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An Approximation Method for the Analysis of GI / G /1 Queues

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  • Jingwen Li

    (The National University of Singapore, Republic of Singapore)

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.

Suggested Citation

  • Jingwen Li, 1997. "An Approximation Method for the Analysis of GI / G /1 Queues," Operations Research, INFORMS, vol. 45(1), pages 140-144, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:140-144
    DOI: 10.1287/opre.45.1.140
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