Traffic Dynamics and Mode Choice's Delay Effect Under Traffic Restriction in Two-Mode Networks

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.