Delay cycle analysis of finite-buffer M/G/1 queues and its application to the analysis of M/G/1 priority queues with finite and infinite buffers

Abstract

In this paper, we develop a new type of delay cycle analysis for single-class finite-buffer M/G/1 queues, and then analyze M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers using the proposed delay cycle analysis. For this type of priority queues, we derive the waiting time distributions of high- and low-priority customers, as well as the loss probability of high-priority customers, under the nonpreemptive and preemptive-resume priority disciplines. Compared with M/G/1 priority queues with infinite buffers for both classes, the priority discipline has more significant impacts on system performance in the priority queues in question, especially on the queue waiting time and stability conditions of low-priority customers. This is explored in theoretical propositions, as well as in numerical examples.