Exponential Bounds for Queues with Markovian Arrivals

Duffield, N. G. (1993) Exponential Bounds for Queues with Markovian Arrivals. (Preprint)

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Abstract

Exponential bounds P[queue ≥ b] ≤ φe^(-γb) are found for queues whose increments are described by Markovian Additive Processes. This is done 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.

Item Type: Article
Uncontrolled Keywords: Queueing Theory, Large Deviations, Martingales, Risk Theory, Markov Additive Processes, ATM Multiplexers, Effective Bandwidths
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:11
Last Modified: 19 Jul 2018 09:24
URI: http://dair.dias.ie/id/eprint/712

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