaently, the ecommended length i the lage pat of the maximum ight-tun queue length and the maximum though queue length. When the maximum though queue length i geate than the ight-tun queue length, the though volume i the dominant facto that influence the length until the ight-tun volume gow up to the extent at which the maximum ight-tun queue length exceed the though volume; on the contay, the ecommended ight-tun length i ubject to the ight-tun volume. Futhemoe, it i ditinctive that thee ae no exact ecommended length in the table when

10 C=120,g=45, P=95% and the ight-tun volume exceed 500veh/h and though volume upae 550veh/h. It jut becaue 500veh/h and 550veh/h ae epectively the citical ight-tun volume and the citical though volume. 2. The effect of geen-to-cycle atio on the toage length The toage length ha a tong elationhip with the geen-to-cycle atio, which i hown in table2: Table 2 The effect of geen-to-cycle atio on the ecommended length (hould note the unit fo all the numbe in all table, like m, feet ) geen-to-cycle time atio geen-to-cycle time atio geen-to-cycle time atio Right-tun (g/c)=0.75(c=60,g=45, P=95%) (g/c)=0.5(c=90,g=45, P=95%) (g/c)=0.375(c=120,g=45, P=95%) volume(vphpl) Though taffic volume(vphpl) Though taffic volume(vphpl) Though taffic volume(vphpl) / / / / / / / / / / / / The ecommended length inceae a geen-to-cycle atio deceae, epecially when ight-tun volume i in high level. That becaue unde the ame flow level, the queue length in low geen-to-cycle atio become geate than the length in high atio. 3. The compaative analyi of the ecommended length between two cae: RTOR and O-RTOR A compaative analyi ha been pefomed in thi pape and the eult i hown in table 3. Table 3 the compaion of the ecommended length fo both cae RTOR and O RTOR geen-to-cycle time atio (g/c) = 0.5 (C=90, g=45, P=95%) Right-tun volume (vphpl) Though taffic volume 150 (vphpl) Though taffic volume 300 (vphpl) Though taffic volume 450 (vphpl) Though taffic volume 600 (vphpl) O RTOR O RTOR O RTOR O RTOR RTOR CROSS TRAFFIC RTOR CROSS TRAFFIC RTOR CROSS TRAFFIC RTOR CROSS TRAFFIC Take the typical ituation (g/c=0.5) a an example, the ecommended length i geneally le when RTOR i pemitted than RTOR i pohibited, epecially when ight-tun volume i high. With egad to

11 the cae that RTOR i pemitted, the ecommended length inceae with the inceae of the co taffic volume becaue the numbe of the vehicle that can potentially make a ight tun duing the ed phae educe a the co taffic inceae. In ome cae, hown in table 3, the ecommended length emain unchanged when the ight-tun volume o co taffic volume inceae. That becaue the maximum queue length of the though lane, which i not ubject to the co taffic, i alway geate than the ight-tun queue length until the ight-tun volume i up to the citical point at which the maximum queue length of the ight-tun lane i geate. 6. DISSCUSIO The analytical method of detemining the toage length ha been dicued unde the ame confidence level. In thi ection, the effect of confidence level on the length i dicued, and then the eult of the length hown in table 3 i validated with imulation. 6.1 The impact of confidence level on ecommended length of ight-tun lane The P value (confidence level) i actually the confidence pobabilitie of no-oveflow and no-blockage, eflecting the level of the etiction fo oveflow and blockage. The equiement fo the ecommended toage length will be impoved with the iing of the P value. Take the cae when geen-to-atio equal to 0.5 a an example, the tend of the maximum queue length changing with atuation atio unde diffeent P value i hown a follow: Figue 3 the tend of the maximum queuing length changing with atuation atio unde diffeent P value A i hown in figue 3, diffeent cuve go in the ame way, though the length with high P value i lage than the one with low P value. Futhemoe, the citical point of the atuation atio on which the citical volume depend i till located in the place whee atuation atio i 0.85, being unelated to the P value. In thi way, the citical volume in diffeent P value will be the ame a the one when P equal to 95%. Howeve, the atuation atio inceae geatly a the P value ie up unde the ame condition of volume and ignal timing. Conideing diffeent cae: O RTOR o RTOR, co taffic (400, 800, 1200), Right-tun volume (150, 250, 350,450,550,650) and though taffic volume (150, 300, 450, 600), P (80%, 90%, 98%), the ecommended length of ight-tun lane ae obtained in table 4. It i demontated in table 4 that the ecommended toage length inceae when the P value i iing. Paticulaly, when the P value i lage than 90%, thi gowth tend eem to become obviou with the inceaing of the ight-tun volume. Fo example, when ight-tun volume i 550veh/h, the diffeence of ecommended length between P=90% and P=80% i ignificantly malle compaing with the cae

12 Right-tun volume (vphpl) between P=90% and P=98%; while thi diffeence i not that big when ight-tun volume i le than 550veh/h. Conequently, the impact of confidence level on ecommended length depend not only on the P value itelf but alo on ight-tun volume. Table 4 Recommended length of ight-tun lane unde diffeent P value (O RTOR) O RTOR geen-to-cycle time atio (g/c) = 0.5 (C=90, g=45) Though taffic volume Though taffic volume Though taffic volume Though taffic volume 150 (vphpl) 300 (vphpl) 450 (vphpl) 600 (vphpl) P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% Recommended length of ight-tun lane unde diffeent P value (RTOR) co taffic=400 Right-tun RTOR geen-to-cycle time atio (g/c) = 0.5 (C=90, g=45) co taffic=400 (vphpl) volume (vphpl) Though taffic volume 150 (vphpl) Though taffic volume 300 (vphpl) Though taffic volume 450 (vphpl) Though taffic volume 600 (vphpl) P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% Recommended length of ight-tun lane unde diffeent P value, co taffic=800 Right-tun RTOR geen-to-cycle time atio (g/c) = 0.5 (C=90, g=45) co taffic=800 (vphpl) volume (vphpl) Though taffic volume 150 (vphpl) Though taffic volume 300 (vphpl) Though taffic volume 450 (vphpl) Though taffic volume 600 (vphpl) P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% Recommended length of ight-tun lane unde diffeent P value, co taffic=1200 Right-tun RTOR geen-to-cycle time atio (g/c) = 0.5 (C=90, g=45) co taffic=1200(vphpl) volume (vphpl) Though taffic volume 150 (vphpl) Though taffic volume 300 (vphpl) Though taffic volume 450 (vphpl) Though taffic volume 600 (vphpl) P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98% P=80% P=90% P=98%

13 Veification of the eult of the ecommended length by VISSIM imulation The appoach maked ed in the diagam below i the objective appoach fo tudy. Figue 4 the netwok model of imulation The ecommended toage length of the ight-tun lane peented in table 3 ae validated in thi ection uing VISSIM imulation. Table 3 conit of a combination of input vaiable: O RTOR o RTOR, co taffic (400, 800, 1200), Right-tun volume (150, 250, 350,450,550,650) and though taffic volume (150, 300, 450, 600). VISSIM wa un 96 time (3600 fo each time with a total of 5760 min imulation time); the numbe of time when lane oveflow and/o lane blockage occu i obeved. The eult how that 85% to 96% of the total time, no oveflow and/o no blockage occued (figue 5). Thu, the ecommended length in table 3 ae eaonable and convictive. Figue 5 the Reult of VISSIM Validation Fo tudying whethe P value affect the accuacy of the ecommended length, the eult in table 4 ae alo validated uing VISSIM imulation. Table 4 conit of a combination of input vaiable: Right-tun volume (150, 250, 350, 450, 550, 650) and though taffic volume (150, 300, 450, 600), P

14 value (80%, 90%, 98%). VISSIM wa un 72 time (3600 fo each time with a total of 4320 min imulation time). It i found that 80% to 92% of the time no oveflow and/o no blockage occued, which i located in the acceptable level. Theefoe, ecommended length in thi pape ae eaonable and the vaiation of P value ha little influence on the accuacy of ecommended length model of thi tudy. 7. COCLUSIOS In thi pape, the tudy of detemining the toage length i pefomed, conideing two cae (RTOR and O RTOR). Fo each cae, two citeia ae dicued: oveflow and blockage. Two imple and eaie-to-olve model, compaing with the fome guideline, ae developed baed on Queuing Theoy Pinciple fo detemining the toage length of ight-tun lane. The effect of atuation atio and confidence level on the toage length ae alo dicued, and the citical point fo each cae ae given out to avoid coting too much in the contuction of ight-tun lane jut fo little taffic volume inceaing, which i little tudied in exiting guideline. Then the ecommended length in typical cae ae povided, and the effect of pimay facto on the length i alo dicued. Finally, the compaative analyi unde diffeent confidence level i tudied. Thee ae till ome emaining iue expected to be tudied in the futue eeach. The impact of pedetian & bicycle activitie and tanit vehicle & bu top location which have not been taken into conideation fo detemining the toage length in thi pape. Actually, co taffic flow i not the only taffic team that ight-tun vehicle need to un co; pedetian and bicycle may alo hold up the nomal ight-tun movement, epecially when the volume i in high level. A tanit vehicle ha a much longe body than a ca, which mean the popotion of tanit vehicle affect the toage length in actual ditance. Futhemoe, the bu location appoaching an inteection ha an effect on the aangement of the ight-tun lane, which may affect the toage length. The two emaining iue ae the main diection fo the futue eeach. We ae planning to make a deep exploation to examine the effect of pedetian & bicycle and bu location on the toage length. ACKOWLEDGEMET Thi eeach i uppoted by the Chinee ational Science Foundation (CSF) unde gant # The autho would alo like to thank the anonymou efeee fo thei contuctive uggetion. REFERECES 1. Shinya Kikuchi, opadon Konpaet. Detemining the Length of the Right-Tun Lane at a Signalized Inteection. Jounal of the Tanpotation Reeach Boad, o.1726, TRB, ational Reeach Council, Wahington, D.C., 2007, pp Feng-Bo Lin. Right-Tun-on-Red Chaacteitic and Ue of Auxiliay Right-Tun Lane. Tanpotation Reeach Recod 1010, ational Reeach Council, Wahington D.C., 1985, pp Tian, Z. and. Wu. Pobabilitic Model fo Signalized Inteection Capacity with a Shot Right-Tun Lane. Jounal of Tanpotation Engineeing, ASCE, Vol. 132, o. 3, 2006, pp Tako, A.P. Pedicting Right Tun on Red. In Tanpotation Reeach Recod: Jounal of the

15 Tanpotation Reeach Boad, o. 1776, TRB, ational Reeach Council, Wahington, D.C., 2001, pp Pline, J.L., ed. Taffic Engineeing Handbook, 5th edition, Intitute of Tanpotation Enginee. Pintice Hall, Englewood Cliff, ew Jeey, 1999, pp Fedeal Highway Adminitation. Signalized Inteection: Infomational Guide. FHWA, Viginia, Ameican Aociation of State Highway and Tanpotation Official. A Policy on Geometic Deign of Highway and Steet. AASHTO, Wahington, D.C, Stove, V.G. and F.J. Koepke. Tanpotation and Land Development. IntituteofTanpotation Enginee. Pentice Hall, Englewood Cliff, ew Jeey, 1988, pp Delawae DOT. DelDOT Road Deign Manual Chapte 7 Inteection. Delawae Depatment of Tanpotation, Acceed May 20, Califonia DOT. Highway Deign Manual Englih Veion Chapte 400 Inteection At Gade. Diviion of Deign, Califonia Depatment of Tanpotation, Acceed June 15, Minneota DOT. Road Deign Manual Chapte 5 At-Gade Inteection. Deign Sevice Section, Minneota Depatment of Tanpotation, Acceed May 20, Floida DOT. Manual of Unifom Minimum Standad fo Deign, Contuction and Maintenance fo Steet and Highway. Floida Depatment of Tanpotation, Acceed June 16, Wahington State DOT. Deign Manual M Chapte 910 Inteection At Gade. Wahington State Depatment of Tanpotation, Acceed June 15, Tenneee DOT. Roadway Deign Guideline. Deign Diviion, Tenneee Depatment of Tanpotation, Acceed June 16, Jingyuan Wang, Wei Wang. Calculation of Stoage length fo Left Lane with Potected Phae. Jounal of Southeat Univeity. anjing, 2010, vol. 40, pp Gatti, J.L. Tun Lane Stoage Length Deign: Theoy fo the Pactitione. In Tanpotation Reeach Recod: Jounal of the Tanpotation Reeach Boad, o. 1737, TRB, ational Reeach Council, Wahington, D.C., 2000, pp APPEDIX Right-tun Volume Veh/h C=60, g=45, P=95% Though Taffic Volume veh/h

16 C=90, g=45, P=95% Right-tun Though Taffic Volume veh/h Volume Veh/h C=120,g=45, P=95% Right-tun Though Taffic Volume veh/h Volume Veh/h / / / / / / / / / / / / / / / / / / / / 550 / / / / / / / / / / / / / 600 / / / / / / / / / / / / / 650 / / / / / / / / / / / / /