Asymptotic behavior of the expansion method for open finite queueing networks
type: Item
instance of: scholarly article
title: Asymptotic behavior of the expansion method for open finite queueing networks
zbMATH Open document ID: 0662.60105
DOI: 10.1016/0305-0548(88)90008-1
author: Laoucine Kerbache
author: James MacGregor Smith
published in: Computers \& Operations Research
publication date: 1988-01-01T00:00:00Z
review text: The paper presents an approximation technique for the modeling of finite capacity queueing networks. In the first part, the `expansion method', already discussed in earlier papers, is described. The basic idea behind it is the introduction of `holding nodes' representing the additional waiting times incurred by customers due to blocking. In limiting the analysis to exponential service times and an external Poisson arrival process, an exhaustive set of recursive equations is derived based on mean value computation and well-known approximations [see \textit{J. Labetoulle} and \textit{G. Pujolle}, IEEE Trans. Software Eng. SE-6, No.4 (1980)]. In part two, the value of the expansion method with regard to meeting an upper bound throughput criterion [\textit{P. C. Bell}, Oper. Res. Lett. 1, 230-235 (1982; Zbl 0499.90039)] even for quite `unbalanced' service rates is demonstrated.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 4082683
zbMATH Keywords: tandem queues
zbMATH Keywords: decomposition
zbMATH Keywords: approximation technique
zbMATH Keywords: finite capacity queueing networks
zbMATH Keywords: Poisson arrival process
MaRDI profile type: Publication
full work available at URL: 0305-0548(88)90008-1
OpenAlex ID: W2018082481
cites work: Q4166220
cites work: Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions
cites work: Accuracy of the Diffusion Approximation for Some Queuing Systems
cites work: The behaviour of a single queue in a general queueing network
cites work: Approximate behavior of tandem queues
cites work: Networks of Waiting Lines
cites work: Approximate Analysis of General Queuing Networks by Decomposition
cites work: Approximate analysis of exponential queueing systems with blocking
cites work: Throughput Capacity of a Sequence of Queues with Blocking Due to Finite Waiting Room
cites work: Approximations to Stochastic Service Systems, with an Application to a Retrial Model
cites work: Congestion in Blocking Systems-A Simple Approximation Technique
cites work: Finite Queues in Series with Exponential or Erlang Service Times—A Numerical Approach
cites work: An Approximation Method for Open Restricted Queueing Networks
cites work: Approximate analysis of exponential tandem queues with blocking
cites work: Sequential Processing Machines (S.P.M) Analyzed With a Queuing Theory Model
cites work: A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination
cites work: The use of decomposition techniques for the analysis of open restricted queuing networks
description: scientific article; zbMATH DE number 4082683