Optimal dispatching of an infinite capacity shuttle with compound poisson arrivals: Control at a single terminal

Abstract

We consider the optimal control of an infinite capacity shuttle which transports passengers between two terminals. Passengers arrive at each of two terminals according to independent compound Poisson processes. The travel time from one terminal to the other one is a random variable following an arbitrary distribution. The dispatcher can hold the shuttle at only one of the terminals. Thus, when the shuttle is dispatched at terminal 1, it transports all the passengers waiting at terminal 1 to terminal 2 and instantaneously picks up the passengers at terminal 2 and returns to terminal 1. Assuming that the dispatcher has complete information about the number of passengers waiting at each terminal, we consider the following control limit policy: dispatch the shuttle if, and only if, the total number of passengers waiting at both terminals is at least as large as some prespecified control limit, m. In this paper, under a linear cost structure, we provide an explicit expression for the expected cost per unit time as a function of the control value, m, and present a simple and efficient method for computing the optimal control value.