Rigorous Bounds for Loss Probabilities in Multiplexers of Discrete Heterogenous Markovian Sources

Duffield, N. G. (1992) Rigorous Bounds for Loss Probabilities in Multiplexers of Discrete Heterogenous Markovian Sources. (Preprint)

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Abstract

Exponential upper bounds of the form P[queue ≥ b] ≤ φy^(-b) are obtained for the distribution of the queue length in a model of a multiplexer in which the input is a heterogeneous superposition of discrete Markovian on-off sources. These bounds are valid at all queue lengths, rather than just asymptotic in the limit b→∞. The decay constant y is found by numerical solution of a single transcendental equation which determines the effective bandwidths of the sources in the limit b→∞. The prefactor φ is given explicitly in terms of y. The bound provides a means to determine rigorous corrections to effective bandwidths for multiplexers with finite buffers.

Item Type:	Article
Uncontrolled Keywords:	Queueing theory, ATM, effective bandwidths, martingales
Divisions:	School of Theoretical Physics > Preprints
Date Deposited:	19 Jun 2018 14:13
Last Modified:	20 Dec 2022 09:02
URI:	https://dair.dias.ie/id/eprint/735

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