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。
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.
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