Optimal Expulsion Control—A Dual Approach to Admission Control of an Ordered-Entry System

In this paper we obtain the optimal admission control policy for a first-come, first-served (FCFS) M/M/m ordered-entry queueing system to maximize the expected discounted (and the long-run average) profit (reward minus cost). We introduce a new approach for determining the optimal admission control policy. The underlying idea of this approach is to construct a dual system: a preemptive last-come, first-served (LCFS-P) M/M/m ordered-entry queueing system that is subject to expulsion control. We show that an LCFS-P system with expulsion control is isomorphic to an FCFS system with admission control, and the two systems share the same optimal control policy. Eluding the conventional dynamic programming formulation, we approach the solution from behaviors of individual customers and their impact on the social outcome. This makes our analysis simple and intuitive and reveals a better insight into the structural properties of the optimal control policy. Besides providing formulas to compute the optimal threshold, we use the operational characteristics of the dual system to obtain an easily computable approximation for the optimal threshold. The applicability of the approach transcends well beyond the problem addressed in this paper.