The Optimal Admission and Dispatching Control Policy of a Two-Terminal Transportation System

Abstract

A vehicle provides transportation services between two terminals. Customers requesting services to the other terminal arrive at each of the two terminals according to independent Poisson processes. Each accepted customer brings in a random reward, and there are linear holding and transportation costs incurred by the accepted customers. Each rejected customer incurs a fixed penalty cost. The inter-terminal travel times are i.i.d. Erlang distributed. We show that the policy that maximizes the expected total discounted profit is of the threshold type. For any terminal, the threshold levels of dispatching and of admission are non-increasing functions of the number of customers waiting at the other terminal, and the threshold levels of admission are non-decreasing functions of the distance of the vehicle from the terminal.