Operating Characteristics of a Simple Shuttle under Local Dispatching Rules

We treat a transportation system with Poisson passenger arrivals at each of two terminals and a carrier of capacity one that shuttles back and forth between the terminals. We study the consequences of the control decision: how long should the carrier wait empty at a terminal? This dispatch decision is made without knowledge of the queue at the other terminal. Exact and approximate expressions are obtained for the number of carrier trips per unit time and average queue size at each terminal. They are used to show that it is best never to hold the carrier at the slow terminal and not to randomize in the decision process. Further, we show that holding the carrier at the fast terminal sometimes reduces both trip rate and the sum of the average queue sizes.