The Analysis of Braess’ Paradox and Robustness Based on Dynamic Traffic Assignment Models

The investigation of the paradox and robustness about the traffic network is an important branch of the traffic assignment. In this paper, Braess’ paradox and robustness of the dynamic traffic network are analyzed by the dynamic traffic assignment models. In addition, the relationship of total costs with different traffic assignment models is discussed. The results show that the paradox only occurs in certain range; the robustness of the network and the relationship of total traffic costs are changed as the traffic demand changes, which provides theoretical guidance for the urban transportation planning. 1. Introduction In recent years, the proposal of the intelligent transportation system (ITS) forces people to investigate the dynamic traffic assignment (DTA). The mathematical programming [1, 2], the optimal control [3, 4], and the variational inequality (VI) [5, 6] were proposed, respectively, and labeled as three main analytical approaches. Specially, the optimal control includes dynamic user equilibrium (DUE) [7–11] and dynamic system optimal (DSO) [12]. Braess’ paradox is an important phenomenon during the traffic assignment [13], which has been widely investigated in the scientific literatures [14–16], such as X. Zhang and H. M. Zhang [17] studied the route choices and a novel paradox in queuing networks; Pas and Principio [18] gained the specific range that the paradox occurs when the link cost only depends on the link flow. Braess’ paradox is rooted in the essence of the user equilibrium (UE) assignment where each user minimizes his/her own travel time between an origin and a destination. The most previous work mainly focuses on the paradox under the static traffic. In recent years, the paradox of the dynamic traffic assignment began to develop, such that Arnott et al. [19] discussed the properties of the dynamic traffic equilibrium including a paradox; Hallefjord et al. [20] analyzed the traffic paradox when the travel demand is elastic; Zhang et al. [21] investigated Braess’ paradox in the dynamic traffic assignment. In this paper, we investigate the paradox phenomenon of the dynamic traffic network using VI method and assuming the link cost at time is related to the flow of this link and the adjacent links at the same paths at time . The robustness, as an important index valuing the stability of the system, is usually used to study the network under the partial degradation. In the process of studying the robustness, it is generally classified into the following two classes according to whether the system structure remains intact: (i) certain