Extreme Value Theory for Queues Via Cycle Maxima |
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Authors: | Søren Asmussen |
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Affiliation: | (1) Department of Mathematical Statistics, Lund University, Box 118, 221 00 Lund, Sweden |
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Abstract: | The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum of the queueing process during a regenerative cycle . For simple queues, methods for obtaining the distribution of both explicitly and asymptotically are reviewed. In greater generality, the study leads into Wiener–Hopf problems. Extensions to queues in a Markov regime, for example governed by Markov-modulated Poisson arrivals, are also considered. |
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Keywords: | exponential change of measure Markov additive process Markov-modulation rare event regenerative process semi-regeneration subexponential distribution Wiener– Hopf method |
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