Modeling and Dynamic Scheduling of a Queueing System with Blocking

We consider the problem of dynamically controlling N queues that compete for the service attention of a single server. The system under study consists of finite queues and the performance objective is to avoid situations in which any of the queues are full. We also consider a system in which the queues are fed by the server and the objective is to avoid situations in which any of the queues are empty, and a mixed system consisting of both types of queues. The goal of this paper is to characterize the optimal decision rule for controlling these systems. We do so by examining several properties which are usually possessed by simple form optimal rules: (1) The existence of a monotonic switching curve for a two-dimensional system, (2) independence of system size, and (3) decomposability of the rule for an N-dimensional system. Examining our system we show that the optimal decision rule for the two-queue system is indeed characterized by a monotonic switching curve. Moreover, under identical arrival rates and identical departure rates the switching curve is usually characterized by a forty five degree straight line.