13th COTA International Conference of Transportation Professionals (CICTP 2013)

Transcription

1 Avalable onlne at ScenceDrect Proceda - Socal and Behavoral Scen ce s 96 ( 203 ) th COTA Internatonal Conference of Transportaton Professonals (CICTP 203) An Improved Optmzaton Method for Isolated Sgnalzed Intersecton Based on the Temporal and Spatal Resources Integraton Shanglu He a *, We Wang a, Jan Zhang a, Je Yang a a School of Transportaton, Southeast Unversty, No.2, S Pa Lou, Xuanwu Dstrct, Nanng Cty, 20096, Chna Abstract Recent studes ndcate that the optmzaton desgn methods for the solated sgnalzed ntersecton, whch ntegrate the temporal and spatal resources, can acheve more effectve optmal desgn relatvely. Ths paper presents extenson wor to further mprove the lane-based method from two aspects of ntegratng temporal and spatal resources. One s adustng exstng constrants to reserve some conflct movements. The other s addng a constrant to reflect the adverse effects caused by the lmtaton of short lane. The lane marngs and sgnal settngs are taen as bnary-type control varables to form BMILP formulas solved by Lngo. The East Beng Rd and Danfeng St ntersecton n Nanng, Chna s taen as an example. Optmzaton and smulaton results ndcate that the new method can obtan better operaton performance than the lane-based method, and t s able to reflect the practcal operatonal performance of the ntersecton whch s nfluenced by short lane wthn lmted length. 203 The The Authors. Publshed Publshed by Elsever by Elsever Ltd. Open B.. access under CC BY-NC-ND lcense. Selecton and and/or peer-revew peer-revew under responsblty under responsblty of Chnese of Overseas Chnese Transportaton Overseas Transportaton Assocaton (COTA). Assocaton (COTA). Keyword: Isolated sgnalzed ntersecton; Temporal and spatal optmzaton; Short lane; Bnary-Mxed-Integer-Lnear-Programmng (BMILP). Introducton In practce, ntersecton can be controlled n varous ways, whereas solated sgnal-controlled ntersectons are stll appled wdely. The operatonal performance of most solated sgnalzed ntersectons does not functon well, mostly because the temporal and spatal resources of the ntersecton are not fully used. There s potental reserved capacty of the ntersecton, whch can be optmzed by ntegratng the temporal and spatal resources. In a word, t s meanngful to study the optmzaton method for solated sgnalzed ntersectons. * Correspondng author. Tel.: ; fax: E-mal address: slhemcey@26.com The Authors. Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty of Chnese Overseas Transportaton Assocaton (COTA). do: 0.06/.sbspro

2 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Ths paper s organzed as follows: Secton 2 s for lterature revew. Secton 3 presents the proposed optmzaton method, whch ncludes the defnton of nput data and control varables, basc and addtonal constrants and the optmzaton obectve. Secton 4 employs feld ntersecton data to valdate and compare the mproved method wth the one proposed by Wong. Fnally, secton 5 gves some concludng remars and recommendatons for future study. 2. Lterature Revew The frst attempt, whch combnes the actual lane-use wth sgnal settngs nto a desgn framewor to smultaneously optmze lane-use and sgnal settngs, was realzed by Lam et al. (997). Ther fndngs ndcated that a proper match between the lane-use and sgnal settngs certanly mproved the overall performance of an ntersecton. Recently, the lane-based optmzaton method combnng the desgn of lane marngs and sgnal settngs for solated sgnalzed ntersecton was developed and ts formulaton was a drect extenson of the phase-based method n whch all phase-based varables and relevant controllng constrants are adopted and adusted accordngly to ntegrate wth other new lane-based varables and constrants. The lane marngs were optmzaton framewor. The lane-based method was formulated as a mathematcal program n whch a set of lnear constrants s set up to ensure the feasblty and safety of the resultant optmzed lane marngs and sgnal settngs. The ntersecton capacty maxmzaton and cycle length mnmzaton problems were formulated as BMILP whch are solvable by any standard branchand-bound routne (Wong and Wong, 2003a, b, c; Wong et al., 2006). By addng new nteger varables to represent the numbers of approach lane n traffc arms, an extenson wor to obtan results of approach- and extlane numbers, lane marngs and sgnal settngs smultaneously was presented (Wong et al., 20). In manland, Chna, the researches about the optmzaton method for ntegratng temporal and spatal resources of solated sgnalzed ntersectons are manly phased optmzaton method. The optmzaton process ncludes three phases. Frstly, generate an ntal desgn of ntersecton lane marngs and sgnal settngs. Secondly evaluate the ntal desgn by smulaton. If the evaluaton result s not satsfed, optmzaton of ntersecton desgn wll be taen out. The optmzed desgn wll be smulated and evaluated agan, thus a recurson procedure s formed (Wang, 2006; Lu et al., 2009). However ths method s complex and tme consumng. Apparently lane-based method has an advantage n optmzng solated sgnalzed ntersecton. In the recent lterature, all conflcts n the ntersecton were prevented. However when the amount of vehcles n conflctng traffc flow s small, they may have a small mpact on the performance of ntersecton. So s t stll necessary to avod all the conflct movements? Moreover current methods do not consder the effect of short lane, whch neglects the effect of queue blocage to or from the short-lane secton and leads to a reduced total capacty of the approach (Wu, 2007). Further study about the nfluence of short lane should be carred on. 3. Methodology 3.. Input data and control varables To mplement the proposed optmzaton method for the temporal and spatal desgn of an solated sgnalzed ntersecton, dverse nput data and control varables are requred and defned as follows: Nomenclature. Input data () Intersecton geometry data N Number of arms n an solated ntersecton

3 698 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) A,,, N Number of approach lanes n the arm E,,, N Number of ext lanes n the arm (2) Movements on the ntersecton (u,v) c (3) Sgnal data mn max A par of vehcle movements enterng an ntersecton A set contanng all vehcle movements A subset of referrng to ncompatble movements whch are selected to be prevented c ( c ) Mnmum (Maxmum) cycle length Q,,, N ;,, N Actual traffc demand turnng flows,, g,,, N ;,, N Mnmum green duratons for average lanes, g, (,, N ); (,, A ) Optmum green duratons for short lanes, (,) uv, uv Mnmum clearance tmes (4) Saturaton flow data s,,, N ;,, A Lane saturaton flows for straght-ahead movement,, p,,, N ;,, A Maxmum acceptable degree of saturaton,,,, N ;,, N Converson factor of turnng movement to straght-ahead movement n the calculaton of lane saturaton flows 2. Control varables () Bnary varables,,,,, N;,, N ;,, A Permtted movement at lane from arm to arm, (, ),(, ),, l, m l m c Successor functons of conflct turnng movement (,) and (l,m) (2) Contnuous varables q,,, N ;,, N ;,, A Assgned lane flows n desgn,,, Common flow multpler Recprocal of cycle length c B,,, N ;,, N Begnnngs of green for turnng movements, D,,, N ;,, N Duratons for green for turnng movements, b,,, N ;,, A Begnnngs of green on approach vehcle lanes

4 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) d,,, N ;,, A Duraton of green on approach vehcle lanes, 3.2. Basc constrants Based on the method proposed by Wong (2003a, b, 20), the basc constrants of mproved method can be dvded nto three categores, whch are movement constrants, flow constrants and sgnal constrants. The three nds of constrants referrng to channelzaton, flow and sgnal respectvely are three crucal factors n the ntersecton desgn. Tae a crossroad ntersecton as an example, see Fg, the detaled constrants are ntroduced as follows A Ext lanes Approach lanes E 3 4 Arm A Fg.. A crossroad example ntersecton of arm and lane confguraton 3.2. Movement constrants Constrant : Mnmum permtted movement on approach lanes N,, Constrant 2: Mnmum ext lanes n ether arm Constrant 3: Prohbted movement A,,,,, N ;,, A () E,,, N ;,, N (2) A,,, Q,,, N ;,, N (3) and,, q,, 0,,, N ;,, N ;,, A (4) where s an arbtrary large postve constant number. Constrant 4: Permtted movements across adacent lanes,,, N;,, N 2; m,, N ;,, A (5) m,,,,

5 700 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Flow constrants Constrant 5: Conservaton of traffc demand and assgned flows on approach lanes A s ntroduced to adust the gven actual. A Q q,,, N ;,, N (6),,, Constrant 6: Flow factor between adacent lanes N N ( q,,, ) ( q,,,),,,,,,,, s, s, (2 ) (2 ),, N ;,, N ;,, A Constrant 7: Maxmum acceptable degree of saturaton N d, ( q,,, ),,, N;,, A (8) p s Sgnal constrants,, Constrant 8: Cycle length The recprocal of cycle length, =/C, s defned as a control varable. cmn cmax (9) Constrants 9: Lane sgnal settngs (,, ) b, B, (,, ),,, N;,, N ;,, A (0) and (,, ) d, D, (,, ),,, N;,, N ;,, A () Constrant 0: Begnnngs of green B, 0,,, N;,, N (2) Constrant : Duraton of green D, g,,,, N;,, N (3) Constrant 2: Order of sgnal dsplays n dfferent stuatons avodng selected conflcts Conflcts n the ntersecton can be dvded nto three types,.e., mergng, splttng, and crossng. The three types of conflct cause dfferent degree of danger to the ntersecton. Splttng s not under consderaton n the formulaton. Crossng s most dangerous, so ths nd of conflcts should be prohbted totally. When traffc flow n mergng conflcts s small, the effect caused by mergng can be neglected. The set of ncompatble sgnal phases, c, can therefore be derved from, whch s the set of crossng (or crossng and mergng) conflcts chosen to be prevented. For any two ncompatble sgnal phases (, ) and (l, m) n c, the order of sgnal dsplays s controlled by the bnary-type successor functon (Heydecer, 992),,, l, m(=0 or ). The followng constrant can be presented for the successor functons: Constrant 3: Clearance tme, lm,, lm,,,, ((, ),( l, m )) c (4) D (2 ) D B, (,) uv (5) l, m,, l, m,, l, m, n,, u, v (7)

6 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Addtonal constrant At an solated sgnalzed ntersecton, there are normally turnng lanes for left-turn or rght-turn flows, whch have lmted length. Usually, the current lane-based methods do not exactly treat short lane at sgnalzed ntersecton. The short lanes are treated as exclusve lanes. Such a treatment neglects the effect of queue blocage to or from the short-lane secton. s4, s4,2 s4,3 s ( s4, s4,2) g / g s4,3 exclusve lane = Saturaton flow s4, s4,2 exclusve lane =2 short lane =3 g 2 g g t Fg. 2. Example of an approach arm wth short lane Fg. 3. Saturaton flow of approach arm changng over tme It had also been found that the approach capacty wth short left-turn or rght-turn lanes s specfcally related to the length of short lane, the rato between the through and turnng vehcles and the green tme both for through and turnng vehcles (Wu, 2007). Tae Fgure 2 as an example, let s 4,, s 4,2 represent the saturaton flow of exclusve lanes and s 4,3 s the saturaton flow of short lane. If the length of short lane s nsuffcent, when the green starts, three lanes can be fully used durng the frst g tmes and the total saturaton flow of the approach arm 4 s s 4, s 4,2 s 4,3. g s the tme needed to let all the vehcles on short lane to depart. In the followng g 2 tmes, the short lane cannot be used, so the saturaton flow of approach s reduced to s 4, s 4,2. Referrng to Fgure 3, the effectve saturaton of short lane can be calculated as s s g / g. 4,3 4,3 s 4,3 and g should satsfy the requrement as follows: s4,3 Ls /( lcg ), g Lt s / l c. where L s s the length of short lanes; l c s the average length occuped by each car on short lane and every car taes average tme t to depart from the ntersecton; g s the green tme of the phase. If g g, a vehcle queue on short lane can be released entrely, and s4,3 s 4,3 means that the short lane s not fully used. If g g, a vehcle queue on short lane can also be released entrely. If g g, a vehcle queue on short lane cannot depart at one tme, there wll be a queue agan. When g g and g g, s4,3 s 4,3 and the short lane s fully used. So n order to fully use the short lane and avod queung agan, we set an addtonal constrant. Constrant 4: Optmal duraton of green for short lane wth lmted length g Only f the duraton of green for short lane s equal to (the optmum green duraton for short lane), can the short lane be fully used and blocage queue be prevented. When an ntersecton has short lanes n lmted length, the followng constrant s requred. d, g, g Lt l s number of short lane (6),, s / c

7 702 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Optmzaton obectve One mportant desgn aspect of sgnalzed ntersecton s to maxmze the capacty of the ntersecton wth the for the vehcle movements n the ntersecton wll ncrease n proporton to the demand matrx (Wong et al., 2006), the problem becomes one of determnng the largest common multpler, max, whch can be max < then ndcates that the ntersecton s overloaded by 00(- max ) percent, and a value of max > ndcates a reserve capacty of 00( max -) percent. So the maxmzaton of s the optmzaton obectve of the ntersecton capacty maxmzaton problem. 4. Implementaton In ths secton a real ntersecton s taen as an example. Wth feld data, the capacty maxmzaton can be effectvely formulated as a Bnary-Mxed-Integer-Lnear-Program (BMILP) and standard branch-and-bound technque s appled to solve for the global optmum soluton. The processng software LINGO s adopted to solve BMILP and acheve the optmzaton results. Then the optmzaton scenaros are compared usng smulaton software SYNCHRO Data sources The East Beng Rd and Danfeng St ntersecton, located at Nanng, Chna, s a typcal four-arm sgnalzed ntersecton wth short lanes. The south, west, north and east arms are Danfeng Street (), East Beng Road (2), Anren Street (3) and East Beng Road (4) respectvely (see Fg 4). Anren Street arm 3 Approach lanes Ext lanes Ext lanes East Beng Road arm 2 Approach lanes Approach lanes Ext lanes East Beng Road arm 4 Approach lanes Ext lanes Danfeng Street arm (a) Screenshot from google map (b) schematc dagram of the ntersecton Fg. 4. Layout of the East Beng Rd and Danfeng St ntersecton 4.. Geometrc condtons More detal nformaton about the ntersecton geometrc condtons are lst n Table. Table. Geometrc condton of East Beng Rd and Danfeng St Intersecton Approach East Beng Road (4) Anren Street (3) East Beng Road (2) Danfeng Street ()

8 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Number of lanes (channelzaton) 4 (L,2T,R) 5 (2L,2T,R) 4 (L,2T,R) 4 (L,2T,R) Length of short lane (m) Traffc flow condtons The pea-hour traffc flow of East Beng Rd and Danfeng St Intersecton s presented n table 2, whch s obtaned by artfcal countng method. Table 2 Pea hour traffc flow of East Beng Rd and Danfeng St ntersecton (pcu/h) Ext Approach Three optmzaton cases Case Based on the lane-based method (Wong 2003a), all mergng and crossng conflcts are avoded. Maxmze Subect to constrants n ()-(5), avodng all nds of conflcts. Case 2 The left-turn demand traffc flows Q 2,3 and Q 4, are comparatvely low, so the mergng conflct movements (2,3,4,3) and (2,,4,) can be reserved. In Case 2, the optmzaton obectve stll subects to basc constrants, whle Constrants 2 and Constrants 3 are adusted to reserve the ncompatble movements (2,3,4,3) and (2,,4,). Maxmze Subect to constrants n ()-(5), reservng mergng conflcts (2,3,4,3) and (2,,4,) on the ntersecton. Case 3 Due to the traffc nvestgaton, blocage queue of short-lane occurred on arm and arm 3 sometmes, whch reduced the ntersecton capacty,.e. the lmtaton of short-lane s requred to be consdered n the constrants. Based on Case 2, Case 3 adds the addtonal constrant, consderng the lmt of short-lane on arm and arm3. Maxmze Subect to constrants n ()-(6), reservng mergng conflcts (2,3,4,3) and (2,,4,) on the ntersecton Optmzaton method Three cases mentoned n Secton 4..3 are formulated nto three BMILPs, whch can be solved easly by LINGO. In order to solve these three formulas, some parameters stll need to be llustrated n ths secton. Frst, maxmum cycle length s set to be 20s n all cases. The maxmum acceptable degrees of saturaton on -ahead movement (n tcu/h) s estmated by the formula, whch s proposed by Kmber et al. ( Q, s tabulated n Table 2 n pcu/h. To account for the effects of dfferent turnng movements, tcu converson factors,.3 and. and are the

9 704 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) numercal factors appled to all rght-turn and left-turn vew of the effect of ther turnng paths. And.0 wll be appled for all straght-ahead movements. The mnmum green duratons g, are 5s for 6s. The average length occuped by each car on short lane s assumed to be 0m and every car taes average tme t to depart from the ntersecton s 4.8s Results Table 3 summarzes the general optmzaton results ncludng the maxmzed common flow multplers, the correspondng optmzed reserve capactes and the optmzed recprocal of cycle lengths of the three cases. All three programs ran on a PC equpped wth Intel Core 7 processor cloced at 3.40 GHz and 4.00 GB of RAM. It can be observed from the Case and Case 2 that 3.54% more traffc based on the gven demand flow matrx could enter the ntersecton and the degrees of saturaton of all approach traffc lanes are stll under 90%. Whle the lmtaton of short-lane length s consdered, the operatonal performance n terms of the reserve capacty s reduced. There s only 26.47% reserve capacty n Case 3, whch s smlar to the real operatonal performance of ntersecton wth lmted short-lanes. When the desgn obectve s to maxmze the capacty, the optmzed cycle length s all bndng at the maxmum allowable lmt whch s 20s for all three cases. The computng tmes for all three cases tae less than 2mn and as expected, tend to have the same change as the number of varables changes. Table 3 Summary of optmzaton results Case max Optmzed reserve capacty (%) Optmzed (s-) Runtme of LINGO (hh:mm:ss) /20 00:0: /20 00:0: /20 00:0:40 Fg. 5(a) plots the results of the optmal lane marngs for the ntersecton capacty maxmzaton n the three study cases. It can be observed that the desgn of lane marngs for optmal control of traffc s smlar for all three cases, whch ndcates the addton of mergng conflcts and the consderaton of short-lane have relatvely small mpact on channelzaton. The complcated cycle structure s formed automatcally durng optmzaton. Optmzed sgnal stages and groups are determned wth mnmal manual nput (see Fg. 5(b)). Arm 2 Arm 2 Arm 2 Arm Case Arm Case 2 Arm Case 3 (a) Optmzaton results of channelzaton

10 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) Case Case 2 Case 3 (b) Optmzaton results of sgnal Fg. 5. Optmzaton results 4.4. Comparatve Analyss For further comparson, smulaton models of three optmzaton results are bult by SYNCHRO 7. The ntersecton confguraton and lane marngs are based on Table and Fg. 5. Matrx of Q, (see Table 2) are nput as the demand traffc flow. The sgnal of ntersecton s set based on Fg. 6. The total smulaton tme s 90mn and recordng tme s 60mn. A summary of the smulaton results for three cases s shown n Table 4. ehs entered and ehs exted represent the capacty of ntersecton. It can be observed that Case and Case 2 have almost the same capacty and Case 3 has less capacty, whch s consstent wth the optmzaton results (see Table 3) and also valdates that short-lane wth lmted length reduce the capacty of ntersecton. Comparng Case wth Case 2, from the rows of the travel tme and total delay n Table 4, t can be llustrated that the operaton performance of Case 2 s better than Case. However, as some conflcts are reserved, the total stops are ncreasng n Case 2 compared to Case. Compare Case 2 to Case 3. Due to the nfluence caused by the lmtaton of short-lane, the operaton performance of ntersecton s worse. Accordng to the comparson analyss, the mproved optmzaton method (e.g., Case 2) s effectve and attractve. Table 4 SmTraffc smulaton summary Case 2 3 ehs entered ehs exted Travel tme (hr) Total delay (hr) Total stops Conclusons and Future Wor In ths paper, an mproved optmzaton method s presented for ntegratng temporal and spatal resources of solated sgnalzed ntersecton. Based on the lane-based desgn method (Wong, 2003a), two changes are made. One s redefnng the constrants to select conflct movements whch should be avoded. Other constrants of optmal green duraton for short-lane wthn lmted length are added. The capacty of an ntersecton s maxmzed through maxmzng the common flow multpler that s formulated as a BMILP problem, whch s solved by a standard branch-and-bound routne n LINGO. Three cases wth dfferent constrants are presented. Accordng to the comparatve analyss, the mproved optmzaton method (e.g., Case 2) s effectve

11 706 Shanglu He et al. / Proceda - Socal and Behavoral Scences 96 ( 203 ) and attractve. What s more, wth the addtonal constrants, the mproved optmzaton method can obtan better results whch are closer to the practcal stuaton. In the future, the cycle length and delay mnmzaton problems can be formulated. Pedestran phases should needed to get the crtcal traffc flow of conflct movements that can be reserved. Further researches are Acnowledgements Ths wor was supported by Innovaton Proect of Graduate Students of Jangsu Provnce of Chna (NO: CXLX-042). References Lam, W.H.K., Poon, A.C.K., Mung, G.K.S.. (997). Integrated model for lane-use and sgnal-phase desgns. ASCE Journal of Transportaton Engneerng, ol.23, No.2, C.K Wong, S.C Wong. (2003a). Lane-based optmzaton of sgnal tmngs for solated unctons. Transportaton Research part B: Methodologcal, ol.37, C.K Wong, S.C Wong. (2003b). A lane-based optmzaton method for mnmzng delay at solated sgnal-controlled unctons. Journal of mathematcal modelng and algorthms, ol.2, No.4, C.K Wong, S.C Wong. (2003c). Lane-based optmzaton of traffc equlbrum settngs for area traffc control. Journal of advanced transportaton, ol.36, No.3, C.K Wong, S.C Wong, C.O. Tong. (2006). A lane-based optmzaton method for the mult-perod analyss of solated sgnal-controlled unctons. Transportmetrca, ol.2, No., C.K Wong, B.G. Heydecer. (20) Optmal allocaton of turns to lanes at an solated sgnal-controlled uncton, Transportaton Research Part B: Methodologcal, ol Wang Jngyuan. (2006). Study on practcal methods of optmzaton for ntegratng tmng and spacng resources n sgnalzed ntersectons. Nanng, PhD thess, Southeast Unversty. Lu Pehua, Yu Quan, Lu Jnguang, Lu Xaomng. (2009). Combnaton optmzaton of Canalzaton and sgnal tmng n sgnalzed ntersecton, Journal of Transport Informaton and Safety, ol.27, No.3, Nng Wu. (2007).Total approach capacty at sgnalzed ntersectons wth shared-short lanes: a generalzed model based on smulaton study, presented at the Transportaton Research Board 86th Annual Meetng, preprnt R.M. Kmber, M. McDonald, N. Hounsell. (986). The predcton of saturaton flows for road unctons controlled by traffc sgnals. TRRL Report, RR67. Transport and Road Research Laboratory, Crowthorne. Heydecer, B.G. (992). Mathematcs n Transport and Plannng and Control(pp:57-67). Clarendon Press, Oxford.