Morning commute in a single-entry traffic corridor with early and late arrivals

• Study the dynamic properties of traffic flow in a single-entry corridor with consideration of both early and late arrivals.• Find the closed-form system optimum and quasi-analytic user equilibrium solutions of departure and arrival flows.• Perfect the work by DePalma and Arnott (2012) who did not consider late arrivals.

The purpose of this paper is to extend the work of DePalma and Arnott (2012) by investigating the solutions for social optimum (SO) and user equilibrium (UE) assignment in a single-entry traffic corridor with consideration of both early and late arrivals. The LWR model and the Greenshields' relation are used to describe the dynamic properties of traffic flow. The closed-form SO solution and quasi-analytic UE solution are developed and well illustrated by numerical examples. It is shown that the SO assignment is associated with a smooth cumulative outflow curve, while the UE assignment will result in recursively generated cumulative inflow and outflow curves. In UE, however, the system finally becomes a free flow state.