 An Approximation Method for the Analysis of GI / G /1 QueuesJingwen Li
Operations Research, 1997, vol. 45, issue 1, 140-144 Abstract: We study in this paper an approximation method for the calculation of various performance measures of a GI / G /1 queue. Instead of solving the waiting time directly, we analyze the idle-period distribution as the starting point. The result is then taken as input to many known results to get other performance measures. We show that the distribution of the GI / G /1 idle period satisfies a nonlinear integral equation. This equation directly leads to an accurate approximate solution of the idle-period distribution of the GI / G /1 queue where the interarrival times have a generalized hyperexponential distribution ( GH ). Since all distribution functions can be approximated by a GH distribution at any given accuracy (Botta and Harris [Botta, R. F., C. M. Harris. 1986. Approximation with generalized hyperexponential distributions: Weak convergence results. Queueing Systems 2 169–190.]), the solution method developed in this paper serves as a unified basis for the analysis of GI / G /1 queues. Keywords: queues; approximations; analysis of GI/G/1 queues; probability; distributions; analysis of the idle-period distribution of GI/G/1 queues; queues; algorithms; solving GI/G/1 queues (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:45:y:1997:i:1:p:140-144 Access Statistics for this article More articles in Operations Research from INFORMS Contact information at EDIRC. |
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