Priority queue with customer upgrades

Abstract

Abstract This article is concerned with a general multi‐class multi‐server priority queueing system with customer priority upgrades. The queueing system has various applications in inventory control, call centers operations, and health care management. Through a novel design of Lyapunov functions, and using matrix‐analytic methods, sufficient conditions for the queueing system to be stable or instable are obtained. Bounds on the queue length process are obtained by a sample path method, with the help of an auxiliary queueing system. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012