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Online IPA Gradient Estimators in Stochastic Continuous Fluid Models

Author

Listed:
  • Y. Wardi

    (Georgia Institute of Technology)

  • B. Melamed

    (Rutgers University)

  • C.G. Cassandras

    (Boston University)

  • C.G. Panayiòtou

    (Boston University)

Abstract

This paper applies infinitesimal perturbation analysis (IPA) to loss-related and workload-related metrics in a class of stochastic flow models (SFM). It derives closed-form formulas for the gradient estimators of these metrics with respect to various parameters of interest, such as buffer size, service rate, and inflow rate. The IPA estimators derived are simple and fast to compute, and are further shown to be unbiased and nonparametric, in the sense that they can be computed directly from the observed data without any knowledge of the underlying probability law. These properties hold out the promise of utilizing IPA gradient estimates as ingredients of online management and control of telecommunications networks. While this paper considers single-node SFMs, the analysis method developed is amenable to extensions to networks of SFM nodes with more general topologies.

Suggested Citation

  • Y. Wardi & B. Melamed & C.G. Cassandras & C.G. Panayiòtou, 2002. "Online IPA Gradient Estimators in Stochastic Continuous Fluid Models," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 369-405, November.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:2:d:10.1023_a:1020892306506
    DOI: 10.1023/A:1020892306506
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    References listed on IDEAS

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    1. Konstantopoulos, Takis & Zazanis, Michael & De Veciana, Gustavo, 1996. "Conservation laws and reflection mappings with an application to multiclass mean value analysis for stochastic fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 139-146, December.
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    Cited by:

    1. Yao Zhao & Benjamin Melamed, 2006. "IPA Derivatives for Make-to-Stock Production-Inventory Systems with Backorders," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 191-222, June.
    2. Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
    3. Xia, Li & Cao, Xi-Ren, 2012. "Performance optimization of queueing systems with perturbation realization," European Journal of Operational Research, Elsevier, vol. 218(2), pages 293-304.
    4. Benjamin Melamed & Yihong Fan & Yao Zhao & Yorai Wardi, 2010. "IPA derivatives for a discrete model of make-to-stock production-inventory systems with backorders," Annals of Operations Research, Springer, vol. 181(1), pages 1-19, December.
    5. (Yale) Gong, Yeming & Yücesan, Enver, 2012. "Stochastic optimization for transshipment problems with positive replenishment lead times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 61-72.
    6. Yihong Fan & Benjamin Melamed & Yao Zhao & Yorai Wardi, 2009. "IPA Derivatives for Make-to-Stock Production-Inventory Systems With Backorders Under the (R,r) Policy," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 159-179, June.
    7. Mourani, Iyad & Hennequin, Sophie & Xie, Xiaolan, 2008. "Simulation-based optimization of a single-stage failure-prone manufacturing system with transportation delay," International Journal of Production Economics, Elsevier, vol. 112(1), pages 26-36, March.

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