Day-to-day traffic assignment models provide a powerful tool to analyze the time evolution of traffic flow within transport networks. In day-to-day dynamics, most models assume that there are only private cars on traffic networks and travelers update their choices each day. However, there are mainly two traffic modes, i.e. cars and buses, and travelers may not change their mode choices frequently. In this paper, a period-to-period traffic assignment model is proposed to capture traffic dynamics under traffic restrictions by considering interactions among different modes and introducing a delay about travelers’ mode choice. The existence and uniqueness of the equilibrium are analyzed. The linear stability of the equilibrium is analyzed and the eigenvalue range of Jacobian matrix is estimated by using the Gershgorin circle theorem. Both theoretical analyses and numerical simulations indicated that compared to the system with no mode choice, mode choice behaviors could improve the stability of the equilibrium. Additionally, mode choice behaviors with delay might further increase the stability domain and dampen oscillations on the cost and the flows. This study explains the evolution patterns of transportation networks under traffic policy and provides guidance for network design and management.

中文翻译：

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两模式网络中流量限制下的流量动力学和模式选择的延迟效应

日常交通分配模型提供了一个强大的工具，可以分析交通网络内交通流的时间演变。在日常动态中，大多数模型都假设交通网络上只有私家车，旅行者每天都会更新选择。但是，主要有两种交通模式，即汽车和公共汽车，旅行者可能不会经常更改其模式选择。本文提出了一种周期到阶段的交通分配模型，通过考虑不同模式之间的相互作用并引入有关旅行者选择模式的延迟，来捕获交通约束下的交通动态。分析了均衡的存在性和唯一性。利用Gershgorin圆定理，分析了平衡的线性稳定性，并估计了雅可比矩阵的特征值范围。理论分析和数值模拟均表明，与没有模式选择的系统相比，模式选择行为可以提高平衡的稳定性。此外，具有延迟的模式选择行为可能会进一步增加稳定性，并抑制成本和流量的波动。这项研究解释了交通政策下交通网络的发展模式，并为网络设计和管理提供了指导。