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Performance optimization of queueing systems with perturbation realization

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  • Xia, Li
  • Cao, Xi-Ren

Abstract

After the intensive studies of queueing theory in the past decades, many excellent results in performance analysis have been obtained, and successful examples abound. However, exploring special features of queueing systems directly in performance optimization still seems to be a territory not very well cultivated. Recent progresses of perturbation analysis (PA) and sensitivity-based optimization provide a new perspective of performance optimization of queueing systems. PA utilizes the structural information of queueing systems to efficiently extract the performance sensitivity information from a sample path of system. This paper gives a brief review of PA and performance optimization of queueing systems, focusing on a fundamental concept called perturbation realization factors, which captures the special dynamic feature of a queueing system. With the perturbation realization factors as building blocks, the performance derivative formula and performance difference formula can be obtained. With performance derivatives, gradient-based optimization can be derived, while with performance difference, policy iteration and optimality equations can be derived. These two fundamental formulas provide a foundation for performance optimization of queueing systems from a sensitivity-based point of view. We hope this survey may provide some inspirations on this promising research topic.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:293-304
    DOI: 10.1016/j.ejor.2011.07.039
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    References listed on IDEAS

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    Cited by:

    1. Stavros Lopatatzidis & Jasper Bock & Gert Cooman & Stijn Vuyst & Joris Walraevens, 2016. "Robust queueing theory: an initial study using imprecise probabilities," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 75-101, February.
    2. Xia, Li, 2014. "Service rate control of closed Jackson networks from game theoretic perspective," European Journal of Operational Research, Elsevier, vol. 237(2), pages 546-554.
    3. Xia, Li & Shihada, Basem, 2015. "A Jackson network model and threshold policy for joint optimization of energy and delay in multi-hop wireless networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 778-787.
    4. Xiangqian Xu & Zhexuan Zhou & Yajie Dou & Yuejin Tan & Tianjun Liao, 2018. "Sustainable Queuing-Network Design for Airport Security Based on the Monte Carlo Method," Sustainability, MDPI, vol. 10(2), pages 1-19, January.
    5. O’Reilly, Małgorzata M., 2014. "Multi-stage stochastic fluid models for congestion control," European Journal of Operational Research, Elsevier, vol. 238(2), pages 514-526.

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