双向绿波带优化算法.pdf

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第 1l卷第 1期 2011年 2 月 Journal of Transportation Systems Engineering and Information Technology February 201 1 交通运输系统工程与信息 V01．11 NO．1 文章编号： 1009—6744 (2011)01—0061—12 Variable-Bandwidth Progression O ptim ization in Traffi c Operation HU Pei—feng ，TIAN Zong—zhong ，YUAN Zhen—zhou ， JIA Shun—ping (1．Department of Civil& Environmental Engineering，University of Nevada，Reno，NV ，USA 89557 2． School of Traffic and Transportation，Beijing Jiaotong University，Beijing 1 00044，China) Abstract： Attempts are often made to find an optim al coordinated control plan for a group of traffi c signals in urban areas，such that platoons of vehicles can proceed through a continuous series of green lights without stopping，thereby．reducing considerable unnecessary delay． One main objective of coordinated control is to provide the maximum bandwidth progression by adliusting the offset and phase sequence pattern for each sig— nalized intersection． M ost models and methods currently being used are based on mixed—integer linear pro— gramming (MILP)， which is a mathematical optimization model originally formulated by Little et a1．in 1966． A basic limitation of the M ILP is that it adds a large num ber of com plex constraints for traffic control networks． In this paper， a new simple m ethod is introduced for finding the optim ization plan of arterial and network control by maxim ization of variable bandwidth． This method has not any ”loop’’ constraints and a completely new approach eompares to the M ILP method applied in this field． In addition，the results of two examples this paper provided validity and feasibility of this new approach in real applications of traffic signal coordinati0n contro1． K ey w ords： traffic engineering；traffi c control；variable bandwidth progression； offset； NEM A phase se— quence pattern CLC num ber： U491．51 D ocum ent code： A 交通运行管理中的可变绿波带优化胡佩峰，田宗忠，袁振洲，贾顺平 (1．美国内华达大学雷诺分校土木与环境工程系，雷诺 89557，美国； 2．北京交通大学交通运输学院，北京 100044) 摘要：在城市交通控制中，很多研究尝试为多个信号交叉口设计最优的协调控制方案，从而使得车队在通过多个交叉口时能够获得一系列连续的绿灯信号，无需停车、不间断地运行，这样可减少一些不必要的停车延误时间，而这种停车延误在现实中往往比较可观．此类协调控制的主要目标之一是获取最大绿波带，通过调整各个交叉口之间的相位差以及各个交叉口本身的相序来实现．目前在实际中得到应用的有关模型和方法大多是以混合整数规划为基础的一种线性最优化模型，最早由 Little等人于 1966年提出．这种模型的基本局限性在于，对于面控系统，需要引入数量众多的复杂约束．本文提出了一种新型简便的最优化方法，通过最大化可变绿波带实现对干线和网络各信号交叉口的最优协调控制．从应用范围来看，该方法与混合整数规划方法的不同点在于规避了对实施协调控制的道路网络的封闭性要求，因而是一种全新的方法．此外，本文还利用 2个实例对该方法在交通信号协调控制中的有效性和实用性进行了验证．关键词：交通工程；交通控制；可变绿波带；相位差；NEMA 相位系列中图分类号： U491．51 文献标识码： A 收稿日期：2010-07—26 修回日期：2010—1 1—10 录用日期：2010—12—01 作者简介：胡佩峰 (1981一)，男，博士生．通讯作者：zongt@unr．edu

62 交通运输系统工程与信息 2011年 2月 1 Intl oduction model in 1996． called “M ULTIBAND 一 96”。 which The main objective of coordinated traffic signal could optimize all the signal control variables in a net— control is to keep traffic progressing in a platoon m ini— work． During the same period， the Texas Transporta— mizing delays or stops throughout the signal system ． tion Institute developed “PASSER IV ”， a personal Through proper synchr0nization of signal timing along com puter—based program for optimizing signal timings arterials or urban networks，coordinated control plans for arterials and multi--arterial closed—-loop net-- can effectively reduce stops，delays and excessive fuel works[… ． Currently．many researchers are continu— consumption． Two main m ethods have been used to a— ing to research this topic； however， most recent en— chieve this objective．The first is based on total delay deavors have tried to improve the effi ciency of these minimization in the signal system l 一， and the other models through the help of different m athematical al- focuses on bandwidth maxim ization along an arteri— gorithms【一． Particularly． genetic algorithm s com — a1t ， ] ． Severa1 other researchers have combined the bined with the M ILP are the m ost popular method of delay m inim ization and bandwidth maximization mod— finding the optimal solution fo r coordinated traffi c sig— els to obtain an optimal solution for coordinated signal nal tim ing plans along arterials or in networks． system s[ 一． The methodology presented 、in this pa． This paper presents a new approach to obtain the per achieves an optim al traffi c signal control plan by optim al solution by determ ining the critical variables maximizing total weighted bandwidth of the traffic sig— of coordinated signal control， such as NEM A phase nal system ．Thus，the following literature review fo cu— sequence patterns and offsets． This new approach is ses on research and documents pertaining to band— easy to follow and can be implem ented using common width maxim ization． computer programming languages，such as C ，C ++ ， In 1966． Little et a1．[5 3 first presented a mathe— Visual Basic，et a1． The rem ainder of this paper is matical bandwidth maxim ization model， called the composed of three sections． Following this introduc· mixed—integer linear program (MILP) mode1． Their tion，the first section introduces the new optimization synchronization method produced two possible results： approach．The second section provides two typical ex— (1)the biggest possible bandwidth of equal size for amples to demonstrate the practical applicability of both directions of an arterial，and (2) favoring one the proposed approach． At last， conclusions are direction of an arterial with a large bandwidth and drawn regarding the proposed approach based on the then finding the best possible bandwidth in the oppo— analysis results from the examples． site direction，if feasible． Based on this model，Little et 。1．【lo 3 developed a new mode1 ca11ed ” M AX— 2 M ethodology BAND ” which could yield a global optimal solution， Coordinated traffi c signal control is a strategy to finding cycle time， offsets， and NEM A phase se— provide a smooth flow of traffic along arterials and net— quence patterns to maximize the weighted com bination works，reducing travel times， stops， and delays． Co— of the bandwidths in both directions along an arteria1． ordinated signal systems operate most effi ciently when In 1988． Chang et a1．[… extended this m odel to a traffic volumes between adjacent intersections are new version called “M AXBAND 一 86” which could heavy and signalized intersections are in proxim ity to oDtim ize mu1ti arteria1 networks． Gartner e nZ．[12] each other． W hen traffic between each signalized in— presented an optim ization approach for arterial pro—- tersection can maintain a good platoon structure， co— gression that could generate variable bandwidth in ordination of the signals will be m ore—beneficia1． In which each directional road segm ent obtained an indi— cases where traffi c volumes are low and vehicles arrive vidually weighted bandwidth fo r different traffi c vol— at a signal randomly，or when signals are suffi ciently um e scenarios between intersections． Based on this separated， then coordinated signal control operations approach，Stam atiadis and Gartne developed a new may provide few distinct benefits[ ．

第 11卷第 1期 Variable—Bandwidth Progression Optimization in Traffic Operation 63 Time—space diagram s are a com monly used tool the signal phases at an intersection， including the to depict the quality of signal tim ing and progression． green time plus any change interva1． The cycle length A tim e—space diagram of three intersections is shown in Fig．1，and the associated NEM A phase sequence patterns are shown in Fig． 2． In Fig．1， the cycle of of each signalized intersection should be equal to (or an exact multiple of)the minimum cycle time of all 一厂一厂一厂 9 ；妻一鼢 signals in the coordinated control system ． each intersection is the same though their green tim e (2)Split of a phase． intervals along arterials are different． Assume out— W ithin a cycle， split of a phase is the portion of bound direction is from intersection 1 to 3， and in— tim e allocated to each phase at a signalized intersec— bound direction is the opposite． Bandwidth 1 2 in tion． In this paper，the split of a phase is measured Fig．1， which is the bandwidth between intersection 1 by seconds and are considered as the effective green and 2 in the outbound direction，is greater than Band— tim e fo r the phase． width 23． Additionally， the offset reference point is (3)NEMA phase sequence pattern． the end of the barrier on the side street． Thus， the NEMA phase sequences used in this paper are offset of intersection 1 is zero，and the offset of inter— NEM A phase sequences， which employ a ‘‘dual ring section 2 and 3 is shown in Fig．1． In Fig．2， four concurrent” timing process and predetermined phase NEMA phase sequences along the arterial are shown order to label the operation sequence for each individ— clearly， whereas not shown for crossing streets． ual movem ent at the signalized intersection． Fig． 2 (1)Cycle length． indicates the four possible patterns of NEM A phase Cycle length is the total signal time to serve all sequences that are analyzed in this paper．融 ■ §《… … ￡j蛆 g《§≥ 。 l §捧《__ _ _目 _一 i … … 《 l 0《《《 ∞ … … 《 ∞ ≈ E ∞ ∞■ ■ ■ ■ ■ 嘲 nbcm喇 D~ ctcn 。，、 ∽ ii &■日鬻％舔 l2g§ §《鞲 … ； ∞∞ l jj聪豳；＼ … … … 一 ■ g_ 口 __ ∞口一％舞以《g l § ■ ■_——— 一。翩 L蝴 ∞ d： cy~Io1 cycI92 Time cycI。3 Cycle4 曩蚕墨ii 曩 Grei~THm For琢嘲la}1触婚m0m 曩嚣 G潞辅 TimeForLoll Tum Movernent Outbound Direct~ 曩曩譬鬣蓦翟露 Gre9n T；m0 For L磅囊 Tum Movement-n lnbound Dtreaion Fig．1 Time space diagram of a coordinated traffic signal control plan (4)Offset reference point． and the system m aster clock，which is defined as that The offset reference point is a specified point that point within a cycle in which the local controller’s creates an association between the local signal clock offset is measured relative to the m aster clock． In this

64 交通运输系统工程与信息 2011年 2月 nalized intersection to achieve the maximum band— width． The cycle length and split optimizations are not covered in this study． 2．1 Arterial coordination m odel To develop a multi．．bandwidth m odel fo r an arte．． rial street．the basic objective funotion and severa1 variables must first be introduced．The basic objective is to find the maximum weighted sam of multi--band-- width in both directions through finding the offset and NEM A phase sequence pattern of each signalized in— tersection． A com prehensive search is used for maxi． mizing the objective function in this paper．To consid- er the problem more generally，assum e there are a to- — — — — — — — ain Artery— ———— ——— + 一 Cross Street— l— One Cycle ——————————————————— ’ 。 ‘ 。。。。。。。。。。。。。。。。。。。。。。。 ’ 。 ’ — — T im e —— —————————— — —— ‘ — —‘——一。。。 ’ 。’一 Fig．2 Four possible NEM A phase sequence patterns ta1 of N signalized interseetions with two directions of with overlap travel at each intersection．The objective function is paper，the offset reference point is defined as a point that the end of barrier on the main street，or the start of any phase(through phase or left phase)in arterial street direction (Fig．1)． (5)Offset． The term offset that is dependent on the offset ref- erence point，is used for controlling the start time refer— ring to the master controller．The offset ranges from zero to the cycle length of the signalized intersection． Offset is a critical parameter to determ ine the effect of coordi— nation in signalized intersections(Fig．1)． (6)Bandwidth． defined as： B =B(0l，02，… ，0Ⅳ，P5l，PS2，… ，PJsⅣ)(1) = ∑ ‘ + 一 (2) ¨∑ = ∑ (Ci,i+l， +。)×6(0 ，PS ，GOBT ， × 6 GIBL ，d 十． +l ，s ． + l ， 0 +l， + PS +I，GOBT +l，GIBL +I，C ，R ，13 +l，R +1) ¨∑ + k(c… ．， … ． )x b(0 ，PS ， + GIB Ti，GOBL ，d +1 × 6 ，8 +I ．；， 0 +l，P5 +l，．十 GIB T + ，GOBL +．，C ，R ，C ；+ 。，R +，) (3) Bandwidth is described as the am ount of green time available for vehicles to travel through a system N 一 1 = ∑ [ (c … +．)×6(0 ，PS ， E J at a determined progression speed． Each direction on GOBT ，GIBL ，d +I，s ． + l ， 0 +l， the arterial street has its own bandwidth． Bandwidths PS +J，GOBT +l，GIBL +l，C ，R ，C +，，R +1) in the same direction in a street can vary between ad— + (c ．，． )x b(0 ，PS ，G1BT ， jacent signalized intersections．To suinmarize，there GOBL ，d +1 5 +I ，．． i ，0 l，P 。+l， are four principal signal timing parameters for deter— GIBT +。，GOBL +．，C ，R ，C +。，R +。)] (4) mining the optimal solution of coordinated traffic sig— where， nal contro1．which are as follows： (a)Cycle length． (b) Green time splits of each phase． (e)NEMA phase sequence． (d)Offsets． This study focuses on determining the optimal B(0．，02，… ，0Ⅳ，PsI，P52，… ，PsⅣ! =ob— jective function，which is a function of variables：O1， O2，… ，OⅣ，PSl，PS2，… ，PSⅣ(s)and which is the weighted suIn of multi—bandwidth in both directions， N —l ∑k +i×b +I=weighted sum of multi—bandwidths l 1 NEMA phase sequence pattern and offset of each sig— in outbound direction along the arterial street(s)，

第 11卷第 1期 Variable—Bandwidth Progression Optimization in Traffic Operation 65 ∑ k…， ×b…， =weighted sum of multi—band— and iin inbound direction (veh／h)． Furthermore， two other important variables are widths in inbound direction along the ,a~efial street(s)， defined as follows： k【If+l= (c +l， +1) =weight coefficient of C ：cycle length of signalized intersection i(s)， link between interseetion i and i十 1 in outbound direc— and tion ， R ： red interval in the arterial street direction at = (c… ．， … ． ) =weight coefficient of ． intersection i(s)． link between intersection + l and i in inbound direc— Thus， the optimal solution can be obtained by tion ， the following process： b ， +I =outbound bandwidth between intersection Maximize B = B(0．，02，… ，0 ，PS．，PS2， i and i+ 1 (s)， … ， PS ) (5) b +l = inbound bandwidth between intersection i subject to the conditions + 1 and i(s)， O，：offset of intersection i(s)， PS = NEM A phase sequence pattern at intersec— tion i，and the value of PS can only be 1，2，3，4 ， GOBT = effective green tim e of outbound through movement phase(s)， 0 ≤ O < C for i= 1，2，… ，N (6) PS ， = 1，2，3，or 4 for i= 1，2，… ，N (7) and assum ing other param eters are predetermined． To determine the value of Eq． (1)，four rune— _呈 tions must be defined． The first function is the weight m H d d coeffi cient function in the outbound direction， which GOBL = effective green tim e of outbound left is expressed as： movement phase(s)， GIBL = effective green time of inbound left 川 = k(ci i+l ~Vi , , e 出 i+ 1) × ( (8) movement phase(s)， Here， n n C ． GIB T = effective green tim e of inbound through oL ： a coeffi cient whose value is greater than 0． O movement phase(s)，，卢 =a coefficient whose value is greater than or ．一．础 +1 = distance between intersection i and i+ 1 equal to 0． d ． (111)， d +1 ． = distance between intersection i+ 1 and i (m)， |三． _吾毗 O s。。+I = averdge speed of progression along the direction from intersection i and i+ 1(m／s)， and， ki+l i = C i+I i~Vi+I , , , i) ×( r (9) 吐 e 5 +l = average speed of progression along the b…+l=b(0 ，JPS ，GOBT ，GIBL ，d +I， direction from intersection i+ 1 and i(m／s)， s +l，0 +l，PS +J，GOBT +l，GIBL +l， c +l：total capacity(or capacity of the through C ，R ，C +．，R +1) lanes)of an arterial street in the segment between in— C i十1 tersection i and i+ 1 in outbound direction (veh／h)，： ∑f(J，0 ，PS ，GOBT ，GIBL—d，， c +I ：total capacity(or capacity of the through lanes) of an arterial street in the segment between in— tersection i+ l and i in inbound direction (veh／h)， v +J=total volume (or through vohllIle)of aI1 arterial street in the segment between intersection i and i+1 in outbound direction (veh／h)，and =total volume (or through volume)of an s +l，0 +1，尸S +l’GOBT +1，GIBL +1，C ， R ，C ，R ) c i+i (10) = ∑fo( ，0 ，PS ，GOBT ，GIBL ， d +，～s… ，C ，R )×fo( ，0 ，PS… ， GOBT + ，GIBL + ，C +．，R + ) (11) arterial street in the segment between intersection i+ 1 where ( ，o ，P5… ，GOBT… ，GIBL… ，C… ，

R +1)is an 0～1 function that determines whether the MA phase sequence pattern (PS… )，effective green 交通运输系统工程与信息 2011年 2月 signal light is available for this th rough movement at ． time of the outbound though movement(GOB T… )， time j．“1”means that vehicles can go through the in— effective green tim e of the inbound left turn movement tersection in the outbound direction．and “0’’ means lI (GIBL… )，the cycle length(C… )，and red interval that vehicles cannot pass the intersection at this time．． This function is determined by the offset(O… )，NE— ．n D ， ¨ ，， in arterial street direction(R )at the signal inter— ， section i+ 1． This function can be defined as：， PS ，GOBT… ，GIBL… ，C… ，R… ) ifJ > 0&J≤ (0 一R… 一GIBL )，or 0 < (J一0 )％ C… &( 一 0 )％ C ≤ GOBTi+。，if PS… = 1，3 otherwise，if PS +l = 1，3 if(0 + 一R +l— GOBT +。) < & ≤ (O 。一R。+。)， (12) or GIBL < (J一0 )％ C &(J～0 )％ C ≤ (GOBTi+i+GIBL )，if PS… =2，4 otherwise，if PS +l = 2，4 (J_，0f，P|s ，GOBT ，GIBL ，d +J s… ，C ，R )is the Here，J and J satisfy the following relationship： shift offo(J ，0i，PSf，GOBT ，GIBL ，C ，R ) can be J= (J +t + )mod(C ) (13) obtained by movingfo(J ，0 ，P ，GOBT ，GIBL ，C ， To explain this m ethod clearly and sim ply， the R )with time t +l= d +l／s +l along the direction parameters and functions along the outbound direction of coordination，as seen in Fig．3．Eq．(10)means are shown in Fig． 3 which describes the process of that the total bandwidth between jntersection i and how to obtain the bandwidth 12 by Eqs． (10) to i+ 1 equals the sum of time for vehicles going through (13)in detail． the upstream intersection i can also pass the current For inbound direction，the functions can be de- intersection i + 1． Fig．’3 shows that the outbound fined based on the ahove method． The equations are bandwidth is 5 s which is the SHill of five “1” in one as follows： cycle． d +，，： b(0 ，PS ，GIBT~，GOBL ，d +)． s +，．，， 0 +，， PS +l，GIBT +，，GOBL。+ 。，C ，R ，C +l，R +I) C = ∑f(J，0 ，PS ，GIBT ，GOBL—d+I． ,Si+l,i，0 ， J=1 PS +l，GIBT +l，GOBL +l，C ，R ，C +l，R +1) ci = ∑A(J，o川，PS ，GIBT…，GOBL -，C ，R ～d I．1，s ，。) 』 1 x (J，0 ，Ps ，GIBT ，GOBL ，C ，R ) (14) where ( ，0 ，PJs。，G1BT ，GOBL ，C ，R )is a function is determined by the offset(O )，NEMA 0 — 1 function that determ ines whether the signal light phase sequence pattern(PS：)，effective green time of is available for this through nlovenlent at time “1” inbound though movement 0 GlBTi ，effective green means that vehicles can go through the intersection in the inbound direction。 and “0” m eans that vehicles cannot pass through the intersection at this time． This time of outbound left turn movement(GOBL )，the cycle length (C )，and red interval in arterial street direction(R )at the signal intersection i．This func—

t 第 11卷第 1期 0 n C a n b e d e r 己= e d { ．， Variable—Bandwidth Prggression Optimization in Traffic Operation 67 D ， PS ，GIBT ，GOBL ，C ，R ) 1， if(0 一R 一 GIBT ) ≤ & < (O 一R )， or GOBL… ≤ (J一0 )％ C &( 一0 )％ C < (GOBL +GIBT )，if PS = 1，3 0， otherwise，ifPS = 1，3 (15) 1， ifJ≥ 0 < (0 一R 一GOBL )，or 0 ≤ (J一0 )％ C &( 一0 )％ C < GIBT；，if PS ： 2，4 otherwise， ifPS = 2，4 (J，0… ，Ps ，GIBT ，GOBL ，C ，R ，d ， The optim ization function can be determined by s… ． ) is the shift of (J ， 0… ， P5 ， GIBT… ， Eqs．(5)through (16)．The total weighted sum of GOBL +l，C l，R 1)and can be obtained by moving bandwidth changes with the variation of offset and (J ，0 ，PS ，GIBTi+ ，GOBL ，C ，R ) NEMA phase sequence patterns for each signalized in— with tim e t。+ l ， i = d +J ．／s +1 ． along the inbound di— terseetion． The best solutions are obtained when the rection of coordination．。 weighted snm of bandwidth is the m aximum am ongst Here，J and J satisfy the following relationship： all the scenarios． J = (J +t ． )rood(C ) (16) l · 量 0 Inl erseoti m 2 、 r CI=20 I— =20 ‘ l 1 ．} ‘2篁 r —l 孽T笋 10 s ．．o， p。。BT惦 L C，．R，l12 +PS2．GoBT2 l8L2 Rz 一 Oz．PSzGOBT2。GIB j．C2。Pa) 6 O1，PSi GOBTt．GI{ L1 t．R’“ 鳓}l黼一——霸翻／， { G鑫L2礴。G eT2礴8 PS==3 ／ D，／ l ~rsectj on1 ＼ tnbo盛u ndn／／f。 Ol。P8t．GOBT1．I ；,IBLI et．R1 j ／／ G0BTI=8$ Gt~．bt=4 s }l -／嚣薯薯誊《g嚣 ∞瓣 #∞ ， ___目__l ‘ 8 8 § g§ 《 _日__目一 E E《《 #饕藿g# 。 ——一 ∞ ■ $§《《 __口__一 I一．1 tl 2=15{ I GOB 8 G国lT r1=7g PS~=I Legend： Cycle Cycle2 Time Cycle3 G-~de4 蕊翟麓露嚣露露2§ 翟 G拇en Time For LeftTurn Movement in Outbo und Direction Green Tim口For Through Mov@ment 一蕊整四 Green T|me For LeftTurn Movement in Inbound Direction Fig．3 An illustration to explain how to obtain the outbound bandwidth 2．2 Netw ork cO0rdinati0n m odel ordination mode1． However， some additional parame— For networks，the basic idea of how to obtain an ters m ust be explained to describe the network model optimal coordination plan is sim ilar to the arterial CO— clearly． A 3 × 3 network is shown in Fig． 4． The goa1

68 交通运输系统工程与信息 2011年 2月 nal control plan in a traflfie network with M horizontal arterial streets and N vertical arterial streets can be obtained through the following process： Maximize B =B(01l， H ， 0l2 ． Ⅳ，… ，0lⅣ ． H ， 02l ， H ， 022 H，… ，02Ⅳ ，． … ，， 0肘l ， H ， 0肼2 ． H ， … ， Fig．4 An example of 3 ×3 network OMN H，Psn H，Psl2 H}… ，Ps1N H， PS21 ． H ， PS22 月，… ，PS2Ⅳ ．． … ，， Psm ，PS H，… ，PSMN H， P5l1 ． PSl2 ，， … ，， PSlⅣ ， P52l ，．， P 22 ，， … ， PS2Ⅳ ， … ， JPSMi ，．， PSm … ，．， ) (17) Subject to the constraints 0 ≤ 0 H < C for i= 1，2，… ，；J_= 1，2，… ，， N H ：horizontal arterial street in network in Fig．5． PS = 1，2，3 or 4 for i= 1，2，… ，M ； = 1， 2，… ，N ； H ：horizontal arterial street in network in Fig．5． PS ，． = 1，2，3 or 4 for i=1，2，。一，M ；J：1， 2，… ，N ；：vertical arterial street in network in net- work in Fig．5． Assume all other parameters are predetermined in this m ode1． A com prehensive search is also used for maximizing the objective function in here． o ，PS； H and Ps v must be determined to pro。 duce the maximum weighted sum of bandwidth of traf- tic network．Eq． (17)can be expanded as follows： ∑ “ ，＼ ∑ 川 + Fig．5 Relationship between offset in vertical and horizontaI directions for each signalized intersection of this network model is to obtain the maximum M Ⅳ 一 l weighted sum of all 24 possible bandwidths based on B=∑ ∑ (k Ⅷ ×b 。， I i J = 1 given conditions and constraints． One issue that m ust + k 'j Ij’H x bl，J l i H + be addressed before explaining this model is the con— straint of offset in the vertical direction when the offset in the horizontal direction is changing at one signal— x bJ ， ‘， + l， ized intersection (Fig．5)． When the offset in the where， horizontal direction is shining from time A to B (one cycle)at intersection 1 1，the offset in vertical direc— tion is moving from time A to B (also one cycle)． This means only offsets along one arterial street fo r all signalized intersections in the network needs to be an— k．．i．i“ H = weight coefficient of link between in— tersection 3 and 3+ 1 in outbound direction along the ith horizontal arterial street， k J+l，』， = weight coefficient of link between in— ， alyzed． Cross street offsets can be determined in the tersection +1 and j in inbound direction along the th process of searching the optimal solution，which saves horizontal arterial street， a large amount of computer calculation tim e．十1． = weight coefficient of link between in— ， The optimal solution for a coordinated traffic sig— tersection i and i + 1 in outbound direction along the

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