Morning Commute in a Single-Entry Traffic Corridor with No Late Arrivals

This paper analyzes a model of early morning traffic congestion, that is a special case of the model considered in Newell (1988). A fixed number of identical vehicles travel along a single-lane road of constant width from a common origin to a common destination, with LWR flow congestion and Greenshields’ Relation. Vehicles have a common work start time, late arrivals are not permitted, and trip cost is linear in travel time and time early. The paper explores traffic dynamics for the Social Optimum, in which total trip cost is minimized, and for the User Optimum, in which no vehicle’s trip cost can be reduced by altering its departure time. Analytical and, when possible, closed-form solutions are presented, along with numerical examples