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Extreme Values in ON/OFF Models of Teletraffic under Permanent and Periodic Measurements

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Abstract

The asymptotic behavior of stream intensity extreme values in ON/OFF models of teletraffic under permanent and periodic measurements is studied. It is assumed that the intensity of each source has a distribution with a heavy (regularly varying) tail. A joint limiting distribution for maxima with a common linear normalization, marginal distributions, and the distribution of the maxima ratio are obtained. The extremal index for a sequence of periodic measurements is calculated.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. V. Lebedev

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  1. A. V. Lebedev
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Correspondence to A. V. Lebedev.

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Original Russian Text © A.V. Lebedev, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 4, pp. 9–15.

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Lebedev, A.V. Extreme Values in ON/OFF Models of Teletraffic under Permanent and Periodic Measurements. Moscow Univ. Math. Bull. 73, 137–142 (2018). https://doi.org/10.3103/S0027132218040022

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