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Exponents for the tails of distributions in some polling models

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Abstract

The tail asymptotics of the distribution of the waiting-time W in some polling models is investigated. When this is of the form P[W > ϰ] ∼ αϰβe -ηϰ for some α,β,η, we show how to calculate the exponents β and η, and we establish the extent and form of their dependence on the distributions of the service-time and switchover-time. The exponents are expressed in terms of the fixed points and Lyapunov exponents of a dynamical system which we associate with the recursion which is used to calculate the moment generating functions of the waiting time.

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  1. AT&T Laboratories, Room A175, 180 Park Avenue, Florham Park, NJ, 07932-0971, USA

    N.G. Duffield

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  1. N.G. Duffield
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Duffield, N. Exponents for the tails of distributions in some polling models. Queueing Systems 26, 105–119 (1997). https://doi.org/10.1023/A:1019120905658

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  • DOI: https://doi.org/10.1023/A:1019120905658

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