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Improved design of queuing simulation experiments with highly heteroscedastic responses

Author

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  • Cheng, R.C.H.
  • Kleijnen, J.P.C.

    (Tilburg University, School of Economics and Management)

Abstract

Simulation experiments for analysing the steady-state behaviour of queueing systems over a range of traffic intensities are considered, and a procedure is presented for improving their design. In such simulations the mean and variance of the response output can increase dramatically with traffic intensity; the design has to be able to cope with this complication. A regression metamodel of the likely mean response is used consisting of two factors, namely, a low-degree polynomial and a factor accounting for the exploding mean as the traffic intensity approaches its saturation. The best choice of traffic intensities at which to make simulation runs depends on the variability of the simulation output, and this variability is estimated using analytical heavy traffic results. The optimal numbers of customers simulated at each traffic intensity are built up using a multistage procedure. The asymptotic properties of the procedure are investigated theoretically. The procedure is shown to be robust and to be more efficient than more naive procedures. A result of note is that even when the range of interest includes high traffic intensities, the highest traffic load simulated should remain well away from its upper limit; but the number of customers simulated should be concentrated at the higher traffic intensities used. Empirical results are included for simulations of a single server queue with different priority rules and for a complicated queueing network. These results support the theoretical results, demonstrating that the proposed procedure can increase the accuracy of the estimated metamodel significantly compared with more naive methods.
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Suggested Citation

  • Cheng, R.C.H. & Kleijnen, J.P.C., 1996. "Improved design of queuing simulation experiments with highly heteroscedastic responses," Other publications TiSEM d8a325a9-82bf-4d23-839e-2, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:d8a325a9-82bf-4d23-839e-264c40acc7fd
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    References listed on IDEAS

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    1. 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.
    2. Kleijnen, J.P.C. & van Groenendaal, W.J.H., 1992. "Two-stage versus sequential sample-size determination in regression analysis of simulation experiments," Other publications TiSEM cac61c9f-0967-4f5a-aab1-9, Tilburg University, School of Economics and Management.
    3. Jack P. C. Kleijnen, 1992. "Regression Metamodels for Simulation with Common Random Numbers: Comparison of Validation Tests and Confidence Intervals," Management Science, INFORMS, vol. 38(8), pages 1164-1185, August.
    4. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    5. Søren Asmussen, 1992. "Queueing Simulation in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 84-111, February.
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    Cited by:

    1. Kleijnen, J.P.C. & Sanchez, S.M. & Lucas, T.W. & Cioppa, T.M., 2003. "A User's Guide to the Brave New World of Designing Simulation Experiments," Other publications TiSEM a6910d11-f9bc-4246-b1a7-2, Tilburg University, School of Economics and Management.
    2. Kleijnen, Jack P. C., 2005. "An overview of the design and analysis of simulation experiments for sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 164(2), pages 287-300, July.
    3. Lucy E. Morgan & Luke Rhodes-Leader & Russell R. Barton, 2022. "Reducing and Calibrating for Input Model Bias in Computer Simulation," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2368-2382, July.
    4. Feng Yang & Bruce Ankenman & Barry L. Nelson, 2007. "Efficient generation of cycle time‐throughput curves through simulation and metamodeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 78-93, February.
    5. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    6. Kleijnen, Jack P. C. & van Beers, Wim C. M., 2005. "Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments," European Journal of Operational Research, Elsevier, vol. 165(3), pages 826-834, September.
    7. Sungmin Park & John W. Fowler & Gerald T. Mackulak & J. Bert Keats & W. Matthew Carlyle, 2002. "D-Optimal Sequential Experiments for Generating a Simulation-Based Cycle Time-Throughput Curve," Operations Research, INFORMS, vol. 50(6), pages 981-990, December.
    8. Sigal Levy & David Steinberg, 2010. "Computer experiments: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 311-324, December.
    9. Jack P. C. Kleijnen & Susan M. Sanchez & Thomas W. Lucas & Thomas M. Cioppa, 2005. "State-of-the-Art Review: A User’s Guide to the Brave New World of Designing Simulation Experiments," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 263-289, August.
    10. Reis dos Santos, Pedro M. & Isabel Reis dos Santos, M., 2009. "Using subsystem linear regression metamodels in stochastic simulation," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1031-1040, August.
    11. Feng Yang & Bruce E. Ankenman & Barry L. Nelson, 2008. "Estimating Cycle Time Percentile Curves for Manufacturing Systems via Simulation," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 628-643, November.

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