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Variability Functions for Parametric-Decomposition Approximations of Queueing Networks

Author

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  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636)

Abstract

We propose an enhancement to the parametric-decomposition method for calculating approximate steady-state performance measures of open queueing networks with non-Poisson arrival processes and nonexponential service-time distributions. Instead of using a variability parameter c a 2 for each arrival process, we suggest using a variability function c a 2 \rho, 0 a 2 \rho should be 0 for \rho near 0 or 1, but c a 2 \rho can assume arbitrarily large values for appropriate intermediate \rho. We present a full network algorithm with variability functions, showing that the idea is implementable. We also show how simulations of single queues can be effectively exploited to determine variability functions for difficult external arrival processes.

Suggested Citation

  • Ward Whitt, 1995. "Variability Functions for Parametric-Decomposition Approximations of Queueing Networks," Management Science, INFORMS, vol. 41(10), pages 1704-1715, October.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:10:p:1704-1715
    DOI: 10.1287/mnsc.41.10.1704
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    Cited by:

    1. Feng Dong & Qiguo Gong & Hui Wang & Siyuan Yi & Yue Cai, 2019. "Rest Breaks Arrange Based on Empirical Studies of Productivity in Manufacturing Industry," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 9(9), pages 1043-1066, September.
    2. 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.
    3. Sunkyo Kim, 2005. "Approximation of multiclass queueing networks with highly variable arrivals under deterministic routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 399-408, August.
    4. Rabta, Boualem, 2013. "A hybrid method for performance analysis of G/G/m queueing networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 38-49.
    5. Sunkyo Kim, 2011. "Modeling Cross Correlation in Three-Moment Four-Parameter Decomposition Approximation of Queueing Networks," Operations Research, INFORMS, vol. 59(2), pages 480-497, April.
    6. Wu, Kan & Zhao, Ning, 2015. "Dependence among single stations in series and its applications in productivity improvement," European Journal of Operational Research, Elsevier, vol. 247(1), pages 245-258.
    7. Van Nyen, Pieter L. M. & Van Ooijen, Henny P. G. & Bertrand, J.W.M.J. Will M., 2004. "Simulation results on the performance of Albin and Whitt's estimation method for waiting times in integrated production-inventory systems," International Journal of Production Economics, Elsevier, vol. 90(2), pages 237-249, July.
    8. Kim, Sunkyo, 2004. "The heavy-traffic bottleneck phenomenon under splitting and superposition," European Journal of Operational Research, Elsevier, vol. 157(3), pages 736-745, September.

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