Analysis of the M/G/1 queue under a mixed and combind priority discipline

Abstract

We propose and analyze a mixed and combined preemptive/nonpreemptive priority discipline. As the discretion rule for preemption, three schemes are based on the parameters of the lower-priority job are considered elapsed service time, elapsed to original service time ratio, and remaining service time. In this work, by using the busy-period analysis technique we analyze an M/G/1 queueing system with multiple priority classes of jobs. As preemptive rules, we consider the preemptive-resume, preemptive-repeat-identical, and preemptive-repeat-different policies. These three preemptive rules are analyzed. The key idea of analysis is based on the consideration of a busy period as a composite of delay cycles. As results, we present the exact Laplace-Stieltjes transforms of residence time, completion time, wating time, and the z-transform of the number of jobs in the system.