Technical Note—Further Results on an Infinite Capacity Shuttle with Control at a Single Terminal

The infinite capacity shuttle system that is described by Ignall and Kolesar (Ignall, E., P. Kolesar. 1974. Optimal dispatching of an infinite capacity shuttle: Control at a single terminal. Opns. Res.22 1008–1024.) is considered. Passengers arrive at each of two terminals according to independent Poisson Processes. The vehicle can be held at only one of the terminals. When the vehicle is dispatched it transports all of the passengers waiting at terminal 1 to terminal 2, immediately picks up the passengers at terminal 2 and returns to terminal 1. It is known that under general conditions the optimal vehicle dispatching policy is a control limit policy: Dispatch the shuttle if and only if the number of passengers waiting at both terminals is at least as large as some cutoff value. In this paper a method for computing the optimal cutoff value is presented. In addition we examine the savings that result when using a control limit policy rather than the more traditional policy of scheduled periodic service. Last, we prove a conjecture by Ignall and Kolesar regarding the optimal policy for instances when the dispatcher does not know the number of passengers waiting at terminal 2.