交通运输系统工程与信息 ›› 2021, Vol. 21 ›› Issue (5): 125-138.
龙建成*,郭嘉琪
收稿日期:
2021-03-23
修回日期:
2021-04-24
接受日期:
2021-05-07
出版日期:
2021-10-25
发布日期:
2021-10-21
作者简介:
龙建成(1983- ),男,湖南祁东人,教授,博士。
基金资助:
LONG Jian-cheng*,GUO Jia-qi
Received:
2021-03-23
Revised:
2021-04-24
Accepted:
2021-05-07
Online:
2021-10-25
Published:
2021-10-21
Supported by:
摘要: 动态交通分配(Dynamic Traffic Assignment,DTA)理论是智能交通系统中最重要的关键技 术基础之一,也是当前交通科学中最活跃的研究领域之一,其模型可以广泛应用于离线的交通规 划及政策评估和在线的智能交通系统应用。本文首先回顾了DTA理论50年来的发展历程,总结 了不同发展阶段形成的重要理论和方法。其次介绍了DTA问题的两个基本构成:出行选择准则 和交通流传播模型,指出这两个基本组成部分通过走行时间函数(或阻抗函数)来关联,并总结了 DTA 问题中主要的出行选择准则、主要的交通流传播模型、重点关注的交通行为、走行时间函 数。依据出行者的出行选择内容、交通状况掌握、出行需求弹性、出行决策时间跨度以及用户类 型等对动态交通分配问题进行分类,并详细比较分析不同类型动态交通分配问题之间的差异。 进一步,介绍了DTA问题主要的解析模型,依据时间是否连续和使用的决策变量分别对DTA模 型进行分类,并总结了不同类型DTA模型的主要优缺点。介绍了不同出行选择准则下DTA问题 的主要求解方法,并评述求解方法的收敛性、效率等。此外,还概述了DTA模型在交通规划、交通 政策评估、交通控制与管理等方面的应用。最后,对DTA理论的进一步发展进行展望,指出DTA 理论和方法可以在5方面取得突破:动态网络加载模型的高效计算方法和性态良好的动态阻抗函 数,大规模交通网络上DTA问题的有效求解算法,超级网络上基于活动链的DTA模型,DTA模型 在交通管理与控制中的应用,未来智能网联环境下DTA模型及其应用。
中图分类号:
龙建成, 郭嘉琪. 动态交通分配问题研究回顾与展望[J]. 交通运输系统工程与信息, 2021, 21(5): 125-138.
LONG Jian-cheng, GUO Jia-qi. Review and Prospect of Dynamic Traffic Assignment Research[J]. Journal of Transportation Systems Engineering and Information Technology, 2021, 21(5): 125-138.
[1] RAN B, BOYCE D. Modeling dynamic transportation networks[J]. Springer-Verlag, 1996, 6(1): 76. [2] VICKREY W S. Congestion theory and transport investment[J]. The American Economic Review, 1969, 59 (2): 251-260. [3] YAGAR S. Dynamic traffic assignment by individual path minimisation and queuing[J]. Transportation Research, 1971, 5(33): 179-196. [4] MERCHANT D K, NEMHAUSER G L. A model and an algorithm for the dynamic traffic assignment[J]. Transportation Science, 1978, 12(3): 183-199. [5] MERCHANT D K, NEMHAUSER G L. Optimality conditions for a dynamic traffic assignment model[J]. Transportation Science, 1978, 12(3): 200-207. [6] HO J K. A successive linear optimization approach to the dynamic traffic assignment problem[J]. Transportation Science, 1980, 14(4): 295-305. [7] CAREY M. Optimal time-varying flows on congested networks[J]. Operations Research, 1987, 35(1): 58-69. [8] FRIESZ T L, LUQUE J, TOBIN R L, et al. Dynamic network traffic assignment considered as a continuoustime optimal-control problem[J]. Operations Research, 1989, 37(6): 893-901. [9] SMITH M J. The stability of a dynamic model of traffic assignment-an application of a method of lyapunov[J]. Transportation Science, 1984, 18(3): 245-252. [10] FRIESZ T L, BERSTEIN D H, SMITH T E, et al. A variational inequality formulation of the dynamic network user equilibrium problem[J]. Operations Research, 1993, 41(1): 179-191. [11] DAGANZO C F. The cell transmission model: A simple dynamic representation of highway traffic[J]. Transportation Research Part B: Methodological, 1994, 28(4): 269-287. [12] DAGANZO C F. The cell transmission model, Part II: Network traffic[J]. Transportation Research Part B: Methodological, 1995, 29(2): 79-93. [13] LIGHTHILL M J, WHITHAM G B. On kinematic waves II. A theory of traffic flow on long crowded roads[J]. Proceedings of the Royal Society, 1955, 229(1178): 317- 345. [14] RICHARDS P I. Shock waves on the highway[J]. Operations Research, 1956, 4(1): 42-51. [15] LO H K, SZETO W Y. A cell-based variational inequality formulation of the dynamic user optimal assignment problem[J]. Transportation Research Part B: Methodological, 2002, 36(5): 421-443. [16] SZETO W Y, LO H K. A cell- based simultaneous route and departure time choice model with elastic demand[J]. Transportation Research Part B: Methodological, 2004, 38(7): 593-612. [17] HAN L, UKKUSURI S, DOAN K. Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity[J]. Transportation Research Part B: Methodological, 2011, 45(10): 1749- 1767. [18] UKKUSURI S V, HAN L, DOAN K. Dynamic user equilibrium with a path based cell transmission model for general traffic networks[J]. Transportation Research Part B: Methodological, 2012, 46(10): 1657-1684. [19] ZILIASKOPOULOS A K. A linear programming model for the single destination system optimum dynamic traffic assignment problem[J]. Transportation Science, 2000, 34 (1): 37-49. [20] LIN W H, WANG C. An enhanced 0-1 mixed-integer LP formulation for traffic signal control[J]. IEEE Transactions on Intelligent Transportation Systems, 2004, 5(4): 238-245. [21] NIE Y. A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem[J]. Transportation Research Part B: Methodological, 2011, 45(2): 329-342. [22] ZHU F, UKKUSURI S V. A cell based dynamic system optimum model with non-holding back flows[J]. Transportation Research Part C: Emerging Technologies, 2013, 36: 367-380. [23] ZHENG H, CHIU Y C, MIRCHANDANI P B. On the system optimum dynamic traffic assignment and earliestarrival flow problems[J]. Transportation Science, 2015, 49 (1): 13-27. [24] NGODUY D, HOANG N H, VU H L, et al. Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks[J]. Transportation Research Part B: Methodological, 2016, 92: 148-169. [25] CAREY M, SRINIVASAN A. Externalities, average and marginal costs, and tolls on congested networks with time-varying flows[J]. Operations Research, 1993, 41(1): 217-231. [26] YPERMAN I. The link transmission model for dynamic network loading[D]. Leuven, Belgium: Katholieke Universiteit Leuven, 2007. [27] OSORIO C, FLÖTTERÖD G, BIERLAIRE M. Dynamic network loading: A stochastic differentiable model that derives link state distributions[J]. Transportation Research Part B: Methodological, 2011, 45(9): 1410- 1423. [28] HAN K, PICCOLI B, FRIESZ T L. Continuity of the path delay operator for dynamic network loading with spillback [J]. Transportation Research Part B: Methodological, 2016, 92: 211-233. [29] HIMPE W, CORTHOUT R, TAMPÈRE M C. An efficient iterative link transmission model[J]. Transportation Research Part B: Methodological, 2016, 92: 170-190. [30] SONG W, HAN K, WANG Y, et al. Statistical metamodeling of dynamic network loading[J]. Transportation Research Procedia, 2017, 23: 263-282. [31] RAADSEN M P H, BLIEMER M C J, BELL M G H. An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time[J]. Transportation Research Part B: Methodological, 2016, 92: 191-210. [32] BLIEMER M C J, RAADSEN M P H. Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation[J]. Transportation Research Part B: Methodological, 2019, 126: 442-470. [33] RAADSEN M P H, BLIEMER M C. Continuous-time general link transmission model with simplified fanning, Part II: Event- based algorithm for networks[J]. Transportation Research Part B: Methodological, 2019, 126: 471-501. [34] LONG J, HUANG H J, GAO Z, et al. An intersectionmovement-based dynamic user optimal route choice problem[J]. Operations Research, 2013, 61(5): 1134- 1147. [35] LONG J, SZETO W Y, GAO Z, et al. The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems[J]. Transportation Research Part B: Methodological, 2016, 83: 179-206. [36] JIANG Y, SZETO W Y, LONG J, et al. Multi- class dynamic traffic assignment with physical queues: intersection-movement-based formulation and paradox[J]. Transportmetrica A: Transport Science, 2016, 12(10): 878-908. [37] FRIESZ T L, HAN K. The mathematical foundations of dynamic user equilibrium[J]. Transportation Research Part B: Methodological, 2019, 126: 309-328. [38] HOOGENDOORN S P, BOVY P H L. Dynamic useroptimal assignment in continuous time and space[J]. Transportation Research Part B: Methodological, 2004, 38(7): 571-592. [39] JIANG Y, WONG S C, HO H W, et al. A dynamic traffic assignment model for a continuum transportation system [J]. Transportation Research Part B: Methodological, 2011, 45(2): 343-363. [40] DU J, WONG S C, SHU C W, et al. Revisiting Jiang's dynamic continuum model for urban cities[J]. Transportation Research Part B: Methodological, 2013, 56: 96-119. [41] DU J, WONG S C, SHU C W, et al. Reformulating the Hoogendoorn- Bovy predictive dynamic user- optimal model in continuum space with anisotropic condition[J]. Transportation Research Part B: Methodological, 2015, 79: 189-217. [42] LONG J, SZETO W Y, DU J, et al. A dynamic taxi traffic assignment model: A two-level continuum transportation system approach[J]. Transportation Research Part B: Methodological, 2017, 100: 222-254. [43] BAN X, PANG J S, LIU H X, et al. Modeling and solving continuous- time instantaneous dynamic user equilibria: A differential complementarity systems approach[J]. Transportation Research Part B: Methodological, 2012, 46(3): 389-408. [44] MA R, BAN X, PANG J S. Continuous- time dynamic system optimum for single-destination traffic networks with queue spillbacks[J]. Transportation Research Part B: Methodological, 2014, 68: 98-122. [45] MA R, BAN X, SZETO W Y. Emission modeling and pricing on single-destination dynamic traffic networks[J]. Transportation Research Part B: Methodological, 2017, 100: 255-283. [46] LAM W H K, YIN Y. An activity-based time-dependent traffic assignment model[J]. Transportation Research Part B: Methodological, 2001, 35(6): 549-574. [47] LIU P, LIAO F, HUANG H J, et al. Dynamic activitytravel assignment in multi-state super-networks[J]. Transportation Research Part B: Methodological, 2015, 81: 656-671. [48] CANTELMO G, VITI F. Incorporating activity duration and scheduling utility into equilibrium-based dynamictraffic assignment[J]. Transportation Research Part B: Methodological, 2019, 126: 365-390. [49] LONG J, WANG C, SZETO W Y. Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons[J]. Transportation Research Part B: Methodological, 2018, 115: 166-206. [50] LONG J, SZETO W Y. Link- based system optimum dynamic traffic assignment problems in general networks [J]. Operations Research, 2019, 67(1): 167-182. [51] HUANG Y P, XIONG J H, SUMALEE A, et al. A dynamic user equilibrium model for multi- region macroscopic fundamental diagram systems with timevarying delays[J]. Transportation Research Part B: Methodological, 2020, 131: 1-25. [52] NGODUY D, HOANG N H, VU H L, et al. Multiclass dynamic system optimum solution for mixed traffic of human- driven and automated vehicles considering physical queues[J]. Transportation Research Part B: Methodological, 2021, 145: 56-79. [53] KAMGA C N, MOUSKOS K C, PAASWELL R E. A methodology to estimate travel time using dynamic traffic assignment (DTA) under incident conditions[J]. Transportation Research Part C: Emerging Technologies, 2011, 19(6): 1215-1224. [54] YU H, MA R, ZHANG H M. Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network[J]. Transportation Research Part B: Methodological, 2018, 110: 302-325. [55] LIN W H, LIU H. Enhancing realism in modeling merge junctions in analytical models for system- optimal dynamic traffic assignment[J]. IEEE Transactions on Intelligent Transportation Systems, 2010, 11(4): 838- 845. [56] PEL A J, BLIEMER M C J, HOOGENDOORN S P. Hybrid route choice modeling in dynamic traffic assignment[J]. Transportation Research Record, 2009, 2091: 100-107. [57] HUANG H J. Fares and tolls in a competitive system with transit and highway: The case with two groups of commuters[J]. Transportation Research Part E: Logistics and Transportation Review, 2000, 36(4): 267-284. [58] VAN DEN BERG V, VERHOEF E T. Congestion tolling in the bottleneck model with heterogeneous values of time [J]. Transportation Research Part B: Methodological, 2011, 45(1): 60-78. [59] CAREY M, WATLING D. Dynamic traffic assignment approximating the kinematic wave model: System optimum, marginal costs, externalities and tolls[J]. Transportation Research Part B: Methodological, 2012, 46(5): 634-648. [60] UKKUSURI S, WALLER S T. Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions[J]. Networks and Spatial Economics, 2008, 8 (4): 383-406. [61] LIN D Y. A dual variable approximation- based descent method for a bi-level continuous dynamic network design problem[J]. Computer-Aided Civil and Infrastructure Engineering, 2011, 26(8): 581-594. [62] ZHU T, LONG J, LIU H. Optimal official work start times in activity-based bottleneck models with staggered work hours[J]. Transportmetrica B: Transport Dynamics, 2019, 7(1): 657-683. [63] LI Y, UKKUSURI S V, FAN J. Managing congestion and emissions in transportation networks with dynamic carbon credit charge scheme[J]. Computers & Operations Research, 2018, 99: 90-108. [64] XIAO L L, HUANG H J, LIU R. Congestion behavior and tolls in a bottleneck model with stochastic capacity[J]. Transportation Science, 2015, 49(1): 46-65. [65] FLORIAN M, MAHUT M, TREMBLAY N. Application of a simulation-based dynamic traffic assignment model[J]. European Journal of Operational Research, 2008, 189(3): 1381-1392. [66] ZHANG X N, ZHANG H M. Simultaneous departure time/ route choices in queuing networks and a novel paradox [J]. Networks and Spatial Economics, 2010, 10(1): 93- 112. [67] WALLER S T, MOUSKOS K C, KAMARYIANNIS D, et al. A linear model for the continuous network design problem[J]. Computer-Aided Civil and Infrastructure Engineering, 2006, 21(5): 334-345. [68] KAROONSOONTAWONG A, WALLER S T. Robust dynamic continuous network design problem[J]. Transportation Research Record Journal of the Transportation Research Board, 2007, 2029: 58-71. [69] OSAWA M, FU H, AKAMATSU T. First- best dynamic assignment of commuters with endogenous heterogeneities in a corridor network[J]. Transportation Research Part B: Methodological, 2018, 117: 811-831. [70] LO H K. A cell- based traffic control formulation: Strategies and benefits of dynamic timing plans[J]. Transportation Science, 2001, 35(2): 149-164. [71] LIU Y, LAI X, CHANG G L. Cell- based network optimization model for staged evacuation planning under emergencies[J]. Transportation Research Record Journal of the Transportation Research Board, 2006, 1964: 127- 135. [72] CHIU Y C, ZHENG H, VILLALOBOS J, et al. Modeling no- notice mass evacuation using a dynamic traffic flow optimization model[J]. Iie Transactions, 2007, 39(1): 83- 94. [73] 高明霞, 贺国光. 动态系统最优的疏散路线与出发时间综合优化模型[J]. 系統工程, 2009, 27(6): 73-77. [GAO M X, HE G G. Synthetical optimization model of optimal evacuation routes and departure time choice in a dynamic system[J]. Systems Engineering, 2009, 27(6): 73-77.] [74] LEVIN M W. Congestion- aware system optimal route choice for shared autonomous vehicles[J]. Transportation Research Part C: Emerging Technologies, 2017, 82: 229- 247. [75] LI Y, LONG J C, YU M. A time-dependent shared autonomous vehicle system design problem[J]. Transportation Research Part C: Emerging Technologies, 2021, 124: 102956. [76] SZETO W Y, LO H K. Dynamic traffic assignment: Properties and extensions[J]. Transportmetrica, 2006, 2 (1): 31-52. [77] HUANG H J, LAM W H K. Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues[J]. Transportation Research Part B: Methodological, 2002, 36(3): 253-273. [78] 李琰, 周八益, 周溪召. 多用户动态交通分配模型的算 法研究[J]. 上海海运学院学报, 2004, 25(1): 87-91. [LI D, ZHOU B Y, ZHOU X Z. A new algorithm for the multiclass dynamic traffic assignment (DTA) [J]. Journal of Shanghai Maritime University, 2004, 25(1): 87-91.] [79] 任华玲, 高自友. 动态交通分配中一种离散 VI 模型的 算法研究[J]. 土木工程学报, 2004, 37(3): 107- 110. [REN H L, GAO Z Y. A modified approach on discreted variational inequality model in dynamic traffic network [J]. China Civil Engineering Journal, 2004, 37(3): 107- 110.] [80] 任华玲, 高自友. 考虑出发时间选择的动态用户最优 模型[J]. 交通运输系统工程与信息, 2007, 7(3): 83-89. [REN H L, GAO Z Y. Dynamic user optimal model with departure time-application of bilevel programming in dynamic traffic assignment[J]. Journal of Transportation Systems Engineering and Information Technology, 2007, 7(3): 83-89.] [81] 高自友, 任华玲. 城市动态交通流分配模型与算法 [M]. 北京: 人民交通出版社, 2005. [GAO Z Y, REN H L. Dynamic traffic assignment problems in urban transportation networks: models and methods[M]. Beijing: China Communications Press, 2005.] [82] 李乐园, 张小宁, 张红军. 基于交通瓶颈的动态交通分 配模型[J]. 系统工程理论与实践, 2006, 26(4): 125- 129. [LI L Y, ZHANG X N, ZHANG H J. A model of dynamic traffic assignment based on traffic bottleneck with varying capacity[J]. Systems Engineering Theory and Practice, 2006, 26(4): 125-129.] [83] 连爱萍, 高自友, 龙建成. 基于路段元胞传输模型的动 态用户最优配流问题[J]. 自动化学报, 2007, 33(8): 852-859. [LIAN A P, GAO Z Y, LONG J C. A dynamic user optimal assignment problem of link variables based on the cell transmission model[J]. Acta Automatica Sinica, 2007, 33(8): 852-859.] [84] 李润梅, 汤淑明, 王飞跃. 动态用户最优的变分不等式 分配模型研究综述[J]. 交通运输系统工程与信息, 2006, 6(2): 93-90. [LI R M, TANG S M, WANG F Y. A review of dynamic user-optimal variational inequality traffic assignment[J]. Journal of Transportation Systems Engineering and Information Technology, 2006, 6(2): 93- 90.] [85] BAN X, LIU H X, FERRIS M C, et al. A link- node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations[J]. Transportation Research Part B: Methodological, 2008, 42(9): 823-842. [86] GUO Q, BAN X. Macroscopic fundamental diagram based perimeter control considering dynamic user equilibrium[J]. Transportation Research Part B: Methodological, 2020, 136: 87-109. [87] CHEN H K, FENG G. Heuristics for the stochastic/ dynamic user-optimal route choice problem[J]. European Journal of Operational Research, 2000, 126(1): 13-30. [88] HAN S. Dynamic traffic modelling and dynamic stochastic user equilibrium assignment for general road networks[J]. Transportation Research Part B: Methodological, 2003, 37(3): 225-249. [89] LIM Y, HEYDECKER B. Dynamic departure time and stochastic user equilibrium assignment[J]. Transportation Research Part B: Methodological, 2005, 39(2): 97-118. [90] SZETO W Y, JIANG Y, SUMALEE A. A cell-based model for multi- class doubly stochastic dynamic traffic assignment: A cell-based model for multi- class doubly stochastic DTA[J]. Computer-Aided Civil and Infrastructure Engineering, 2011, 26(8): 595-611. [91] LONG J, SZETO W Y, HUANG H J, et al. An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance[J]. Transportation Research Part B: Methodological, 2015, 74: 182-217. [92] ZHANG P, QIAN S. Path-based system optimal dynamic traffic assignment: A subgradient approach[J]. Transportation Research Part B: Methodological, 2020, 134: 41-63. [93] WARDROP J G. Some theoretical aspects of road traffic research[J]. Proceedings of the Institution of Civil Engineers, Part II, 1952, 1: 325-378. [94] CAREY M, GE Y E. Comparison of methods for path flow reassignment for dynamic user equilibrium[J]. Networks and Spatial Economics, 2012, 12(3): 337-376. [95] SZETO W, WONG S. Dynamic traffic assignment: Model classifications and recent advances in travel choice principles[J]. Open Engineering, 2012, 2(1): 1-18. [96] TIAN L J, HUANG H J, GAO Z Y. A cumulative perceived value-ased dynamic user equilibrium model considering the ravelers' risk evaluation on arrival time [J]. Networks and Spatial Economics, 2012, 12(4): 589- 608. [97] LONG J C, SZETO W Y, DING J X. Dynamic traffic assignment in degradable networks: Paradoxes and formulations with stochastic link transmission model[J]. Transportmetrica B: Transport Dynamics, 2019, 7(1): 336-362. [98] LIU Q, JIANG R, LIU R, et al. Travel cost budget based user equilibrium in a bottleneck model with stochastic capacity[J]. Transportation Research Part B: Methodological, 2020, 139: 1-37. [99] BATISTA S F A, LECLERCQ L. The reference point in dynamic prospect-based user equilibrium: a simulation study[J]. Transportation Letters, 2020, 12(8): 513-527. [100] MUN J. Traffic performance models for dynamic traffic assignment: An assessment of existing models[J]. Transport Reviews, 2007, 27(2): 231-249. [101] NEWELL G F. A simplified theory on kinematic wave in highway traffic, part I: General theory; part II: Queuing at freeway bottlenecks; part III: Multi- destination flows[J]. Transportation Research Part B: Methodological, 1993, 27(4): 281-314. [102] LONG J C, GAO Z Y, SZETO W Y. Discretised link travel time models based on cumulative flows: Formulations and properties[J]. Transportation Research Part B: Methodological, 2011, 45(1): 232-254. [103] CAREY M. Link travel times I: Desirable properties[J]. Networks and Spatial Economics, 2004, 4(3): 257-268. [104] CAREY M. Nonconvexity of the dynamic traffic assignment problem[J]. Transportation Research Part B: Methodological, 1992, 26(2): 127-133. [105] NAGURNEY A. Network economics: A variational inequality approach[M]. Kluwer Academic Publishers. Norwell, Massachusetts, USA, 1993. [106] CAREY M, GE Y E. Retaining desirable properties in discretising a travel-time model[J]. Transportation Research Part B: Methodological, 2007, 41(5): 540-553. [107] ARNOTT R, DE PALMA A, LINDSEY R. Departure time and route choice for the morning commute[J]. Transportation Research Part B: Methodological, 1990, 24(3): 209-228. [108] GUO R Y, YANG H, HUANG H J, et al. Day- to- day departure time choice under bounded rationality in the bottleneck model[J]. Transportation Research Part B: Methodological, 2018, 117: 832-849. [109] WANG D, LIAO F, GAO Z, et al. Tolerance- based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem[J]. Transportation Research Part B: Methodological, 2019, 119: 102-121. [110] HAN K, FRIESZ T L, SZETO W Y, et al. Elastic demand dynamic network user equilibrium: Formulation, existence and computation[J]. Transportation Research Part B: Methodological, 2015, 81: 183-209. [111] HE X, GUO X, LIU H X. A link-based day-to-day traffic assignment model[J]. Transportation Research Part B: Methodological, 2010, 44(4): 597-608. [112] GUO R Y, YANG H, HUANG H J, et al. Day-to-day flow dynamics and congestion control[J]. Transportation Science, 2015, 50(3): 982-997. [113] GUO R Y, YANG H, HUANG H J, et al. Link-based dayto-day network traffic dynamics and equilibria[J]. Transportation Research Part B: Methodological, 2015, 71: 248-260. [114] XIAO F, YANG H, YE H. Physics of day-to-day network flow dynamics[J]. Transportation Research Part B: Methodological, 2016, 86: 86-103. [115] XIAO F, SHEN M, XU Z, et al. Day-to-day flow dynamics for stochastic user equilibrium and a general lyapunov function[J]. Transportation Science, 2019, 53(3): 683- 694. [116] JIN W L. Stable day-to-day dynamics for departure time choice[J]. Transportation Science, 2020, 54(1): 42-61. [117] YANG H, HUANG H J. The multi-class, multi-criteria tra ffi c network equilibrium and systems optimum problem [J]. Transportation Research Part B: Methodological, 2004, 38(1): 1-15. [118] MAHMASSANI H S, CHANG G L. On boundedly rational user equilibrium in transportation systems[J]. Transportation Science, 1987, 21(2): 89-99. [119] LONG J, CHEN J, SZETO W Y, et al. Link-based system optimum dynamic traffic assignment problems with environmental objectives[J]. Transportation Research Part D: Transport and Environment, 2018, 60: 56-75. [120] RAN B, BOYCE D E, LEBLANC L J. A new class of instantaneous dynamic user-optimal traffic assignment models[J]. Operations Research, 1993, 41(1): 192-202. [121] SMITH M J. A new dynamic traffic and the existence and calculation of dynamic user equilibria on congestion capacity- constrained road networks[J]. Transportation Research Part B: Methodological, 1993, 27(1): 49-63. [122] TONG C O, WONG S C. A predictive dynamic traffic assignment model in congested capacity-constrained road networks[J]. Transportation Research Part B: Methodological, 2000, 34(8): 625-644. [123] MOUNCE R, CAREY M. Route swapping in dynamic traffic networks[J]. Transportation Research Part B: Methodological, 2011, 45(1): 102-111. [124] JANG W, RAN B, CHOI K. A discrete time dynamic flow model and a formulation and solution method for dynamic route choice[J]. Transportation Research Part B:Methodological, 2005, 39(7): 593-620. [125] HAN K, SZETO W Y, FRIESZ T L. Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance[J]. Transportation Research Part B: Methodological, 2015, 79: 16-49. [126] ZHAO Y B, HU J. Global bounds for the distance to solutions of co- coercive variational inequalities[J]. Operations Research Letters, 2007, 35(3): 409-415. [127] LIU H, HE X, HE B. Method of successive weighted averages (MSWA) and self-regulated averaging schemes for solving stochastic user equilibrium problem[J]. Networks and Spatial Economics, 2009, 9(4): 485-503. [128] PEETA S, MAHMASSANI H. System optimal and user equilibrium time-dependent traffic assignment in congested networks[J]. Annals of Operations Research, 1995, 60(1): 80-113. [129] SHEN W, NIE Y, ZHANG H M. On path marginal cost analysis and its relation to dynamic system- optimal traffic assignment[C]. Allsop RE, Bell MGH, Heydecker BG, ed. Proc. 17th Internat. Sympos. Transportation Traffic Theory. Elsevier, New York, 2007: 327-360. [130] QIAN Z, SHEN W, ZHANG H M. System- optimal dynamic traffic assignment with and without queue spillback: Its path-based formulation and solution via approximate path marginal cost[J]. Transportation Research Part B: Methodological, 2012, 46(7): 874-893. [131] ZHENG H, CHIU Y C. A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem[J]. Transportation Science, 2011, 45(1): 121-137. [132] DOAN K, UKKUSURI S V. On the holding-back problem in the cell transmission based dynamic traffic assignment models[J]. Transportation Research Part B: Methodological, 2012, 46(9): 1218-1238. [133] PAVLIS Y, RECKER W. A Mathematical Logic Approach for the transformation of the linear conditional piecewise functions of dispersion- and-store and cell transmission traffic flow models into linear mixed-integer form[J]. Transportation Science, 2009, 43(1): 98-116. |
[1] | 郭烈, 胥林立, 秦增科, 王旭. 自动驾驶接管影响因素分析与研究进展[J]. 交通运输系统工程与信息, 2022, 22(2): 72-90. |
[2] | 徐猛, 刘涛, 钟绍鹏, 姜宇. 城市智慧公交研究综述与展望[J]. 交通运输系统工程与信息, 2022, 22(2): 91-108. |
[3] | 程君, 张立炎, 陈启宏. 一种基于地图辅助的自动驾驶视-惯融合定位方法[J]. 交通运输系统工程与信息, 2022, 22(2): 117-126. |
[4] | 王国栋, 刘立, 孟宇, 马智萍, 郑淏清, 顾青, 白国星. 一体式车辆避撞轨迹规划与跟踪控制[J]. 交通运输系统工程与信息, 2022, 22(2): 127-136. |
[5] | 马东方, 陈曦, 吴晓东, 金盛. 基于强化学习的干线信号混合协同优化方法[J]. 交通运输系统工程与信息, 2022, 22(2): 145-153. |
[6] | 许波桅, 王玲玲, 李军军. 自动化码头多级作业超网络延误传导特性研究[J]. 交通运输系统工程与信息, 2022, 22(2): 280-289. |
[7] | 田会娟, 刘嘉伟, 翟佳豪, 邓琳琳. 基于多入侵线的视频车速检测方法[J]. 交通运输系统工程与信息, 2022, 22(1): 49-56. |
[8] | 贾彦峰, 曲大义, 赵梓旭, 王韬, 宋慧. 基于安全势场的网联自主车辆跟驰行为决策及模型[J]. 交通运输系统工程与信息, 2022, 22(1): 85-97. |
[9] | 刘文, 汪文博. 基于秩最小化矩阵去噪的船舶轨迹重构方法[J]. 交通运输系统工程与信息, 2022, 22(1): 106-114. |
[10] | 赵建东, 陈溱, 焦彦利, 张凯丽, 韩明敏. 重点营运车辆的异常驾驶行为识别研究[J]. 交通运输系统工程与信息, 2022, 22(1): 282-291. |
[11] | 徐东伟, 彭航, 商学天, 魏臣臣, 杨艳芳. 基于图自编码-生成对抗网络的路网数据修复[J]. 交通运输系统工程与信息, 2021, 21(6): 33-41. |
[12] | 游峰, 梁健中, 曹水金, 肖智豪, 吴镇江, 王海玮. 面向多目标跟踪的密集行人群轨迹提取和运动语义感知[J]. 交通运输系统工程与信息, 2021, 21(6): 42-54. |
[13] | 王福建, 俞佳浩, 赵锦焕, 梅振宇. 基于站点实时关联度的短时公交客流预测方法[J]. 交通运输系统工程与信息, 2021, 21(6): 131-144. |
[14] | 张毅, 姚丹亚, 李力, 裴华鑫, 晏松, 葛经纬. 智能车路协同系统关键技术与应用[J]. 交通运输系统工程与信息, 2021, 21(5): 40-51. |
[15] | 余祖俊, 张晨光, 郭保青. 基于激光与视觉融合的车辆自主定位与建图算法[J]. 交通运输系统工程与信息, 2021, 21(4): 72-81. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||