Optimal Control of Single-Server Queuing Networks and Multi-Class M/G/1 Queues with Feedback

Abstract

We consider a queuing network with Poisson arrivals at each node. At each service completion epoch, a reward is received and the serviced customer changes nodes or leaves the system according to specified probabilities. In addition, linear holding costs are incurred. The problem is to schedule the server so as to maximize the expected discounted reward over an infinite planning horizon. This model is equivalent to a single-server, multi-class queuing system with feedback of the customers. We study two cases: general service times with a non-preemptive service discipline and exponential service times with a preemptive service discipline. For each case we show that a modified static policy of priority form is optimal and we provide an algorithm for computing an optimal policy.