Boundedly rational departure time choice in a dynamic continuum user equilibrium model for an urban city

Based on Wardrop's first principle, the perfectly rational dynamic user equilibrium is widely used to study dynamic traffic assignment problems. However, due to imperfect travel information and a certain “inertia” in decision-making, the boundedly rational dynamic user equilibrium is more suitable to describe realistic travel behavior. In this study, we consider the departure time choice problem incorporating the concept of bounded rationality. The continuum modeling approach is applied, in which the road network within the modeling region is assumed to be sufficiently dense and can be viewed as a continuum. We describe the traffic flow with the reactive dynamic continuum user equilibrium model and formulate the boundedly rational departure time problem as a variational inequality problem. We prove the existence of the solution to our boundedly rational reactive dynamic continuum user equilibrium model under particular assumptions and provide an intuitive and graphical illustration to demonstrate the non-uniqueness of the solution. Numerical examples are conducted to demonstrate the characteristics of this model and the non-uniqueness of the solution.