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 |
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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: | 15 Dec 2022 14:18 |

URI: | https://dair.dias.ie/id/eprint/700 |

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