Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals

This paper investigates the traffic flow dynamics under the social optimum (SO) principle in a single-entry traffic corridor with staggered shifts from the analytical and numerical perspectives. The LWR (Lighthill–Whitham and Richards) model and the Greenshield's velocity–density function are utilized to describe the dynamic properties of traffic flow. The closed-form SO solution is analytically derived and some numerical examples are used to further testify the analytical solution. The optimum proportion of the numbers of commuters with different desired arrival times is further discussed, where the analytical and numerical results both indicate that the cumulative outflow curve under the SO principle is piecewise smooth.