Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials

An extension of a recent framework for analyzing the time-dependent departure pattern arising in an idealized situation of a pool of commuters going from a single origin to a single destination along a unique route is presented. Congestion along this route is represented using elementary traffic flow theoretic relationships; time-varying patterns of basic traffic variables are derived under user equilibrium conditions, along with the corresponding time-dependent departure pattern of system users. After demonstrating the basic model in the single-route context, an additional dimension of choice is introduced by considering the joint departure time and route choice decisions of users. Results are derived in a simplified two-route context and numerical illustrations provided.