简单闭环路网交通流定常解

张鹏; 吕瑜佩; 郭明旻; 林志阳; 房锐; 李晓洋; 张小宁

doi:10.21656/1000-0887.410100

简单闭环路网交通流定常解

doi: 10.21656/1000-0887.410100

¹上海大学力学与工程科学学院上海市应用数学和力学研究所, 上海 200072;²复旦大学航空航天系, 上海 200433;³云南省交通规划设计研究院有限公司陆地交通气象灾害防治技术国家工程实验室, 昆明 650200;⁴同济大学经济与管理学院, 上海 200092

基金项目: 国家自然科学基金(面上项目)(11672348;11972121)；国家重点研发计划(2018YFB1600900)；国家自然科学基金(重点项目)(71531011)

详细信息

作者简介:
张鹏(1963—), 男, 研究员(E-mail: pzhang@shu.edu.cn)；郭明旻(1976—), 男, 讲师(通讯作者. E-mail: mmguo@fudan.edu.cn).

中图分类号: O29
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- 被引次数: 0
出版历程
- 收稿日期: 2020-04-06
- 修回日期: 2020-12-28
- 刊出日期: 2021-02-01

Steady-State Solutions of Traffic Flow in a Simple Circled Road Network

¹Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, P.R.China;²Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, P.R.China;³National Engineering Laboratory for Surface Transportation Weather Impacts Prevention, Broadvision Engineering Consultants Co., Ltd., Kunming 650200, P.R.China;⁴School of Economics and Management, Tongji University, Shanghai 200092, P.R.China

Funds: The National Natural Science Foundation of China（11672348;11972121）

摘要

摘要: 基于在分岔路口满足用户均衡原理的假定，研究了由三条路段和两个交叉路口组成的简单闭环路网的交通流定常解问题，发现定常解参数及其性态依赖于路网上的车流总数：当车流总数不大于第一个临界值，或不小于第二个临界值时，定常解在每一条路段上均为密度取常数的平凡解；否则，在瓶颈路口（上游最大流量大于下游最大流量的路口）的上游路段将产生激波间断，呈排队等候现象.对分岔路口和交汇路口为瓶颈的情况，分别给出了完整的解析结果
- LWR模型 /
- 用户均衡原理 /
- 交通分配模型 /
- 激波间断 /
- 瓶颈效应
Abstract: The steady-state solutions of traffic flow in a circled road network composed of 3 road sections and 2 junctions were studied under the assumption of the user equilibrium principle at the diverging junction. The results show that, the solution parameters and the dynamic behavior depend continuously on the total number of vehicles in the network. More precisely, the solution suggests a constant density in each road section when the total number of vehicles is not greater than the 1st critical density and not smaller than the 2nd critical density. When the total number of vehicles is between the 2 critical densities, the shock discontinuity or queuing appears upstream towards a bottleneck or a junction where the upstream capacity is greater than the downstream capacity. Complete analytical results were presented with the diverging and the merging junctions as bottlenecks, respectively.
- LWR model /
- user equilibrium principle /
- transportation assignment model /
- shock discontinuity /
- bottleneck effect

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参考文献(22)

[1]	SAW K, KATTI B K, JOSHI G. Literature review of traffic assignment: static and dynamic[J]. International Journal of Transportation Engineering,2015,2(4): 339-347.
[2]	WONG W, WONG S C. Network topological effects on the macroscopic bureau of public roads function[J]. Transportmetrica A: Transport Science,2016,12(3): 272-296.
[3]	LEBACQUE J P. The Godunov scheme and what it means for first order traffic flow models[C]//LESORT J B, ed. Proceedings of the Thirteenth International Symposium on Transportation and Traffic Theory.France, 1995.
[4]	DAGANZO C F. The cell transmission model, part Ⅱ: network traffic[J]. Transportation Research Part B,1995,29(2): 79-93.
[5]	COCLITE G M, GARAVELLO M, PICCOLI B. Traffic flow on a road network[J]. SIAM Journal on Mathematical Analysis,2005,36: 1862-1886.
[6]	GARAVELLO M, NATALINI R, PICCOLI B, et al. Conservation laws with discontinuous flux[J]. Networks and Heterogenous Media,2007,2(1): 159-179.
[7]	LIN Z Y, ZHANG P, DONG L Y, et al. Traffc flow on a road network using a conserved higher-order model[C]// AIP Conference Proceedings.Greece: AIP Publishing, 2015.
[8]	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.
[9]	FRIESZ T L, HAN K, NETO P A, et al. Dynamic user equilibrium based on a hydrodynamic model[J]. Transportation Research Part B: Methodological,2013,47: 102-126.
[10]	ZHANG Z, WOLSHON B, DIXIT V V. Integration of a cell transmission model and macroscopic fundamental diagram: network aggregation for dynamic traffic models[J]. Transportation Research Part C: Emerging Technologies,2015,55: 298-309.
[11]	CHENG Q, LIU Z, SZETO W Y. A cell-based dynamic congestion pricing scheme considering travel distance and time delay[J]. Transportmetrica B: Transport Dynamics,2019,7(1): 1286-1304.
[12]	JIANG Y Q, WONG S C, ZHANG P, et al. Dynamic continuum model with elastic demand for a polycentric urban city[J]. Transportation Science,2017,51(3): 931-945.
[13]	LIN Z Y, WONG S C, ZHANG P, et al. A predictive continuum dynamic user-optimal model for the simultaneous departure time and route choice problem in a polycentric city[J]. Transportation Science,2018,52(6): 1496-1508.
[14]	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 of London（Series A）,1955,22: 317-345.
[15]	RICHARDS P I. Shockwaves on the highway[J]. Operation Research,1956,4: 42-51.
[16]	JIN W L. On the existence of stationary states in general road networks[J]. Transportation Research Part B: Methodological,2015,81: 917-929.
[17]	JIN W L. On the stability of stationary states in general road networks[J]. Transportation Research Part B: Methodological,2017,98: 42-61.
[18]	WU C X, ZHANG P, WONG S C, et al. Steady-state traffic flow on a ring road with up- and down-slopes[J]. Physica A,2014,403: 85-93.
[19]	TORO E F. Riemann Solvers and Numerical Methods for Fluid Dynamics [M]. Heidelberg: Springer-Verlag, 1999.
[20]	姜锐, 吴清松, 朱祚金. 各向异性交通流动力学模型的波动特性[J]. 应用数学和力学, 2002,23(4): 371-375.(JIANG Rui, WU Qingsong, ZHU Zuojin. Kinematic wave properties of anisotropic dynamics model for traffic flow[J]. Applied Mathematics and Mechanics,2002,23(4): 371-375.(in Chinese))
[21]	董力耘, 薛郁, 戴世强. 基于跟车思想的一维元胞自动机交通流模型[J]. 应用数学和力学, 2002,23(4): 331-337.(DONG Liyun, XUE Yu, DAI Shiqiang. One-dimensional cellular automaton model of traffic flow based on car-following idea[J]. Applied Mathematics and Mechanics,2002,23(4): 331-337.(in Chinese))
[22]	罗振东, 徐源. 守恒高阶各向异性交通流模型基于POD方法的降阶外推差分格式[J]. 应用数学和力学, 2015,36(8): 875-886.(LUO Zhendong, XU Yuan. A reduced-order extrapolating FDM for conserved high-order anisotropic traffic flow models[J]. Applied Mathematics and Mechanics,2015,36(8): 875-886.(in Chinese))