An N Server Cutoff Priority Queue Where Customers Request a Random Number of Servers

Abstract

Consider a multi-priority, nonpreemptive, N-server Poisson arrival queueing system. The number of servers requested by an arrival has a known probability distribution. 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 the number of servers busy is at most the respective cutoff number of servers minus the number of servers requested (by the customer) and all higher priority queues are empty. In other words the queueing discipline is in a sense HOL by priorities, FCFS within a priority. All servers requested by a customer start service simultaneously; service completion instants are independent. We derive the priority i waiting time distribution (in transform domain) and other system statistics.