Approximate Formulas for Characteristics of Multichannel LIFO Preemptive-Resume Priority Queueing System

TL;DR

This paper develops approximate formulas for analyzing the performance of a multichannel preemptive-resume priority queueing system with LIFO service, considering arbitrary service time distributions and preemption rules.

Contribution

It introduces novel approximate formulas for sojourn time and system characteristics in a complex multichannel priority queue with LIFO and preemption.

Findings

Derived formulas for sojourn time of priority jobs

Analyzed impact of preemption on system performance

Provided insights into queue behavior under LIFO policy

Abstract

This paper considers a multichannel preemptive-resume priority queueing system with a Poisson input and an arbitrary service time distribution depending on the priority of job. Jobs of the same priority are serviced according to the LIFO rule. If, at moment of job arrival, all servers are busy, and at least one server is busy with the service of a job of a not higher than the priority of arriving job, then the service of a job is preempted such that the priority of preempted job is lowest from the priorities of the jobs in service. The service of a preempted job is resumed later. The paper proposes approximate formulas for the sojourn time of a prescribed priority job and some other characteristics of the system.