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Queueing approximation of suprema of spectrally positive Lévy process

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Abstract

Let W=sup 0≤t<∞(X(t)−β t), where X is a spectrally positive Lévy process with expectation zero and 0<β<∞. One of the main results of the paper says that for such a process X, there exists a sequence of M/GI/1 queues for which stationary waiting times converge in distribution to W. The second result shows that condition (III) of Proposition 2 in the paper is not implied by all other conditions.

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Authors and Affiliations

  1. Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    M. Czystołowski & W. Szczotka

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  1. M. Czystołowski
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  2. W. Szczotka
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Correspondence to W. Szczotka.

Additional information

M.Czystołowski was supported by KBN grant N201 020 32/0816.

W. Szczotka was supported by grant 2787/W/IM.

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Czystołowski, M., Szczotka, W. Queueing approximation of suprema of spectrally positive Lévy process. Queueing Syst 64, 305–323 (2010). https://doi.org/10.1007/s11134-009-9160-7

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  • DOI: https://doi.org/10.1007/s11134-009-9160-7

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