Queuing with Preemptive Priorities or with Breakdown

Abstract

Preemptive priority is defined and contrasted with head-of-the line priority Poisson arrivals at a single server are assumed throughout, and only steady-state solutions are found. The effect on service-time statistics of preempted items re-entering service according to various rules is considered. A formula for the joint probability distribution of queue lengths of two preemptive priority classes is derived assuming negative exponential service statistics. Moments of this queue length distribution are found by a generating function approach. For any number of preemptive priority classes, expected times-in-system are found for a general service time distribution for each class, and for negative exponential service, with the same rate for each class, the generating functions of the delay distributions are also obtained. The similarity of queuing with breakdown to queuing with preemptive priority is pointed out, and two models of breakdown effects are worked out.