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Perturbation analysis of theGI/GI/1 queue

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Abstract

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,θ), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect toθ. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, University of Massachusetts, 01003, Amherst, MA, USA

    Michael A. Zazanis

  2. Department of Industrial Engineering, University of Wisconsin, 1513 University Avenue, 53706, Madison, WI, USA

    Rajan Suri

Authors
  1. Michael A. Zazanis
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  2. Rajan Suri
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Zazanis, M.A., Suri, R. Perturbation analysis of theGI/GI/1 queue. Queueing Syst 18, 199–248 (1994). https://doi.org/10.1007/BF01158763

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  • DOI: https://doi.org/10.1007/BF01158763

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