Time-dependent model for departure time and route choices in networks with queues

A multiperiod time-dependent model for departure time and route choices in networks with residual queues is presented. The proposed model is meant to be used for strategic transportation planning, taking into account the effects of time-dependent queues that are carried over to the next period. The departure time choice is based on an incremental logit model, whereas the route choice follows an extended user equilibrium (UE) principle. This model is formulated as the variational inequality (VI) problem, which accounts for the major features of networks with residual queues, including the effects of queue delay and traffic flow truncation due to road exit capacity. The Jacobi method is used to solve the VI problem. In the proposed solution method, the diagonalization subproblem is equivalent to the steady state extended UE assignment for networks with queues. A simple numerical example is used to illustrate the application of the solution method.