On an optimal policy for diverting traffic flow from a congested area

Abstract

This work investigates policies for diverting traffic flow from a main way where some flowstopping incident has occurred. The model chosen for describing the main way congestion is basically a queuing model: vehicles that are trapped by the accident can leave the jam, but at a slower than normal rate, and the congestion will terminate when the waiting queue becomes empty. The new feature introduced is that there exists a branching point in the upstream of the congested area that gives a controller (either human or automatic) the ability of diverting a fraction of vehicular flow towards some uncongestioned auxilary way. The objective aimed is to minimize a cost function that measures 1) the amplitude of the congestion asthe total number of vehicles involved in the jam, the jam duration, and the total vehicle-hours waited, and 2) diversion costs that may take into account the lengthening in travel time incurred by diverted drivers.
Traffic diversion policies are analyzed by using a Markov (birth-and-death) model. It is shown that the best rule leads simply to divert an arriving vehicle if and only if the current queue length exceeds some given upper limit.