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Multi-stage stochastic fluid models for congestion control

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  • O’Reilly, Małgorzata M.

Abstract

We consider multi-stage stochastic fluid models (SFMs), driven by applications in telecommunications and manufacturing in which control of the behavior of the system during congestion may be required. In a two-stage SFM, the process starts from Stage 1 in level 0, and moves to Stage 2 when reaching threshold b2 from below. Stage 1 starts again when reaching threshold b1b2. Finally, we discuss a generalization to multi-stage SFMs. We use matrix-analytic methods and derive efficient methodology for the analysis of this class of models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:238:y:2014:i:2:p:514-526
    DOI: 10.1016/j.ejor.2014.04.010
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    References listed on IDEAS

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    1. R. Malhotra & M. Mandjes & W. Scheinhardt & J. Berg, 2009. "A feedback fluid queue with two congestion control thresholds," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 149-169, August.
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    3. Van Houdt, Benny, 2012. "Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience," European Journal of Operational Research, Elsevier, vol. 220(3), pages 695-704.
    4. Nigel Bean & Małgorzata O’Reilly, 2008. "Performance measures of a multi-layer Markovian fluid model," Annals of Operations Research, Springer, vol. 160(1), pages 99-120, April.
    5. 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.
    6. Bean, Nigel G. & O'Reilly, Malgorzata M. & Taylor, Peter G., 2005. "Hitting probabilities and hitting times for stochastic fluid flows," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1530-1556, September.
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