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Tail asymptotics for a Lévy-driven tandem queue with an intermediate input

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Abstract

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper, we consider only light-tailed inputs. For the Brownian input case, we derive exact tail asymptotics for the marginal stationary distribution of the second buffer content, while weaker asymptotic results are obtained for the general Lévy input case. The results generalize those of Lieshout and Mandjes from the recent papers (Lieshout and Mandjes in Math. Methods Oper. Res. 66:275–298, 2007 and Queueing Syst. 60:203–226, 2008) for the corresponding tandem queue without an intermediate input.

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Authors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Masakiyo Miyazawa

  2. Wrocław University, Wrocław, Poland

    Tomasz Rolski

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  1. Masakiyo Miyazawa
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  2. Tomasz Rolski
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Correspondence to Masakiyo Miyazawa.

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Miyazawa, M., Rolski, T. Tail asymptotics for a Lévy-driven tandem queue with an intermediate input. Queueing Syst 63, 323 (2009). https://doi.org/10.1007/s11134-009-9146-5

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  • DOI: https://doi.org/10.1007/s11134-009-9146-5

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