An N Server Cutoff Multi-Priority Queue

Abstract

Consider a multi-priority, nonpreemptive, N-server Poisson arrival queueing system. Service times are negative exponential. In order to save available servers for higher priority customers, arriving customers of each lower priority are deliberately queued whenever the number of servers busy equals or exceeds a given priority-dependent cutoff number. A queued priority i customer enters service the instant there are fewer than the respective cutoff number of servers busy and all higher priority queues are empty. The principal result is the priority i waiting time mean, second moment, and distribution (in transforms). The analysis is extended to systems in which any subset of priority levels may overflow to some other system, rather than join infinite capacity queues. The paper concludes with illustrative computational results.