Scheduling Queues with Customer Transfers

Abstract

We consider a multiclass single-server system wherein customers of each class form their own queue and can either abandon the system or transfer to other queues while waiting. A system manager makes dynamic scheduling decisions to minimize system-wide waiting cost. We solve the stochastic control problem under both infinite-horizon discounted and average cost criteria. By studying a Brownian control problem that arises in the conventional heavy traffic regime, we identify (under each cost criterion) an asymptotically optimal policy that prioritizes across different classes according to a workload-dependent dynamic index rule. The proposed policies acknowledge the impact of customer transfers on the optimal allocation of service resources and generate rich managerial insights. One of the technical difficulties in the proof of the asymptotic optimality result is to identify a natural stability condition and formally show that the sequence of diffusion-scaled processes is uniformly stable under that condition.