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Exponential bounds for queues with Markovian arrivals

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Abstract

Exponential bounds ℙ[queue≥b]≤ϕe γb are found for queues whose increments are described by Markov Additive Processes. This is done by application of maximal inequalities to exponential martingales for such processes. Through a thermodynamic approach the constant γ is shown to be the decay rate for an asymptotic lower bound for the queue length distribution. The class of arrival processes considered includes a wide variety of Markovian multiplexer models, and a general treatment of these is given, along with that of Markov modulated arrivals. Particular attention is paid to the calculation of the prefactor ϕ.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

    N. G. Duffield

  2. School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland

    N. G. Duffield

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  1. N. G. Duffield
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Duffield, N.G. Exponential bounds for queues with Markovian arrivals. Queueing Syst 17, 413–430 (1994). https://doi.org/10.1007/BF01158702

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  • DOI: https://doi.org/10.1007/BF01158702

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