Social optimum for evening commute in a single-entry traffic corridor with no early departures

In this paper, we investigate the evening commute behaviors on the social optimum (SO) state in a single-entry traffic corridor with no early departures. Differing from the previous studies on evening commute, the dynamic properties of traffic flow are analyzed with the LWR (Lighthill-Whitham-Richards) model. The properties of optimum cumulative inflow curve with general desired departure time distribution curve are deduced, and then the analytic solutions for common desired departure time in SO are obtained. Three numerical examples are carried out to capture the characteristics of evening commuting behaviors under different values of time. The analytic and numerical results both indicate that the rarefaction wave originating from the first entry point influences the whole or part of the outflow curve. No shock wave exists through the commuting process. In addition, the cost curves show that the trip cost increases and the departure delay cost decreases with departure time, whereas the travel time cost first increases then decreases with departure time under the SO principle.