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Transient analysis of a stationary Lévy-driven queue

Author

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  • Ivanovs, Jevgenijs
  • Mandjes, Michel

Abstract

In this paper we study a queue with Lévyinput, without imposing any a priori assumption on the jumps being one-sided. The focus is on computing the transforms of all sorts of quantities related to the transient workload, assuming the workload is in stationarity at time 0. The results are simple expressions that are in terms of the bivariate Laplace exponents of ladder processes. In particular, we derive the transform of the minimum workload attained over an exponentially distributed interval.

Suggested Citation

  • Ivanovs, Jevgenijs & Mandjes, Michel, 2015. "Transient analysis of a stationary Lévy-driven queue," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 341-347.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:341-347
    DOI: 10.1016/j.spl.2015.09.010
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    Cited by:

    1. Albrecher, Hansjörg & Ivanovs, Jevgenijs, 2017. "Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 643-656.

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