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Moments Computation for General Markov Fluid Models

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  • Hédi Nabli

    (University of Sfax)

Abstract

This paper derives new algorithms for the computation of moments in general Markov fluid models. The first one is recursive: the nth moment is obtained from the preceding moment via a linear system. We show that these moments depend basically on buffer occupancy. Also, our approach proposes a unified code that does not distinguish between the case where the effective input rates matrix is invertible and the case where it is singular. The second algorithm is based on the matrix analytic method. These results are illustrated through numerical examples, where are considered server supporting multiple output rates. Keeping the traffic intensity constant, we study the impact of output rates management on the average fluid level.

Suggested Citation

  • Hédi Nabli, 2022. "Moments Computation for General Markov Fluid Models," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2055-2070, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09903-4
    DOI: 10.1007/s11009-021-09903-4
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    References listed on IDEAS

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    1. Abdelghafour Es-Saghouani & Michel Mandjes, 2011. "Transient analysis of Markov-fluid-driven queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 35-53, July.
    2. Eleonora Deiana & Guy Latouche & Marie-Ange Remiche, 2021. "Fluid Flow Model for Energy-Aware Server Performance Evaluation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 801-821, September.
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