Mind your own customers and ignore the others: Asymptotic optimality of a local policy in multi-class queueing systems with customer feedback

Abstract

This work contributes to the investigation of optimal routing and scheduling policies in multi-class multi-server queueing systems with customer feedback. We propose a new policy, dubbed local policy that requires access to only local queue information. Our new local policy specifies how an idle server chooses the next customer by using the queue length information of not all queues, but only those this server is eligible to serve. To gain useful insights and mathematical tractability, we consider a simple W model with customer feedback, and we establish limit theorems to show that our local policy is asymptotically optimal among all policies that may use the global system information, with the objective of minimizing the cumulative queueing costs measured by convex functions of the queue lengths. Numerical experiments provide convincing engineering confirmations of the effectiveness of our local policy for both W model and a more general non-W model.