A Regional Coordinated Signal Control Method Based on Game Theory

Transcription

1 Research Journal of Applied Sciences, Engineering and Technology 6(6): , 201 ISSN: ; e-issn: Maxwell Scienific Organizaion, 201 Submied: Ocober 1, 2012 Acceped: December 28, 2012 Published: June 0, 201 A Regional Coordinaed Signal Conrol Mehod Based on Game Theory Ke-Cheng Xu, Jian-Ming Hu and Yi Zhang Deparmen of Auomaion, Tsinghua Universiy, Beijing, , China Absrac: Signal conrol for muli-inersecions is a ho issue in raffic research. Inelligen Vehicle and Infrasrucure Coordinaion Sysem (IVICS) helps us o develop much more accurae and effecive signal conrol sraegy. This sudy presens a sysem wih a new algorihm o opimize he conrol sraegies. This sysem collecs he daa in real ime and develops sraegies in he form of game ree. The evaluaion algorihm for he conrol sraegy of each inersecion is pu forward. And hen a new regional coordinaed signal conrol sraegy is proposed based on game ree heory. The global opimal sraegy can be obained from he gaming of all he inersecions. In oher words, all he inersecions acquire he opimal se of conrol sraegies when each inersecion acquires heir own opimal sraegy. This sudy uilizes VISSIM o verify he proposed algorihm. Compared wih ha of he fixed cycle conrol sysem, he simulaion sudy implemened in a road nework wih five inersecions shows ha he proposed algorihm is effecive in coordinaing muliple inersecions, especially when he raffic flow densiy is mean or close o he sauraion. Keywords: Game ree, game heory, IVICS, signal conrol INTRODUCTION In recen years, Inelligen Vehicle and Infrasrucure Cooperaion Sysem (IVICS), also named as VII (Vehicle Infrasrucure Inegraion) has become a research ho opic in Inelligen Transporaion Sysems. IVICS is composed by RSUs(Road-Side Uni) and vehicles equipped wih OBU (On-Board Uni), which can sense and ransmi local raffic parameers o RSU by wireless muli-hop communicaion. I may provide a brand new idea for raffic conrol because more precise, accurae and fine-grained vehicle and raffic informaion can be obained, communicaed and shared among vehicles and roadside infrasrucures. Also we noice ha as a successful heory in economics, Game Theory considers individuals relaed wih each oher as inelligen agens and analyzes he influences beween individuals o find he balanced poin. A lo of researchers have shown grea ineress in how o inroduce i o he ransporaion and raffic engineering, such as roue guidance (Anasasios and John, 1991; Eian e al., 2001; Jeffrey and Vicor, 2002), raffic modeling (Fisk, 1984, 1986; Hai, 1995; Michael, 2000; Kia e al., 2002; Lian-Ju and Zi-You, 2007), signal conrol (Hai, 1995; Owen and Moshe, 2007), risk and securiy (Francesca, 2007). Compared o he fruiful work in raffic modeling, he collaboraion beween signal conrol and Game Theory is relaively less. The major difficul for signal conrol is ha how o design he evaluaion funcion which can represen and evaluae he complex muual influences among inersecions. Wihou his funcion, we can evaluae he signal conrol sraegies wih a unified sandard and as a resul, we canno find he opimal one. This sudy uilizes Game Theory as he analyzing mehod, proposes an evaluaion funcion for inersecions and demonsraes a new muli-inersecion signal conrol mode based on IVICS informaion. And his sudy focuses on a five-inersecion area and evaluaes he influences among all he inersecions and discusses how hey coordinae wih each oher. All he inersecions can ge he opimal conrol sraegy based on differen raffic condiions. THE MODELING OF SIGNAL CONTROL BASED ON GAME THEORY This sudy is based on IVICS informaion. Five inersecions are included in he research area. To simplify he sudy and validae he efficiency of he proposed signal iming algorihm, we merely focus on he raffic conrol for vehicles and ignore he pedesrians, bicycles and U-urn vehicles. Besides, here are only red ligh and ligh in each cycle lengh. No proeced lef-urn phase is discussed eiher. Considering he driving behavior, minimum ime and maximum ime in each phase are defined for each inersecion in order o realize exension and o make sure he vehicles go hrough he inersecion smoohly and safely as well. Corresponding Auhor: Jian-Ming Hu, Deparmen of Auomaion, Tsinghua Universiy, Beijing, China, California PATH, ITS, Universiy of California, Berkeley, 94704, CA, Tel.: (+86)

2 End updae search layer Yes updae search layer? uilize he opimal sraegy search he ree No Res. J. Appl. Sci. Eng. Technol., 6(6): , 201 Sar collec and updae dae No reach he minimum ime? Yes evaluae he curren raffic condiion form he ree of he game Fig. 1: The flow char of he signal conrol sraegy opimizaion based on game ree If he signal conrol is regarded as a decisionmaking process, a signal conrol model is designed o deermine wheher o exend he ime or no. Therefore, he process of raffic signals can be considered as a sequenial decision-making process in some sense. For he circumsance of muliple inersecions, he process of signal conrol can be reaed as a game. Each inersecion can be considered as a player. The decision of each player is o exend he ime of is curren phase or change phase according o he game evaluaion funcion which will be discussed in he nex secion. For he sake of convenience, we choose an inersecion as he arge inersecion o conrol and call he game inersecion which has influences on i as he relaive inersecion. Assuming he signal iming of he curren inersecion is a phase i and he momen has passed he minimum ime, hen he curren inersecion sars he process of he game and calculaes he game equilibrium soluion. Cerainly, if he minimum ime is no reached, he arge inersecion should keep waiing. When he used ime is larger han he minimum ime, he game-ree-based decision process is called. This process can be regarded as a combinaion of a series of sequenial decisions. During he period of decision, he inersecion makes is decision in each ime uni. Since he decision of he arge inersecion should consider all he decisions of he oher inersecions in he games simulaneously, he sequenial decision during he decision ime is a process of repeaed game. If an opimal sraegy a a momen is o swich he phase, hen he decision process sops and ges ino he decision process of he nex phase. If he opimal sraegy of he decision sequences is sill o exend he ime afer reaching he maximum ime, hen he inersecion will swich o he nex phase auomaically and erminae his decision process. As ime goes, we can ge payoffs of all he combinaions of sraegies from he curren ime o he end ime. This ree composed of he payoffs is defined as a game ree for regional coordinaed raffic conrol. When he condiions menioned above are all saisfied, he sraegy of he arge inersecion mus be he bes because i can ge he payoffs of all he combinaions of sraegies no maer which sraegies will be aken by oher inersecions. The arge inersecion can always obain he opimal sraegy by backracking in he game ree. The conrol sraegy of coordinaed signal conrol sysem for muliple inersecions based on game ree heory is shown in Fig. 1. Once reaching he decision ime, he sysem will evaluae he curren condiion wih he evaluaion funcion and hen develop he game ree according o he searching ime and he number of he searching layers o ge he payoffs afer he expeced ime. Furhermore, we can backrack in he game ree o ge he opimal sraegy. Finally, he opimal sraegy is carried ou and he daa is updaed in real ime. COORDINATED TRAFFIC SIGNAL CONTROL STRATEGY BASED ON GAME THEORY Regarding Game Theory, i is he firs and he mos imporan sep o define he game players, evaluaion funcion and equilibrium soluion. As is menioned in secion 2, in his sudy, all he five inersecions are game players. And he inersecion decides wheher o carry ou he sraegy or no by synheically considering he possible change of he evaluaion funcion value before and afer aking i. The equilibrium of a game is defined as he combinaion of all he opimal sraegies for all he players. We can ge each player s opimal sraegy by game ree. Now, le s discuss how o ge he evaluaion funcion. The evaluaion funcion is deermined by wo aspecs. One is he evaluaion value of he arge inersecion a ha decision momen. This evaluaion value is usually used o decide exension or phase change. Green exension can ge a higher evaluaion value when he queue and delay are long in he curren phase. The oher is he influence of he adjacen inersecions on he arge inersecion. This influence is mainly deermined by he offses. The more appropriae he offse is, he higher he evaluaion value will be. Denoe he evaluaion funcion as F( ), he curren phase as i and he nex phase as i+1. The queue lengh for each lane in phase i can be formulaed as Eq. (1): L ( + ) max L( ) + q( k) s,0 k 1 where, L() is he exising queue lengh, q(k) is he arrival rae of vehicle in one ime uni (such as 1 sec), s is he flow rae of he leaving vehicles in ime, assuming s is a consan in he curren phase (1)

3 Res. J. Appl. Sci. Eng. Technol., 6(6): , 201 Similarly, he queue lengh of red lane in phase i is: ( ) ( ) ( ) Q + Q + q k k 1 (2) where, Q() The queue lengh of he original vehicles a he momen Taking an inersecion wih four phases in one cycle as an example, he inersecion needs o decide wheher o exend he curren ime or no a he momen, he queue lenghs in phase i+1, i+2, i+ all have influence on he curren decision, bu he influence becomes weaker as he number of phase ges bigger. The change of he queue lengh a a cerain place apparenly canno horoughly reflec he curren raffic condiion, so we define an equivalen queue lengh in his sudy. The equivalen queue lengh can reflec he changing rend of he curren queue lengh. The equivalen queue lengh is shown in Eq. (): Li+ Q n 1 F u i+ n () where, L is he queue lengh a curren phase, Q+ is he red queue lengh (queue lengh on red). u(g) is he relaed occupancy rae which can be calculaed wih Eq. (4): u ui u + αu + βu i+ 1 i+ 2 i+ (4) where, α 0.7 and β 0. in his sudy. Equaion (4) represens he differen influences of queue lengh in differen phases. On he oher side, on he red lane (he lane in which he raffic ligh is currenly red), even hough he queue lengh is fairly shor, here are sill some vehicles waiing oo long, which will surely annoy he drivers. So we need o coun he number of he vehicles having waied for a long ime and define he number asn red, which will have an influence on he decisions of inersecions. So, he equivalen queue lengh can be calculaed wih Eq. (5). F L + Q µ N u i i+ n red n 1 (5) where, µ 0.5 in his sudy, which represens he influence weigh. In addiion o he queue lengh, he used ime will also affec he evaluaion value. For example, if he used ime jus exceeds he minimum ime, he inersecion has a grea probabiliy o coninue he curren phase. On he conrary, if used ime is almos close o he maximum ime, he probabiliy of changing phase will be higher. In his sudy, he influence value of he curren ime is defined as he following expression. I curren max e, curren min e, curren < max curren + 1 max min (6) So, he equivalen queue lengh can be calculaed wih Eq. (7): F I L + Q µ N n 1 u i i+ n red (7) Furhermore, we alk abou he influence value of he adjacen inersecions on he arge inersecion. The influence value can be divided ino wo pars. One is he ime of he adjacen inersecions in he curren phase. The longer i is, he bigger he flow rae will be. The oher is he evaluaion value of he curren offse. The evaluaion value reflecs he coordinaion level. The influence value can be seen as he influence on he fuure queue lengh of he arge inersecion. The influence value of he adjacen inersecion can be calculaed according o Eq. (8): 0.5 i j G C ε v (8) where, The curren ime of he adjacen inersecion i j The ime lag εε The offse and is se by he sysem v The ravel ime from he adjacen inersecion o he arge inersecion If i j ε is less han 0, hen 1.05 i j ε cycle G C + v (9) where, cycle The average cycle for he curren raffic condiion To sum up, he evaluaion funcion can be expressed as Eq. (10): f F G SIMULATION AND RESLUTS ANALYSIS (10) Simulaion environmen based on VISSIM: A road nework wih 5 inersecions is esablished by using 1090

4 Res. J. Appl. Sci. Eng. Technol., 6(6): , 201 Table 1: The flow parameers se in simulaion Traffic flow saus Norh Souh Wes Eas Low Mean High VISSIM. The cenral inersecion is chosen as he arge inersecion and adjacen four inersecions are relaive inersecions. VISSIM provides wo mehods o collec daa, i.e., collecing wih Daa Collecion and collecing from Por Com. In his simulaion, we uilize Por COM o acquire he average ravel ime while uilize Daa Collecion o acquire average delay. In his sudy, Visual Basic (VB) is applied o obain and process he simulaion daa and sore hem ino he daabase because he API inerfaces of VISSIM have beer compaibiliy wih VB. Meanwhile, since he daa processing speed of VB is raher slow, we uilize Visual C (VC) o exrac he daa from he daabase and calculae he proposed algorihm. VB ges he opimal sraegy from VC by loading he dynamic link library and conrols he signal in simulaion wih his sraegy. I is he mos imporan o build and search he game ree for he algorihms in VC. As each inersecion has wo opions, exending ime and swiching phase, for a five-inersecion nework, here are 2 differen kinds of sraegies, i.e., each node in he game ree has 2 branches owards he nex layer. Noe ha he ime cos of searching for he opimum in a 2- branch game ree is relaively expensive, i s very imporan o simplify he ree. When making decision for each second, every inersecion only needs o predic he very shor nex period of ime, which only needs o be abou a quarer of a cycle ime and in his sudy is 15 seconds. In his period, we can assume ha he signal will change phase no more han once. So if one node of he game ree is o change phase, we don need o ake is child-nodes ino consideraion, which simplifies he ree grealy. Simulaion resuls and analysis: In General, he sauraion flow densiy for a nework is 600 veh/h. This sudy preses he flow parameers as shown in Table 1. The low, mean and high flow densiy parameers in his simulaion are approximaely 0.2, 0.5 and 0.9 imes he sauraion flow respecively. The simulaion resuls are provided in Fig. 2 and he performance of he algorihm is shown in Table 2. Based on he able and figures above, we can ge he following findings: When raffic flow densiy is low, he effec of he proposed sysem is similar o he fixed ime conrol sysem. The average delay and he average ravel ime are improved by only 1.87 and 0.84% respecively. In his case, here is no necessary o coordinaed conrol hese inersecions. When raffic flow densiy is mean, he effec of he proposed sysem is much beer han he fixed ime conrol sysem apparenly, for average delay is shoren by 8.2% and average ravel ime is shoren by 7.5%. When raffic flow densiy is high, he effecs of boh sysems are no saisfying while he effec of he proposed sysem is sill beer. As we can see from Fig. 2c ha average delay is around 150 sec and average ravel ime closes o 2 min. The performance improves less han ha in meandensiy is probably because he number of vehicles is very close o he capaciy of he nework and he room for his mehod o improve is less, in oher words, he available sraegies ha each inersecion can choose are less. Average Delay (s) Fixed Cycle Time Average Travel Time (min) (a) 1091

5 Res. J. Appl. Sci. Eng. Technol., 6(6): , 201 Average Delay (s) Average Travel Time (min) (b) Average Delay (s) Average Travel Time (min) (c) Fig. 2: (a) Simulaion resuls for low raffic flow densiy, (b) Simulaion resuls for mean raffic flow densiy, (c) Simulaion for high raffic flow densiy Table 2: The performance improvemen percenage Traffic flow saus Average delay (%) Average ravel ime (%) Low Mean High Noe ha we can find he flucuaion of he proposed sysem in he figures of average delay is larger han ha in he figures of average ravel ime, for here are several exremely high poins in he average delay figures. I is because he average delays are acquired by seing daa collecion in VISSIM while he average ravel imes are acquired from Por COM. The laer uilizes all he vehicles daa o calculae while he former uilizes a par of he daa. CONCLUSION This sudy presens a new algorihm o evaluae inersecion condiions for regional raffic conrol. Based on IVICS informaion, he proposed sysem can ge he imely vehicle informaion such as longiude, laiude, speed, lane, headway and so forh o evaluae he condiion for he whole nework. The sysem figures ou he evaluaion values for all he sraegies and searches for an efficien sraegy in he form of he game ree. Based on Game Theory, we only need o focus on he influences beween he arge inersecion and he relaive inersecions and he algorihm aims o evaluae hese influences. The simulaion resul shows ha, by he algorihm based on Game Theory, we find a new idea o deal wih he regional raffic conrol. 1092

6 Res. J. Appl. Sci. Eng. Technol., 6(6): , 201 The fuure ask is o opimize he algorihm furhermore as he influences are really complex. And as our simulaion is conneced wih a simple siuaion bu here are various siuaions in he real world, we need o perform simulaions in oher siuaions. ACKNOWLEDGMENT This sudy was suppored in par by Naional Basic Research Program of China (97 Projec) 2012CB725405, Hi-Tech Research and Developmen Program of China (86Projec) 2011AA110405, he Henry Fok Foundaion (122010) and Naional Naural Science Foundaion of China (NSFC) REFERENCES Anasasios, A.E. and A.S. John, Muli-objecive rouing in inegraed services neworks: A game heory approach. Proceedings. 10h Annual Join Conference of he IEEE Compuer and Communicaions Socieies. Neworking in he 90s (INFOCOM '91). Bal Harbour, FL, pp: Eian, A., B. Tamer, J. Tania and S. Nahum, Rouing ino wo parallel links: Game-heoreic disribued algorihms. J. Parallel Disrib. Compu., 61(9): Fisk, C.S., Game Theory and ransporaion sysems modeling. Transpor. Res. B-Meh., 18 (4-5): Fisk, C.S., A concepual framework for opimal ransporaion sysems planning wih inegraed supply and demand models. Transpor. Sci., 20(1): Francesca, M., A game heory approach for he allocaion of risks in ranspor public privae parnerships. In. J. Projec Manag., 25(): Hai, Y., Traffic assignmen and signal conrol in sauraed road neworks. Transpor. Res. A-Pol., 29(2): Jeffrey, L.A. and J.B. Vicor, A cooperaive muli-agen ransporaion managemen and roue guidance sysem. Transpor. Res. C-Emer., 10 (5-6): Kia, H., K. Tanimoo and K. Fukuyama, A game heoreical analysis of merging-giveway inersecion: A join esimaion model. Proceedings of he 15h Inernaional Symposium on Transporaion and Traffic Theory, pp: Lian-Ju, S. and G. Zi-You, An equilibrium model for urban ransi assignmen based on game heory. Eur. J. Oper. Res., 181(1): Michael, G.H.B., Game heory approach o measuring he performance reliabiliy of ranspor neworks. Transpor. Res. B-Meh., 4(6): Owen, J.C. and E.B.A. Moshe, Game-heoreic formulaions of ineracion beween dynamic raffic conrol and dynamic raffic assignmen. Transpor. Res. Record, 1617: