Lattice path counting and \(M/M/c\) queueing systems
type: Item
instance of: scholarly article
title: Lattice path counting and \(M/M/c\) queueing systems
zbMATH Open document ID: 0836.60099
DOI: 10.1007/BF01148946
author: Kiyoshi Muto
author: Haruo Miyazaki
author: Yoichi Seki
author: Yoshihiro Kimura
author: Yukio Shibata
published in: Queueing Systems
publication date: 1996-05-06T00:00:00Z
review text: The transient solution of \(M/M/c\) queue in a closed form is obtained for the probability of exactly \(i\) arrivals and \(j\) departures within a time interval of length \(t\). The method is based on the well-known combinatorial considerations: the authors count the paths from the origin to \((i,j)\) that have exactly \(r(d)\) \(x\)-steps whose depth from the line \(y = x\) is \(d = 0, \dots, c - 1\). Some numerical examples are considered.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 765316
zbMATH Keywords: transient solution
zbMATH Keywords: queue size
zbMATH Keywords: lattice path counting
zbMATH Keywords: depth of part
zbMATH Keywords: numerical examples
reviewed by: Evsei Morozov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01148946
OpenAlex ID: W1993853939
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description: scientific article; zbMATH DE number 765316