Queuing systems with semi-Markov flow in average and diffusion approximation schemes
type: Item
instance of: scholarly article
title: Queuing systems with semi-Markov flow in average and diffusion approximation schemes
zbMATH Open document ID: 1175.60081
author: V. V. Koroliuk
author: N. Limnios
author: V. S. Korolyuk
published in: Methodology and Computing in Applied Probability
publication date: 2009-06-16T00:00:00Z
review text: A semi-Markov \((SM/M/1/\infty)\) flow including the Markov and the renewal flows as particular cases are studied. By means of using an asymptotic average and a diffusion approximation of the fluctuations for these systems, some quantitative results are obtained. Among others, the fluctuation of the counting process for these systems are derived. The so-called diffusion approximation in these series scheme is given. The main result of this paper is given in the proof of the diffusion approximation of this queueing process. With a large number of places, say \(N\;(N \rightarrow \infty)\), for a fixed time \(t\), it can be approximated by the variable \(N q t + N^{1/2}t\sigma Z\), where \(Z\) is the standard normal random variable, i.e. with the mean zero and variance 1. The method presented in this paper is general and could be used to obtain numerical solutions considered as the Markov flow, and the semi-Markov renewal flow. These results are in my opinion very valuable and suggest the possibility of the numerical solutions for these problems.
reviewed by: Jerzy Martyna
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 58J37
zbMATH DE Number: 5565142
zbMATH Keywords: queueing theory
zbMATH Keywords: Markov renewal processes
zbMATH Keywords: semi-Markov processes
zbMATH Keywords: applications of Markov renewal processes
zbMATH Keywords: perturbations
MaRDI profile type: Publication
full work available at URL: s11009-008-9081-7
OpenAlex ID: W2076024613
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DOI: 10.1007/S11009-008-9081-7
description: scientific article; zbMATH DE number 5565142