基于直线型反λ基本图的交通流分配模型及算法
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摘要
针对现有交通流分配理论难以处理路段拥挤状态的问题,以直线型反λ交通流量、密度和速度基本关系图为基础,提出了给定路段交通状态下的静态交通流分配新方法。通过分析基本关系图,得到两阶段的路段行程时间函数;通过引入路段交通状态指标量,构建节点流量守恒方程,建立了系统最优和用户均衡交通流分配模型;针对非凸的用户均衡模型,通过线性化目标函数中的非凸项,设计了一种有效的分支定界求解算法。数值算例验证了新模型和算法的有效性;新理论扩展了现有路段行程时间函数过于片面的单调递增特征假设,可有效处理路段拥挤状态,提高现有理论的实用性。
The existing traffic assignment theorem hardly dealt with the congested traffic state of link. To solve the above problem,based on the classic straight line inverse λ fundamental diagram,this paper presented a static traffic assignment method with given states of links. Firstly,through analyzing the fundamental diagram,it obtained the travel time function of link with two stages. Secondly,by introducing the indicating label of traffic state of link and constructing the flow conservation equations at nodes,it formulated the system optimal and user equilibrium traffic assignment models. At last,to solve the non-convex user equilibrium model,it proposed a branch and bound algorithm with relaxed partial objective function. This paper used numerical examples to demonstrate the effectiveness of the new model and algorithm. By extending the one-sided assumption of monotone increasing of link travel time function,the new theory can deal with the congested traffic state of link effectively and improve the practicality of existing theories.
The existing traffic assignment theorem hardly dealt with the congested traffic state of link. To solve the above problem,based on the classic straight line inverse λ fundamental diagram,this paper presented a static traffic assignment method with given states of links. Firstly,through analyzing the fundamental diagram,it obtained the travel time function of link with two stages. Secondly,by introducing the indicating label of traffic state of link and constructing the flow conservation equations at nodes,it formulated the system optimal and user equilibrium traffic assignment models. At last,to solve the non-convex user equilibrium model,it proposed a branch and bound algorithm with relaxed partial objective function. This paper used numerical examples to demonstrate the effectiveness of the new model and algorithm. By extending the one-sided assumption of monotone increasing of link travel time function,the new theory can deal with the congested traffic state of link effectively and improve the practicality of existing theories.
引文
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[7]何胜学,董琼,徐福缘.基于网络对偶均衡的交通流分配模型[J].公路交通科技,2010,27(9):105-110.(He Shengxue,DongQiong,Xu Fuyuan. Traffic assignment model based on network dualequilibrium[J]. Journal of Highway and Transportation Re-search and Development,2010,27(9):105-110.)
[8]何胜学,何建佳,徐福缘.基于网络对偶均衡的有边约束的交通流分配模型[J].交通运输系统工程与信息,2011,11(2):100-105.(He Shengxue,He Jianjia,Xu Fuyuan. Side constrained traffic as-signment model based on network dual equilibrium[J]. Transporta-tion Systems Engineering and Information,2011,11(2):100-105.)
[9]何胜学,李秋曼.考虑边约束的网络交通流分配及应用[J].计算机应用研究,2011,28(7):2595-2598.(He Shengxue,Li Qiuman.Side constrained network traffic assignment and application[J]. Appli-cation Research of Computers,2011,28(7):2595-2598.)
[10]Xie Jun,Xie Chi. New insights and improvements of using paired al-ternative segments for traffic assignment[J]. Transportation Re-search Part B:Methodological,2016,93(11):406-424.
[11]Ma Wei,Qian Z. On the variance of recurrent traffic flow for statisti-cal traffic assignment[J]. Transportation Research Part C:Emer-ging Technologies,2017,81(8):57-82.
[12]Guo Renyong,Huang Haijun. A discrete dynamical system of formu-lating traffic assignment:revisiting Smith’s model[J]. Transporta-tion Research Part C:Emerging Technologies,2016,71(2):122-142.
[13]Daganzo C F. The cell transmission model:a dynamic representation ofhighway traffic consistent with the hydrodynamic theory[J]. Transpor-tation Research Part B:Methodological,1994,28(4):269-287.
[14]Daganzo C F. The cell transmission model,partⅡ:network traffic[J]. Transportation Research Part B:Methodological,1995,29(2):79-93.
[15]He Shengxue. Will a higher free-flow speed lead us to a less conges-ted freeway?[J]. Transportation Research Part A:Policy andPractice,2016,85(3):17-38.
[2] Sheffi Y. Urban transportation networks:equilibrium analysis withmathematical programming methods[M]. Englewood Cliffs:Prentice-Hall Inc.,1985.
[3] Dafermos S C,Sparrow F T. The traffic assignment problem for a gene-ral network[J]. Journal of Research of the U. S. National Bu-reau of Standards,1969,73(2):91-118.
[4] Daganzo C F,Sheffi Y. On stochastic models of traffic assignment[J]. Transportation Science,1977,11(3):253-274.
[5] Bar-Gera H. Origin-based algorithm for the traffic assignment problem[J]. Transportation Science,2002,36(4):398-417.
[6]何胜学,范炳全.多用户动态交通流分配模型及算法研究[J].上海理工大学学报,2006,28(5):460-464.(He Shengxue,FanBingquan. Multi-user dynamic traffic assignment model and relevantalgorithm[J]. Journal of University of Shanghai for Science andTechnology,2006,28(5):460-464.)
[7]何胜学,董琼,徐福缘.基于网络对偶均衡的交通流分配模型[J].公路交通科技,2010,27(9):105-110.(He Shengxue,DongQiong,Xu Fuyuan. Traffic assignment model based on network dualequilibrium[J]. Journal of Highway and Transportation Re-search and Development,2010,27(9):105-110.)
[8]何胜学,何建佳,徐福缘.基于网络对偶均衡的有边约束的交通流分配模型[J].交通运输系统工程与信息,2011,11(2):100-105.(He Shengxue,He Jianjia,Xu Fuyuan. Side constrained traffic as-signment model based on network dual equilibrium[J]. Transporta-tion Systems Engineering and Information,2011,11(2):100-105.)
[9]何胜学,李秋曼.考虑边约束的网络交通流分配及应用[J].计算机应用研究,2011,28(7):2595-2598.(He Shengxue,Li Qiuman.Side constrained network traffic assignment and application[J]. Appli-cation Research of Computers,2011,28(7):2595-2598.)
[10]Xie Jun,Xie Chi. New insights and improvements of using paired al-ternative segments for traffic assignment[J]. Transportation Re-search Part B:Methodological,2016,93(11):406-424.
[11]Ma Wei,Qian Z. On the variance of recurrent traffic flow for statisti-cal traffic assignment[J]. Transportation Research Part C:Emer-ging Technologies,2017,81(8):57-82.
[12]Guo Renyong,Huang Haijun. A discrete dynamical system of formu-lating traffic assignment:revisiting Smith’s model[J]. Transporta-tion Research Part C:Emerging Technologies,2016,71(2):122-142.
[13]Daganzo C F. The cell transmission model:a dynamic representation ofhighway traffic consistent with the hydrodynamic theory[J]. Transpor-tation Research Part B:Methodological,1994,28(4):269-287.
[14]Daganzo C F. The cell transmission model,partⅡ:network traffic[J]. Transportation Research Part B:Methodological,1995,29(2):79-93.
[15]He Shengxue. Will a higher free-flow speed lead us to a less conges-ted freeway?[J]. Transportation Research Part A:Policy andPractice,2016,85(3):17-38.