城市轨道交通网络客流分配模型和算法综述
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摘要
城市轨道交通网络客流分配是推算客流分布的基础理论方法.本文首先介绍了既有的城市轨道交通客流分配模型,从客流分配建模中的网络建模架构,乘客出行行为假设和客流分配原理三方面对比分析了既有研究的模型特征.在分配模型分类的基础上,重点阐述了客流分配算法中的网络路径搜索、分配模型求解和客流行为模拟和分布仿真算法的研究进展.最后,提出了我国城市轨道交通客流分配在网络化运营新形势下的研究展望.
The passenger flow assignment for urban rail transit is the basic theory to estimate the flow distribution in network. Firstly, this paper introduced the passenger flow assignment study with comparative analyzing the existing models' characteristics of the supply network framework modeling, passengers' travel behavior hypothesis and passenger flow assignment principle. Based on the classification of the assignment model, this paper focused on the network route searching algorithm, model solving algorithm and passengers' behavior simulation and distribution simulation algorithm in the assignment model. Finally, the passenger flow assignment research prospect under the new situation in China urban rail transit network operation is proposed.
The passenger flow assignment for urban rail transit is the basic theory to estimate the flow distribution in network. Firstly, this paper introduced the passenger flow assignment study with comparative analyzing the existing models' characteristics of the supply network framework modeling, passengers' travel behavior hypothesis and passenger flow assignment principle. Based on the classification of the assignment model, this paper focused on the network route searching algorithm, model solving algorithm and passengers' behavior simulation and distribution simulation algorithm in the assignment model. Finally, the passenger flow assignment research prospect under the new situation in China urban rail transit network operation is proposed.
引文
[1]Trozzi V,Gentile G,Bell M G H,et al.Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths[J].Procedia—Social and Behavioral Sciences,2013:427-454.
[2]Szeto W,Jiang Y.Transit assignment:Approach-based formulation,extra gradient method,and paradox[J].Transportation Research Part B:Methodological,2014:51-76.
[3].Schm(o|¨)cker J.Dynamic capacity constrained transit assignment[D].London:Imperial College London,2006.
[4]Teklu F A.A Markov process model for capacity-constrained transit assignment[D].Leeds:University of Leeds,2008.
[5]Nuzzolo A,Crisalli U.The schedule-based modeling of transportation systems:Recent developments[M]//Schedule-Based Modeling of Transportation Networks:Springer US.2009:1-26.
[6]Nuzzolo A,Russo F,Crisalli U.A doubly dynamic schedule-based assignment model for transit networks[J].Transportation Science,2001,35(3):268-285.
[7]De Cea J,Fernandez E.Transit assignment for congested public transport systems:An equilibrium model[J].Transportation Science,1993,27:33-47.
[8]Kurauchi F,Bell M G H,Schmocker J D.Capacity constrained transit assignment with common lines[J].Journal of Mathematical Modelling and Algorithms,2003,2(4):309-327.
[9]Nielsen L.Route choice in stochastic time-dependent networks[D].University of Aarhus,Denmark,2003.
[10]Moller-Pedersen J.Assignment model of timetable based systems(TPSCHEDULE)[C]//Proceedings of 27th European Transportation Forum,Seminar F,Cambridge,England,1999:159-168.
[11]Poon M H,Wong S C,Tong C O.A dynamic schedule-based model for congested transit networks[J].Transportation Research Part B:Methodological,2004,38(4):343-368.
[12]Nguyen S,Pallottino S,Malucelli F.A modeling framework for passenger assignment on a transport network with timetables[J].Transportation Science,2001,35:238-249.
[13]Hamdouch Y,Lawphongpanich S.Schedule-based transit assignment model with travel strategies and capacity constraints[J].Transportation Research Part B:Methodological,2008,42(7):663-684.
[14]Leurent F,Chandakas E,Poulhes A.A traffic assignment model for passenger transit on a capacitated network:Bi-layer framework,line sub-models and large-scale application[J].Transportation Research Part C:Emerging Technologies,2014,47(1):3-27.
[15]Dial R B.Transit pathfinder algorithm[M].Highway Research Board,1967,205:67-85.
[16]Spiess H,Florian M.Optimal strategies:A new assignment model for transit networks[J].Transportation Research Part B:Methodological,1989,23(2):83-102.
[17]Nguyen,S,Pallottino S.Equilibrium traffic assignment for large scale transit networks[J].European Journal of Operational Research,1988,37:176-186.
[18]刘剑锋,孙福亮,柏埘,等.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2):81-86.Liu J F,Sun F L,Bai Y,et al.Passenger flow route assignment model and algorithm for urban rail transit network[J].Journal of Transportation Systems Engineering&Information Technology,2009,9(2):81-86.
[19]Hamdouch Y,Ho H W,Sumalee A,et al.Schedule-based transit assignment model with vehicle capacity and seat availability[J].Transportation Research Part B:Methodological,2011,45(10):1805-1830.
[20]Lam W H K,Gao Z Y,Chan K S,et al.A stochastic user equilibrium assignment model for congested transit networks[J].Transportation Research Part B:Methodological,1999,33(5):351-368.
[21]Zhang Y,Lam W H K,Sumalee A,et al.The multi-class schedule-based transit assignment model under network uncertainties[J].Public Transport,2010,2(1-2):69-86.
[22]Guo Z.Mind the map!The impact of transit maps on path choice in public transit[J].Transportation Research Part A,2011,45:625-639.
[23]张永生,姚恩建,代洪娜.成网条件下地铁换乘量预测方法研究[J].铁道学报,2013,35(11):1-6.Zhang Y S,Yao E J,Dai H N.Transfer volume forecasting method for the metro in networking conditions[J].Journal of the China Railway Society,2013,35(11):1-6.
[24]Florian M.Deterministic timetable transit assignment[C]//First Asian EMME/2 Users Group Meeting,Shanghai,China,1999.
[25]Nokel K,Wekeck S.Boarding and alighting in frequency-based transit assignment[J].Transportation Research Record:Journal of the Transportation Research Board,2009,2111:60-67.
[26]Nuzzolo A,Crisalli U,Rosati L.A schedule-based assignment model with explicit capacity constraints for congested transit networks[J].Transportation Research Part C:Emerging Technologies,2012,20(1):16-33.
[27]Lampkin W,Saalmans P D.The design of routes,service frequencies,and schedules for a municipal bus undertaking:A case study[J].OR,1967,18:375-397.
[28]周玮腾,韩宝明.考虑列车容量限制的地铁网络客流分配模型[J].华南理工大学学报(自然科学版),2015,43(8):126-134.Zhou W T,Han B M.Passenger flow assignment model of subway networks under train capacity constraint[J].Journal of South China University of Technology(Natural Science Edition),2015,43(8):126-134.
[29]Hamdouch Y,Szeto W Y,Jiang Y.A new schedule-based transit assignment model with travel strategies and supply uncertainties[J].Transportation Research Part B:Methodological,2014:35-67.
[30]Wong S C,Tong C O.Estimation of time-dependent origin-destination matrices for transit networks[J].Transportation Research Part B:Methodological,1998,32:35-48.
[31]Tian Q,Huang H J,Yang H.Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system[J].Transportation Research Part B:Methodological,2007,41(6):616-631.
[32]Leurent F.On seat capacity in traffic assignment to a transit network[J].Journal of Advanced Transportation,2012,46(2):112-138.
[33]Sumalee A,Tan Z,Lam W H K.Dynamic stochastic transit assignment with explicit seat allocation model[J].Transportation Research Part B:Methodological,2009,43(8):895-912.
[34]Daganzo C F,Sheffi Y.On stochastic models of traffic assignment[J].Transportation Science,1977,11(3):253-274.
[35]Carraresi P,Malucelli F,Pallottino S.Regional mass transit assignment with resource constraints[J].Transportation Research Part B,1996,30:81-98.
[36]Friedrich M,Hofsab I,Wekeck S.Timetable-based transit assignment using branch and bound[C]//80th Annual Meeting of TRB,Washington DC,USA,2001.
[37]Cascetta E,Cantarella G E.A day-to-day and within-day dynamic stochastic assignment model[J].Transportation Research Part A:General,1991,25(5):277-291.
[38]Cascetta E.Transportation systems engineering theory and methods[M].Kluwer Academic Publishers,2001.
[39]Dial R B.A probabilistic multipath traffic assignment model which obviates path enumeration[J].Transportation Research,1971,5(2):83-111.
[40]苏娟.城市轨道交通客流分配研究[D].北京:北京交通大学,2009.Su J.Research on passenger flow assignment of urban rail transit[D].Beijing:Beijing Jiaotong University,2009.
[41]毛保华,四兵锋,刘智丽.城市轨道交通网络管理及收入分配理论与方法[M].北京:科学出版社,2007.
[42]徐瑞华,罗钦,高鹏.基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2):110-114.Xu R H,Luo Q,Gao P.Passenger flow distribution model and algorithm for urban rail transit network based on multi-route choice[J].Journal of the China Railway Society,2009,31(2):110-114.
[43]赵路敏,郝庆玲,杜世敏.北京市轨道交通线网客流及票款清分方法[J].都市快轨交通,2009(6):58-60.Zhao L M,Hao Q L,Du S M.Passenger flow and ticket income clearing for Beijing urban rail transit network[J].Urban Rapid Rail Transit,2009(6):58-60.
[44]Szeto W Y,Solayappan M,Jiarig Y.Reliability-based transit assignment for congested stochastic transit networks[J].Computer-Aided Civil and Infrastructure Engineering,2011:311-326.
[45]杨东赤,任华玲,四兵锋,等.基于时刻表的轨道交通网络动态配流模型研究[J].系统工程理论与实践,2015,35(5):1214-1223.Yang D C,Ren H L,Si B F,et al.Research on schedule-based dynamic traffic assignment model for rail transit networks[J].Systems Engineering—Theory&Practice,2015,35(5):1214-1223.
[46]Schm(o|¨)cker J D,Fonzone A,Shimamoto H,et al.Frequency-based transit assignment considering seat capacities[J].Transportation Research Part B:Methodological,2011,45(2):392-408.
[47]Schm(o|¨)cker J D,Bell M G H,Kurauchi F.A quasi-dynamic capacity constrained frequency-based transit assignment model[J].Transportation Research Part B:Methodological,2008,42(10):925-945.
[48]Szeto W Y,Jiang Y,Wong K I,et al.Reliability-based stochastic transit assignment with capacity constraints:Formulation and solution method[J].Transportation Research Part C:Emerging Technologies,2013,35:286-304.
[49]田琼,黄海军.一个考虑早到惩罚的高峰期地铁乘车均衡模型[J].交通运输系统工程与信息,2004,4(4):108-112.Tian Q,Huang H J.An equilibrium ride model for subway passengers with arrival early penalty[J].Communication&Transportation Systems Engineering&Information,2004,4(4):108-112.
[50]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9):1158-1162.Wu X Y,Liu C Q.Traffic equilibrium assignment model specially for urban railway network[J].Journal of Tongji University(Natural Science),2004,32(9):1158-1162.
[51]四兵锋,毛保华,刘智丽.无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6):12-18.Si B F,Mao B H,Liu Z L.Passenger flow assignment model and algorithm for urban railway traffic network under the condition of seamless transfer[J].Journal of the China Railway Society,2007,29(6):12-18.
[52]Fisk C.Some developments in equilibrium traffic assignment[J].Transportation Research Part B:Methodological,1980,14(3):243-255.
[53]Dijkstra E W.A note on two problems in connexion with graphs[J].Numerische Mathematics,1959,1(1):269-271.
[54]Floyd R W.Algorithm 97:Shortest path[J].Communications of the ACM,1962,5(6):345.
[55]李树彬,高自友,林勇,等.大规模交通网络实时路径搜索算法研究[J].交通运输系统工程与信息,2009,9(5):141-147.Li S B,Gao Z Y,Lin Y,et al.Real-time path searching algorithm for large traffic network[J].Journal of Transportation Systems Engineering&Information Technology,2009,9(5):141-147.
[56]Hoffman W,Pavley R.A method for the solution of the Nth best path problem[J].Journal of the ACM,1959,6(4):506-514.
[57]Yen J Y.Finding the k shortest loopless paths in a network[J].Management Science,1971,17(11):712-716.
[58]牛新奇,潘荫荣,胡幼华·K(≤3)条渐次短路径搜索算法的研究[J].计算机工程与应用,2005,41(22):51-53.Niu X Q,Pan Y R,Hu Y H.Research on the algorithm of K-shortest path under single restriction with multiple weights[J].Computer Engineering&Applications,2005,41(22):51-53.
[59]Xu W,He S,Song R,et al.Finding the K shortest paths in a schedule-based transit network[J].Computers and Operations Research,2012,39(8):1812-1826.
[60]Abdulaal M,Leblanc L J.Methods for combining modal split and equilibrium assignment models[J].Transportation Science,1979,13:292-314.
[61]Sheffi Y.Urban transportation networks:Equilibrium analysis with mathematical programming methods[M].Prentice-Hall,Englewood Cliffs,NJ,USA,1985.
[62]四兵锋,高自友,交通运输网络流量分析与优化建模[M].北京:人民交通出版社,2013.Si B F,Gao Z Y.Modeling network flow and system optimization for traffic and transportation system[M].Beijing:China Communications Press,2013.
[63]Bell M G H.Stochastic user equilibrium assignment in networks with queues[J].Transportation Research Part B,1995,29(2):125-137.
[64]刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学,2012.Liu J F.Transfer-based modeling flow assignment with empirical analysis for urban rail transit network[D].Beijing:Beijing Jiaotong University,2012.
[65]Tong C O,Wong S C.A stochastic transit assignment model using a dynamic schedule-based network[J].Transportation Research Part B:Methodological,1998,33(2):107-121.
[66]Cats O.Multi-agent transit operations and assignment model[J].Procedia Computer Science,2013:809-814.
[67]Cats O.An agent-based approach for modeling real-time travel information in transit systems[J].Procedia Computer Science,2014:744-749.
[68]Hassannayebi E,Sajedinejad A,Mardani S.Urban rail transit planning using a two-stage simulation-based optimization approach[J].Simulation Modeling Practice and Theory,2014,49(1):151-166.
[69]高圣国,吴忠.基于旅行时间分布的客流清分模型[J].交通运输系统工程与信息,2011,11(6):124-130.Gao S G,Wu Z.Modeling passenger flow distribution based on travel time of urban rail transit[J].Journal of Transportation Systems Engineering&Information Technology,2011,11(6):124-130.
[70]罗钦.基于网络运营的城市轨道交通客流分布理论及仿真研究[D].上海:同济大学,2009.Luo Q.Theory and simulation analysis of passenger flow distribution based on network operation for urban mass transit[D].Shanghai:Tongji University,2009.
[71]刘玉麟.基于多主体仿真的城市轨道交通网络乘客出行行为研究[D].上海:同济大学,2008.Liu Y L.Traveler behavior study in urban mass transit network based on multi-agent simulation[D].Shanghai:Tongji University,2008.
[72]郑丽娟.基于城市轨道交通网络运营的客流分布预测研究[D].上海:同济大学,2008.Zheng L J.Study of the passenger flow distribution prediction based on URT network operation[D].Shanghai:Tongji University,2008.
[73]姚向明,赵鹏,乔珂.城市轨道交通网络客流分布仿真模型研究[J].交通运输系统工程与信息,2012,12(6):52-59.Yao X M,Zhao P,Qiao K.Modeling dynamic passenger flow distribution of urban rail transit network[J].Journal of Transportation Systems Engineering&Information Technology,2012,12(6):52-59.
[2]Szeto W,Jiang Y.Transit assignment:Approach-based formulation,extra gradient method,and paradox[J].Transportation Research Part B:Methodological,2014:51-76.
[3].Schm(o|¨)cker J.Dynamic capacity constrained transit assignment[D].London:Imperial College London,2006.
[4]Teklu F A.A Markov process model for capacity-constrained transit assignment[D].Leeds:University of Leeds,2008.
[5]Nuzzolo A,Crisalli U.The schedule-based modeling of transportation systems:Recent developments[M]//Schedule-Based Modeling of Transportation Networks:Springer US.2009:1-26.
[6]Nuzzolo A,Russo F,Crisalli U.A doubly dynamic schedule-based assignment model for transit networks[J].Transportation Science,2001,35(3):268-285.
[7]De Cea J,Fernandez E.Transit assignment for congested public transport systems:An equilibrium model[J].Transportation Science,1993,27:33-47.
[8]Kurauchi F,Bell M G H,Schmocker J D.Capacity constrained transit assignment with common lines[J].Journal of Mathematical Modelling and Algorithms,2003,2(4):309-327.
[9]Nielsen L.Route choice in stochastic time-dependent networks[D].University of Aarhus,Denmark,2003.
[10]Moller-Pedersen J.Assignment model of timetable based systems(TPSCHEDULE)[C]//Proceedings of 27th European Transportation Forum,Seminar F,Cambridge,England,1999:159-168.
[11]Poon M H,Wong S C,Tong C O.A dynamic schedule-based model for congested transit networks[J].Transportation Research Part B:Methodological,2004,38(4):343-368.
[12]Nguyen S,Pallottino S,Malucelli F.A modeling framework for passenger assignment on a transport network with timetables[J].Transportation Science,2001,35:238-249.
[13]Hamdouch Y,Lawphongpanich S.Schedule-based transit assignment model with travel strategies and capacity constraints[J].Transportation Research Part B:Methodological,2008,42(7):663-684.
[14]Leurent F,Chandakas E,Poulhes A.A traffic assignment model for passenger transit on a capacitated network:Bi-layer framework,line sub-models and large-scale application[J].Transportation Research Part C:Emerging Technologies,2014,47(1):3-27.
[15]Dial R B.Transit pathfinder algorithm[M].Highway Research Board,1967,205:67-85.
[16]Spiess H,Florian M.Optimal strategies:A new assignment model for transit networks[J].Transportation Research Part B:Methodological,1989,23(2):83-102.
[17]Nguyen,S,Pallottino S.Equilibrium traffic assignment for large scale transit networks[J].European Journal of Operational Research,1988,37:176-186.
[18]刘剑锋,孙福亮,柏埘,等.城市轨道交通乘客路径选择模型及算法[J].交通运输系统工程与信息,2009,9(2):81-86.Liu J F,Sun F L,Bai Y,et al.Passenger flow route assignment model and algorithm for urban rail transit network[J].Journal of Transportation Systems Engineering&Information Technology,2009,9(2):81-86.
[19]Hamdouch Y,Ho H W,Sumalee A,et al.Schedule-based transit assignment model with vehicle capacity and seat availability[J].Transportation Research Part B:Methodological,2011,45(10):1805-1830.
[20]Lam W H K,Gao Z Y,Chan K S,et al.A stochastic user equilibrium assignment model for congested transit networks[J].Transportation Research Part B:Methodological,1999,33(5):351-368.
[21]Zhang Y,Lam W H K,Sumalee A,et al.The multi-class schedule-based transit assignment model under network uncertainties[J].Public Transport,2010,2(1-2):69-86.
[22]Guo Z.Mind the map!The impact of transit maps on path choice in public transit[J].Transportation Research Part A,2011,45:625-639.
[23]张永生,姚恩建,代洪娜.成网条件下地铁换乘量预测方法研究[J].铁道学报,2013,35(11):1-6.Zhang Y S,Yao E J,Dai H N.Transfer volume forecasting method for the metro in networking conditions[J].Journal of the China Railway Society,2013,35(11):1-6.
[24]Florian M.Deterministic timetable transit assignment[C]//First Asian EMME/2 Users Group Meeting,Shanghai,China,1999.
[25]Nokel K,Wekeck S.Boarding and alighting in frequency-based transit assignment[J].Transportation Research Record:Journal of the Transportation Research Board,2009,2111:60-67.
[26]Nuzzolo A,Crisalli U,Rosati L.A schedule-based assignment model with explicit capacity constraints for congested transit networks[J].Transportation Research Part C:Emerging Technologies,2012,20(1):16-33.
[27]Lampkin W,Saalmans P D.The design of routes,service frequencies,and schedules for a municipal bus undertaking:A case study[J].OR,1967,18:375-397.
[28]周玮腾,韩宝明.考虑列车容量限制的地铁网络客流分配模型[J].华南理工大学学报(自然科学版),2015,43(8):126-134.Zhou W T,Han B M.Passenger flow assignment model of subway networks under train capacity constraint[J].Journal of South China University of Technology(Natural Science Edition),2015,43(8):126-134.
[29]Hamdouch Y,Szeto W Y,Jiang Y.A new schedule-based transit assignment model with travel strategies and supply uncertainties[J].Transportation Research Part B:Methodological,2014:35-67.
[30]Wong S C,Tong C O.Estimation of time-dependent origin-destination matrices for transit networks[J].Transportation Research Part B:Methodological,1998,32:35-48.
[31]Tian Q,Huang H J,Yang H.Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system[J].Transportation Research Part B:Methodological,2007,41(6):616-631.
[32]Leurent F.On seat capacity in traffic assignment to a transit network[J].Journal of Advanced Transportation,2012,46(2):112-138.
[33]Sumalee A,Tan Z,Lam W H K.Dynamic stochastic transit assignment with explicit seat allocation model[J].Transportation Research Part B:Methodological,2009,43(8):895-912.
[34]Daganzo C F,Sheffi Y.On stochastic models of traffic assignment[J].Transportation Science,1977,11(3):253-274.
[35]Carraresi P,Malucelli F,Pallottino S.Regional mass transit assignment with resource constraints[J].Transportation Research Part B,1996,30:81-98.
[36]Friedrich M,Hofsab I,Wekeck S.Timetable-based transit assignment using branch and bound[C]//80th Annual Meeting of TRB,Washington DC,USA,2001.
[37]Cascetta E,Cantarella G E.A day-to-day and within-day dynamic stochastic assignment model[J].Transportation Research Part A:General,1991,25(5):277-291.
[38]Cascetta E.Transportation systems engineering theory and methods[M].Kluwer Academic Publishers,2001.
[39]Dial R B.A probabilistic multipath traffic assignment model which obviates path enumeration[J].Transportation Research,1971,5(2):83-111.
[40]苏娟.城市轨道交通客流分配研究[D].北京:北京交通大学,2009.Su J.Research on passenger flow assignment of urban rail transit[D].Beijing:Beijing Jiaotong University,2009.
[41]毛保华,四兵锋,刘智丽.城市轨道交通网络管理及收入分配理论与方法[M].北京:科学出版社,2007.
[42]徐瑞华,罗钦,高鹏.基于多路径的城市轨道交通网络客流分布模型及算法研究[J].铁道学报,2009,31(2):110-114.Xu R H,Luo Q,Gao P.Passenger flow distribution model and algorithm for urban rail transit network based on multi-route choice[J].Journal of the China Railway Society,2009,31(2):110-114.
[43]赵路敏,郝庆玲,杜世敏.北京市轨道交通线网客流及票款清分方法[J].都市快轨交通,2009(6):58-60.Zhao L M,Hao Q L,Du S M.Passenger flow and ticket income clearing for Beijing urban rail transit network[J].Urban Rapid Rail Transit,2009(6):58-60.
[44]Szeto W Y,Solayappan M,Jiarig Y.Reliability-based transit assignment for congested stochastic transit networks[J].Computer-Aided Civil and Infrastructure Engineering,2011:311-326.
[45]杨东赤,任华玲,四兵锋,等.基于时刻表的轨道交通网络动态配流模型研究[J].系统工程理论与实践,2015,35(5):1214-1223.Yang D C,Ren H L,Si B F,et al.Research on schedule-based dynamic traffic assignment model for rail transit networks[J].Systems Engineering—Theory&Practice,2015,35(5):1214-1223.
[46]Schm(o|¨)cker J D,Fonzone A,Shimamoto H,et al.Frequency-based transit assignment considering seat capacities[J].Transportation Research Part B:Methodological,2011,45(2):392-408.
[47]Schm(o|¨)cker J D,Bell M G H,Kurauchi F.A quasi-dynamic capacity constrained frequency-based transit assignment model[J].Transportation Research Part B:Methodological,2008,42(10):925-945.
[48]Szeto W Y,Jiang Y,Wong K I,et al.Reliability-based stochastic transit assignment with capacity constraints:Formulation and solution method[J].Transportation Research Part C:Emerging Technologies,2013,35:286-304.
[49]田琼,黄海军.一个考虑早到惩罚的高峰期地铁乘车均衡模型[J].交通运输系统工程与信息,2004,4(4):108-112.Tian Q,Huang H J.An equilibrium ride model for subway passengers with arrival early penalty[J].Communication&Transportation Systems Engineering&Information,2004,4(4):108-112.
[50]吴祥云,刘灿齐.轨道交通客流量均衡分配模型与算法[J].同济大学学报(自然科学版),2004,32(9):1158-1162.Wu X Y,Liu C Q.Traffic equilibrium assignment model specially for urban railway network[J].Journal of Tongji University(Natural Science),2004,32(9):1158-1162.
[51]四兵锋,毛保华,刘智丽.无缝换乘条件下城市轨道交通网络客流分配模型及算法[J].铁道学报,2007,29(6):12-18.Si B F,Mao B H,Liu Z L.Passenger flow assignment model and algorithm for urban railway traffic network under the condition of seamless transfer[J].Journal of the China Railway Society,2007,29(6):12-18.
[52]Fisk C.Some developments in equilibrium traffic assignment[J].Transportation Research Part B:Methodological,1980,14(3):243-255.
[53]Dijkstra E W.A note on two problems in connexion with graphs[J].Numerische Mathematics,1959,1(1):269-271.
[54]Floyd R W.Algorithm 97:Shortest path[J].Communications of the ACM,1962,5(6):345.
[55]李树彬,高自友,林勇,等.大规模交通网络实时路径搜索算法研究[J].交通运输系统工程与信息,2009,9(5):141-147.Li S B,Gao Z Y,Lin Y,et al.Real-time path searching algorithm for large traffic network[J].Journal of Transportation Systems Engineering&Information Technology,2009,9(5):141-147.
[56]Hoffman W,Pavley R.A method for the solution of the Nth best path problem[J].Journal of the ACM,1959,6(4):506-514.
[57]Yen J Y.Finding the k shortest loopless paths in a network[J].Management Science,1971,17(11):712-716.
[58]牛新奇,潘荫荣,胡幼华·K(≤3)条渐次短路径搜索算法的研究[J].计算机工程与应用,2005,41(22):51-53.Niu X Q,Pan Y R,Hu Y H.Research on the algorithm of K-shortest path under single restriction with multiple weights[J].Computer Engineering&Applications,2005,41(22):51-53.
[59]Xu W,He S,Song R,et al.Finding the K shortest paths in a schedule-based transit network[J].Computers and Operations Research,2012,39(8):1812-1826.
[60]Abdulaal M,Leblanc L J.Methods for combining modal split and equilibrium assignment models[J].Transportation Science,1979,13:292-314.
[61]Sheffi Y.Urban transportation networks:Equilibrium analysis with mathematical programming methods[M].Prentice-Hall,Englewood Cliffs,NJ,USA,1985.
[62]四兵锋,高自友,交通运输网络流量分析与优化建模[M].北京:人民交通出版社,2013.Si B F,Gao Z Y.Modeling network flow and system optimization for traffic and transportation system[M].Beijing:China Communications Press,2013.
[63]Bell M G H.Stochastic user equilibrium assignment in networks with queues[J].Transportation Research Part B,1995,29(2):125-137.
[64]刘剑锋.基于换乘的城市轨道交通网络流量分配建模及其实证研究[D].北京:北京交通大学,2012.Liu J F.Transfer-based modeling flow assignment with empirical analysis for urban rail transit network[D].Beijing:Beijing Jiaotong University,2012.
[65]Tong C O,Wong S C.A stochastic transit assignment model using a dynamic schedule-based network[J].Transportation Research Part B:Methodological,1998,33(2):107-121.
[66]Cats O.Multi-agent transit operations and assignment model[J].Procedia Computer Science,2013:809-814.
[67]Cats O.An agent-based approach for modeling real-time travel information in transit systems[J].Procedia Computer Science,2014:744-749.
[68]Hassannayebi E,Sajedinejad A,Mardani S.Urban rail transit planning using a two-stage simulation-based optimization approach[J].Simulation Modeling Practice and Theory,2014,49(1):151-166.
[69]高圣国,吴忠.基于旅行时间分布的客流清分模型[J].交通运输系统工程与信息,2011,11(6):124-130.Gao S G,Wu Z.Modeling passenger flow distribution based on travel time of urban rail transit[J].Journal of Transportation Systems Engineering&Information Technology,2011,11(6):124-130.
[70]罗钦.基于网络运营的城市轨道交通客流分布理论及仿真研究[D].上海:同济大学,2009.Luo Q.Theory and simulation analysis of passenger flow distribution based on network operation for urban mass transit[D].Shanghai:Tongji University,2009.
[71]刘玉麟.基于多主体仿真的城市轨道交通网络乘客出行行为研究[D].上海:同济大学,2008.Liu Y L.Traveler behavior study in urban mass transit network based on multi-agent simulation[D].Shanghai:Tongji University,2008.
[72]郑丽娟.基于城市轨道交通网络运营的客流分布预测研究[D].上海:同济大学,2008.Zheng L J.Study of the passenger flow distribution prediction based on URT network operation[D].Shanghai:Tongji University,2008.
[73]姚向明,赵鹏,乔珂.城市轨道交通网络客流分布仿真模型研究[J].交通运输系统工程与信息,2012,12(6):52-59.Yao X M,Zhao P,Qiao K.Modeling dynamic passenger flow distribution of urban rail transit network[J].Journal of Transportation Systems Engineering&Information Technology,2012,12(6):52-59.