The effect of the inflow constraint on the solution of the departure time and route choice problem

The link inflow constraint was not considered in the majority of the previous studies in the simultaneous departure time and route choice (SDTRC) problem. To show the link inflow constraint should be considered in modeling the SDTRC problem, this paper studied the effect of the inflow constraint on the solution of the SDTRC problem, which was rarely studied. In this study, a variational inequality (VI) model was presented for the SDTRC with constraints on link inflow and link density and a relaxation with match algorithm is presented for solving the model. The point queue (PQ) model was used in dynamic network loading. The model and algorithm were applied to a network with different level of the link inflow constraints given the density constraint. The results indicated that the solution of the SDTRC problem was highly dependent on the inflow constraints. With loose constraints, the demand can depart at almost the same time and has almost the same generalized costs, the demand is centered around time window, and the unrealistic equilibrium is reached. With stricter constraints, the time-dependent OD demand and the generalized costs for them are different, and the time-dependent OD demand spreads wider as the inflow constraints get stricter. The wider it is spread, the larger the generalized costs and travelling costs are. The solution of the SDTRC with stricter inflow constraints is consistent with the real-world. These indicate that the link inflow constraint must be included in the modeling of the SDTRC problem.