M/M/1 Queueing System with Non-preemptive Priority

TL;DR

This paper analyzes the performance of a non-preemptive M/M/1 queueing system with two priority classes, deriving key performance metrics using a vector Markov process and generating functions.

Contribution

It introduces a novel analytical approach using the complementary variable method to derive distributions and probabilities in a non-preemptive priority queue.

Findings

Derived the generating functions for customer length distributions.

Calculated the probability of server states (busy or free).

Determined average queue lengths for both customer types.

Abstract

The performance of non-preemptive M/M/1 queueing system with two priority is analyzed. By using complementary variable method to make vector Markov process and analyzing the state-change equations of the queueing system, the generating function of two kinds of customers'length distribution are derived under non-preemptive priority .Through further discussion, the probability of the server that it is working or free and average length of two kinds of customers are also derived.