A dynamical system model of formulating day-to-day traffic assignment based on stochastic user equilibrium

We propose a dynamical system model to formulate day-to-day traffic assignment. This model describes the dynamic adjustment process of route flows from day to day and its stationary state is equivalent to the Logit stochastic user equilibrium state. We also analyze several properties of the model, including the equivalence between the stationary state and user equilibrium state and the uniqueness and convergence of its stationary point. The model is given in discrete and general form and hence we introduce a special case of the model. Finally, we apply the model to a numerical example to illustrate its application and properties. The study is helpful for better understanding the adjustment process of route flows from day to day.