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Cell loss probability for M/G/1 and time-slotted queues

Part of: Limit theorems Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

David McDonald  and
François Théberge
David McDonald*
Affiliation:
University of Ottawa
François Théberge*
Affiliation:
University of Ottawa
*
∗ Postal address: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5.
∗ Postal address: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5.
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Abstract

It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1-ρ)/ρ, where ρ is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1-ρ.

Keywords

CBRcell loss probabilityM/G/1overflow probability

MSC classification

Primary: 60K25: Queueing theory 60G50: Sums of independent random variables; random walks
Secondary: 60F10: Large deviations
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1149 - 1156
Copyright
Copyright © by the Applied Probability Trust 2000 

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