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 |
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Uncontrolled Keywords: | Queueing theory, ATM, effective bandwidths, martingales |

Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 19 Jun 2018 14:13 |

Last Modified: | 19 Jul 2018 10:53 |

URI: | http://dair.dias.ie/id/eprint/735 |

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