Day-to-Day Dynamical Evolution of Network Traffic Flow with the Influence of Travel Behavior

In order to improve previous studies neglecting the influence of travelers’ travel behavior on network traffic flow, this study proposes a nonlinear, discrete-time model considering the influence of travelers’ behaviors in cost estimation and route choice. Four parameters are introduced to denote the difference in travelers’ behaviors and travelers are divided into four types: sensible traveler, conservative traveler, sensitive traveler, and follower traveler. The linear stability of the stochastic user equilibrium is analyzed by studying the eigenvalues of the Jacobian matrix. The model proposed in this study is demonstrated on a two-route example and results of this research are as follows: Firstly, three states of network traffic flow evolution can be observed: stability, periodic motion, and chaos. Secondly, the route choice behaviors affect the stability of network traffic flow significantly. Thirdly, Travel cost estimation behaviors also affect the stability of the dynamic system.