Asymptotic Optimality of Balanced Routing in a Multiclass G/G/1 Queue

Abstract

In this paper we consider a multiclass G/G/1 queueing system. When the server is idle, we use a balanced routing control policy to determine what kind of customer is served. Under such a balanced policy, we derive the diffusion limits of the queue length processes and the workload processes. The diffusion limits are the same for these processes regardless the choice of c as long as c ≥ 2. We further show that the proposed balanced routing policy for any fixed c ≥ 2 is asymptotically optimal in the sense that it minimizes the workload over all time in the diffusion limit.