Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers
type: Item
instance of: scholarly article
title: Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers
zbMATH Open document ID: 0664.60094
DOI: 10.1007/BF01150854
author: Kim L. Ong
author: Michael R. Taaffe
published in: Queueing Systems
publication date: 1989-01-01T00:00:00Z
review text: A queueing model having a nonstationary Interrupted Poisson arrival process (IPP(t)), s time-dependent exponential unreliable/repairable servers and finite capacity c is introduced, and an approximation method for analysis of it is developed and tested. Approximations are developed for the time-dependent queue length moments and the system viewpoint waiting time distributions and moments. The approximation involves state- space partitioning and numerically integrating partial-moment differential equations (PMDEs). Surrogate distribution approximations (SDA's) are used to close the system of PMDEs. The approximations allow for analysis using only \((s+1)(s+6)\) differential equations for the queue length moments rather than the \(2(c+1)(s+1)\) equations required by the classic method of numerically integrating the full set of Kolmogorov-forward equations. Effectively hours of cpu time are reduced to minutes for even modest capacity systems. Approximations for waiting time distributions and moments are developed.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4086710
zbMATH Keywords: nonstationary Interrupted Poisson arrival process
zbMATH Keywords: approximation method
zbMATH Keywords: time-dependent queue length
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4086710