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The correlation function of a queue with Lévy and Markov additive input

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  • Berkelmans, Wouter
  • Cichocka, Agata
  • Mandjes, Michel

Abstract

Let (Qt)t∈R be a stationary workload process, and r(t) the correlation coefficient of Q0 and Qt. In a series of previous papers (i) the transform of r(⋅) has been derived for the case that the driving process is spectrally-positive (sp) or spectrally-negative (sn) Lévy, (ii) it has been shown that for sp-Lévy and sn-Lévy input r(⋅) is positive, decreasing, and convex, (iii) in case the driving Lévy process is light-tailed (a condition that is automatically fulfilled in the sn case), the decay of the decay rate agrees with that of the tail of the busy period distribution.

Suggested Citation

  • Berkelmans, Wouter & Cichocka, Agata & Mandjes, Michel, 2020. "The correlation function of a queue with Lévy and Markov additive input," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1713-1734.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1713-1734
    DOI: 10.1016/j.spa.2019.05.015
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    References listed on IDEAS

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    1. Rajeeva L. Karandikar & Vidyadhar G. Kulkarni, 1995. "Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment," Operations Research, INFORMS, vol. 43(1), pages 77-88, February.
    2. A. B. Dieker & M. Mandjes, 2011. "Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 221-267, June.
    3. Ivanovs, Jevgenijs, 2017. "Splitting and time reversal for Markov additive processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2699-2724.
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