具弧容量约束交通均衡流的一种新算法
A New Algorithm for Traffic Equilibrium Flow with Capacity Constraints of Arc
DOI: 10.12677/AAM.2019.87140, PDF, HTML, 下载: 828  浏览: 1,048  国家自然科学基金支持
作者: 周大琼, 林 志, 彭再云, 王泾晶：重庆交通大学数学与统计学院，重庆
关键词: 落差；新算法；弧容量；饱和路径；具弧容量约束的交通均衡问题；Drop； New Algorithm； Arc Capacity； Saturation Path； Traffic Equilibrium Problem with Capacity Constraints of Arc
摘要: 本文主要研究了具弧容量约束交通均衡流的算法。 通过可行流x的落差定义，得到了可行流x 是具 弧容量约束交通均衡流的充要条件，并以此构造了具弧容量约束交通均衡流的一种新算法，给出 了计算具弧容量约束交通均衡流的具体步骤，同时用例子对新算法加以说明。
Abstract: In this paper, we mainly research the algorithm of traffic equilibrium flow with capacity constraints of arcs, and obtain the necessary and sufficient condition that feasible flow x is a traffic equilibrium  flow  with  capacity  constraints  of  arcs  by  the  definition  of the drop of feasible flow x, a new algorithm of traffic equilibrium flow with capacity constraints of arcs is constructed, and the concrete steps of calculating the traffic equilibrium flow with capacity constraints of arcs are given, at the same time, an example is  given to  illustrate the New  Algorithm.
文章引用：周大琼, 林志, 彭再云, 王泾晶. 具弧容量约束交通均衡流的一种新算法[J]. 应用数学进展, 2019, 8(7): 1212-1223. https://doi.org/10.12677/AAM.2019.87140

参考文献

[1] Wardrop, J. (1952) Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers, Part II, 1, 325-378.
https://doi.org/10.1680/ipeds.1952.11259
[2] Beckmann, M.J., McGuire, C.B. and Winsten, C.B. (1956) Studies in the Economics of Trans- portation. Yale University Press, New Haven.
[3] Lin, Z. (2010) The Study of Traffic Equilibrium Problems with Capacity Constraints of Arcs.Nonlinear Analysis: Real World Applications, 11, 2280-2284.
https://doi.org/10.1016/j.nonrwa.2009.07.002
[4] Lin, Z. (2010) On Existence of Vector Equilibrium Flows with Capacity Constraints of Arcs.Nonlinear Analysis: Theory, Methods & Applications, 72, 2076-2079.
https://doi.org/10.1016/j.na.2009.10.007
[5] Lin, Z. (2015) An Algorithm for Traffic Equilibrium Flow with Capacity Constraints of Arcs.Journal of Transportation Technologies, 5, 240-246.
https://doi.org/10.4236/jtts.2015.54022
[6] Xu, Y.D. and Li, S.J. (2014) Vector Network Equilibrium Problems with Capacity Constraints of Arcs and Nonlinear Scalarization Methods. Applicable Analysis, 93, 2199-2210.
https://doi.org/10.1080/00036811.2013.875160
[7] Tian, X.Q. and Xu, Y.D. (2012) Traffic Network Equilibrium Problems with Capacity Con- straints of Arcs and Linear Scalarization Methods. Journal of Applied Mathematics, 2012,Article ID: 612142.
https://doi.org/10.1155/2012/612142
[8] Xu, Y.D., Li, S.J. and Teo, K.L. (2012) Vector Network Equilibrium Problems with Capacity Constraints of Arcs. Transportation Research Part E: Logistics and Transportation Review, 48, 567-577.
https://doi.org/10.1016/j.tre.2011.11.002
[9] Chiou, S.W. (2010) An Efficient Algorithm for Computing Traffic Equilibria Using Transyt Model. Applied Mathematical Modelling, 34, 3390-3399.
https://doi.org/10.1016/j.apm.2010.02.028
[10] Xu, M., Chen, A., Qu, Y. and Gao, Z. (2011) A Semismooth Newton Method for Traffic Equilibrium Problem with a General Nonadditive Route Cost. Applied Mathematical Modelling, 35, 3048-3062.
https://doi.org/10.1016/j.apm.2010.12.021
[11] Chen, A., Zhou, Z. and Xu, X.D. (2012) A Self-Adaptive Gradient Projection Algorithm for the Nonadditive Traffic Equilibrium Problem. Computers & Operations Research, 39, 127-138.
https://doi.org/10.1016/j.cor.2011.02.018

为你推荐