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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.

To alleviate the traffic congestion on urban expressway, Variable Message Signs (VMS) have been widely employed for diverting some traffic to arterial streets in large cities. The diversion rate is a key parameter to design, operation and evaluation of the VMS. Many works have been done to study the diversion rate by stated preference survey. However, no consistent conclusion has been obtained on the key factors influencing diversion behavior. Therefore, this paper pays attention to analyzing the drivers’ diversion from expressway behavior under different network and traffic conditions, and finding the key factors influencing diversion behavior by using stated preference survey. In the survey, graphical traffic information is provided as scenario simulation. Ordinal regression method is adopted to explore the key factors influencing diversion willingness. Binary logit model is used to explore the divert decision with given traffic information. It is shown that driving years, income, driving style, average trip length, and degree of trust in VMS are the significant factors to diversion willingness. Furthermore, the same VMS displaying state results in different diversion flow at different sites. Those findings are the foundation to optimize traffic information releasing strategy and improve the road network efficiency.