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Planning Queueing Simulations

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  • Ward Whitt

    (AT&T Bell Laboratories, Room 2C-178, Murray Hill, New Jersey 07974)

Abstract

Simple heuristic formulas are developed to estimate the simulation run lengths required to achieve desired statistical precision in queueing simulations. The formulas are intended to help in the early planning stages before any data have been collected. The queueing simulations considered are single replications (one long run) conducted to estimate steady-state characteristics such as expected equilibrium queue lengths. The formulas can be applied to design simulation experiments to develop and evaluate queueing approximations. In fact, this work was motivated by efforts to develop approximations for packet communication networks with multiple classes of traffic having different service characteristics and bursty arrival processes. In addition to indicating the approximate simulation run length required in each case of a designed experiment, the formulas can help determine what cases to consider, what statistical precision to aim for, and even whether to conduct the experiment at all. The formulas are based on heavy-traffic limits for queues (the limiting behavior as the traffic intensity approaches its upper limit for stability) and associated diffusion approximations. In particular, the formulas apply to stochastic processes that can be approximated by reflected Brownian motion, such as the queue-length process in the standard GI/G/1 model.

Suggested Citation

  • Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:11:p:1341-1366
    DOI: 10.1287/mnsc.35.11.1341
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    Citations

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    Cited by:

    1. Kleijnen, J.P.C. & Bettonvil, B.W.M. & van Groenendaal, W.J.H., 1996. "Validation of Simulation Models : Regression Analysis Revisited," Discussion Paper 1996-07, Tilburg University, Center for Economic Research.
    2. Xiang Ma & Antoine Sauré & Martin L. Puterman & Marianne Taylor & Scott Tyldesley, 2016. "Capacity planning and appointment scheduling for new patient oncology consults," Health Care Management Science, Springer, vol. 19(4), pages 347-361, December.
    3. Halim Damerdji & David Goldsman, 1995. "Consistency of several variants of the standardized time series area variance estimator," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1161-1176, December.
    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. Song, Wheyming Tina, 1996. "On the estimation of optimal batch sizes in the analysis of simulation output," European Journal of Operational Research, Elsevier, vol. 88(2), pages 304-319, January.
    6. David Goldsman & Keebom Kang & Andrew F. Seila, 1999. "Cramér-von Mises Variance Estimators for Simulations," Operations Research, INFORMS, vol. 47(2), pages 299-309, April.
    7. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    8. Ehsan Mehdad & Jack P.C. Kleijnen, 2018. "Stochastic intrinsic Kriging for simulation metamodeling," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(3), pages 322-337, May.
    9. Sheldon H. Jacobson & Enver Yücesan, 1999. "On the Complexity of Verifying Structural Properties of Discrete Event Simulation Models," Operations Research, INFORMS, vol. 47(3), pages 476-481, June.
    10. Gamze Tokol & David Goldsman & Daniel H. Ockerman & James J. Swain, 1998. "Standardized Time Series Lp-Norm Variance Estimators for Simulations," Management Science, INFORMS, vol. 44(2), pages 234-245, February.
    11. Ward Whitt & Wei You, 2018. "Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues," Operations Research, INFORMS, vol. 66(1), pages 184-199, January.
    12. Raed Kontar & Shiyu Zhou & John Horst, 2017. "Estimation and monitoring of key performance indicators of manufacturing systems using the multi-output Gaussian process," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2304-2319, April.
    13. Xu Sun & Ward Whitt, 2018. "Creating Work Breaks from Available Idleness," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 721-736, October.
    14. Noah Gans & Garrett van Ryzin, 1999. "Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights," Operations Research, INFORMS, vol. 47(5), pages 675-692, October.
    15. Ockerman, Daniel H. & Goldsman, David, 1999. "Student t-tests and compound tests to detect transients in simulated time series," European Journal of Operational Research, Elsevier, vol. 116(3), pages 681-691, August.
    16. Maddah, Bacel & Nasr, Walid W. & Charanek, Ali, 2017. "A multi-station system for reducing congestion in high-variability queues," European Journal of Operational Research, Elsevier, vol. 262(2), pages 602-619.
    17. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    18. 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.
    19. Peter W. Glynn & Rob J. Wang, 2018. "On the rate of convergence to equilibrium for reflected Brownian motion," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 165-197, June.
    20. Nakayama, Marvin K., 2007. "Fixed-width multiple-comparison procedures using common random numbers for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1330-1349, November.
    21. Rayadurgam Srikant & Ward Whitt, 1999. "Variance Reduction in Simulations of Loss Models," Operations Research, INFORMS, vol. 47(4), pages 509-523, August.
    22. 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.
    23. Chen, Xi & Zhou, Qiang, 2017. "Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 262(2), pages 575-585.
    24. Muhammad El-Taha & Bacel Maddah, 2006. "Allocation of Service Time in a Multiserver System," Management Science, INFORMS, vol. 52(4), pages 623-637, April.

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