Distributions of unexpended services in a D-node Markov-renewal network distinguished by customer class
type: Item
instance of: scholarly article
title: Distributions of unexpended services in a D-node Markov-renewal network distinguished by customer class
zbMATH Open document ID: 0760.65138
DOI: 10.1016/0096-3003(92)90098-L
author: Richard L. Patterson
published in: Applied Mathematics and Computation
publication date: 1993-01-17T00:00:00Z
review text: Customer units from any one of \(K\) distinct classes arrive at random but in a fixed, known order for processing in a \(D\)-node Markov-renewal network that contains at least one absorbing node and no proper closed subsets of nodes. The joint probability function of counts of units in nodes, distinguished by customer class, is derived for the transient case. A numerical method for routinely computing all possible marginal distribution is demonstrated for implementation on off-the-shell spreadsheets or database systems. The model permits explicit computation of counts by units, by class and node, for arrivals that are not Poisson distributed. Case study for a system consisting of Poisson distributed arrivals with constant arrival intensity and two node network is presented in detail.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 96913
zbMATH Keywords: case study
zbMATH Keywords: \(D\)-node Markov-renewal network
zbMATH Keywords: absorbing node
zbMATH Keywords: marginal distribution
reviewed by: Jaromír Antoch
MaRDI profile type: Publication
full work available at URL: 0096-3003(92)90098-l
OpenAlex ID: W2006913618
description: scientific article; zbMATH DE number 96913