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

Wouter Berkelmans, Agata Cichocka and Michel Mandjes

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1713-1734

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.

Keywords: Lévy processes; Reflection; Workload; Markov additive processes (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.05.015

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