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Simterpolation: A Simulation based Interpolation Approximation for Queueing Systems

Author

Listed:
  • Martin I. Reiman

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

  • Burton Simon

    (University of Colorado at Denver, Denver, Colorado)

  • J. Stanford Willie

    (US WEST Advanced Technologies, Boulder, Colorado)

Abstract

In this paper, we approximate moments of the sojourn time distribution in open networks of priority queues via an interpolation approximation. The interpolation is constructed from five random variables (and their covariance matrix) that are simultaneously estimated from a single regenerative simulation of the system at any arrival rate. The random variables are consistent estimates of the zeroth and first-order light traffic limits, the heavy traffic limit, and the value of the function and its derivative at the arrival rate of the simulation. The data yield a least squares estimate of a normalized version of the original function, which, in turn, yields an estimate of the function of interest. This procedure is useful for complex systems because the light and heavy traffic limits needed for an interpolation are not easy to calculate analytically in those cases.

Suggested Citation

  • Martin I. Reiman & Burton Simon & J. Stanford Willie, 1992. "Simterpolation: A Simulation based Interpolation Approximation for Queueing Systems," Operations Research, INFORMS, vol. 40(4), pages 706-723, August.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:4:p:706-723
    DOI: 10.1287/opre.40.4.706
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    Citations

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    Cited by:

    1. Russell C. H. Cheng & Jack P. C. Kleijnen, 1999. "Improved Design of Queueing Simulation Experiments with Highly Heteroscedastic Responses," Operations Research, INFORMS, vol. 47(5), pages 762-777, October.
    2. Saulius Minkevičius & Vladimiras Dolgopolovas & Leonidas L. Sakalauskas, 2016. "A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 37-57, March.
    3. S. Minkevičius & S. Steišūnas, 2006. "About the Sojourn Time Process in Multiphase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 293-302, June.
    4. Cheng, R.C.H. & Kleijnen, J.P.C., 1995. "Optimal design of simulation experiments with nearly saturated queues," Discussion Paper 1995-67, Tilburg University, Center for Economic Research.

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