交通均衡问题的适定性

doi:10.15960/j.cnki.issn.1007-6093.2026.02.004

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 58-68.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.004

交通均衡问题的适定性

曾静^1,†, 向耀¹, 张文燕²

1. 重庆工商大学数学与统计学院, 重庆 400067;
2. 西南财经大学数学学院, 四川成都 611130

收稿日期:2024-10-28 发布日期:2026-06-12
通讯作者: 曾静 E-mail:zengjing1983@ctbu.edu.cn
基金资助:
重庆市研究生导师团队建设项目 (No. yds223010), 重庆工商大学科研创新项目 (No. yjscxx2024-284-242)

The well-posedness of traffic equilibrium problems

ZENG Jing^1,†, XIANG Yao¹, ZHANG Wenyan²

1 School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
2 School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, Sichuan, China

Received:2024-10-28 Published:2026-06-12

摘要/Abstract

摘要： 在交通量分配理论的研究中,均衡模型理论的发展备受瞩目。交通均衡问题通过给定的O/D对需求和成本函数,按照既定的路径选择标准来确定交通网络中的流量分配以及各种性能指标。这种方法论的核心在于,在交通均衡状态下,没有任何交通参与者可以通过单方面改变自己的路径选择来获得更好的出行时间或成本,进而使交通系统的效率和性能最大化。但在现实情况下,由于交通参与者行为的多样性以及交通网络的复杂性,使得均衡状态很难达到。本文定义了交通均衡的一种近似情况——${\varepsilon}$-均衡流,并验证了其存在性。同时,还引入了${\varepsilon}$-均衡流的一类适定性,并建立此适定性成立的充分条件。这为理解和解决交通均衡问题提供了新的理论工具和方法。

关键词: 交通均衡, ${\varepsilon}$-均衡流, 适定性

Abstract: In the study of traffic assignment theory, the development of equilibrium model theory has attracted significant attention. The traffic equilibrium problem aims to determine the flow distribution and various performance metrics in a traffic network by using given O/D pair demand and cost functions, based on established path selection criteria. The core of this methodology lies in the fact that, under a traffic equilibrium state, no participant in the system can improve their travel time or cost by unilaterally changing their path choice, thereby maximizing the efficiency and performance of the traffic system. However, in reality, due to the diversity of traffic participants' behavior and the complexity of traffic networks, achieving a true equilibrium state is often challenging. This paper defines an approximate form of traffic equilibrium ${\varepsilon}$-equilibrium flow and verifies its existence. Additionally, it introduces a type of well-posedness for ${\varepsilon}$-equilibrium flow and establishes sufficient conditions for the validity of this well-posedness, providing new theoretical tools and methods for understanding and solving traffic equilibrium problems.

Key words: traffic equilibrium, ${\varepsilon}$-equilibrium flow, well-posedness

中图分类号:

O221.2

曾静, 向耀, 张文燕. 交通均衡问题的适定性[J]. 运筹学学报（中英文）, 2026, 30(2): 58-68.

ZENG Jing, XIANG Yao, ZHANG Wenyan. The well-posedness of traffic equilibrium problems[J]. Operations Research Transactions, 2026, 30(2): 58-68.

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交通均衡问题的适定性

The well-posedness of traffic equilibrium problems

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