Performance analysis of a GI/M/1 queue with single working vacation
type: Item
instance of: scholarly article
title: Performance analysis of a GI/M/1 queue with single working vacation
zbMATH Open document ID: 1222.60072
published in: Applied Mathematics and Computation
publication date: 2011-02-21T00:00:00Z
review text: A GI/M/1 queue with a single working vacation is considered. This queue in which during the vacation period the server works at a lower rate rather than stopping completely, can be used in production management with multiple working vacations during the repair of the machines, etc. The model formulation of the GI/M/1 queue was based on an embedded Markov chain. The steady-state queue length distributions at arrival and arbitrary epochs for this model were obtained by means of the Neuts' matrix-geometric approach. Some technical foundations, such as the closeness property of the conditional probability of \(\Gamma\)-distributions, and results for the waiting time of arbitrary customers are obtained. The effect of the critical model parameters on the performance measures in the D/M/1 and \(E_{2}/M/1\) with single working vacation queues were studied by means of solving numerical examples. It was demonstrated that the working vacation policy can decrease the number of the waiting customers in these systems and enhance the system efficiency. To summarize, the obtained results will be very useful for the modelling of computer networks, communication systems and production management.
reviewed by: Jerzy Martyna
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B18
zbMATH DE Number: 5853791
zbMATH Keywords: queues and service
zbMATH Keywords: performance evaluation
zbMATH Keywords: network models
author: Jihong Li
author: Nai-Shuo Tian
MaRDI profile type: Publication
full work available at URL: j.amc.2010.11.045
OpenAlex ID: W1985237154
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DOI: 10.1016/J.AMC.2010.11.045
description: scientific article; zbMATH DE number 5853791