Large deviations, the shape of the loss curve, and economies of scale in large multiplexers

Botvich, D. D. and Duffield, N. G. (1994) Large deviations, the shape of the loss curve, and economies of scale in large multiplexers. (Preprint)

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Abstract

We analyse the queue Q^L at a multiplexer with L inputs. We obtain a large deviation result, namely that under very general conditions: lim_(L→∞) L^(-1)log(P[Q^L > Lb]) = -I(b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. This provides an improvement on the usual effective bandwidth approximation P[Q^L > b] ≈ e^(-δb), replacing it with P[Q^L > b] ≈ e^(LI(b/L)). The difference I(b) - δb determines the economies of scale which are to be obtained in large multiplexers. If the limit ν = -lim_(t→∞) tλ_t(δ) exists (here λ_t is the finite time cumulant of the workload process) then lim_(b→∞) (I(b) - δb) = ν. We apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. We obtain expressions for ν in these cases. ν is zero for independent arrivals, but positive for arrivals with positive correlations. Thus economies of scale are obtainable for highly bursty traffic expected in ATM multiplexing.

Item Type: Article
Uncontrolled Keywords: Large deviations, scaling limits, ATM multiplexers, heterogeneous superpositions
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:10
Last Modified: 18 Jul 2018 14:17
URI: http://dair.dias.ie/id/eprint/700

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