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Cell loss asymptotics for buffers fed with a large number of independent stationary sources

Part of: Limit theorems Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Nikolay Likhanov  and
Ravi R. Mazumdar
Nikolay Likhanov*
Affiliation:
Institute for Problems of Information Transmission
Ravi R. Mazumdar*
Affiliation:
University of Essex
*
∗Postal address: Institute for Problems of Information Transmission, 19 Bolshoi Karetnyi, GSP-4, Moscow 101447, Russia.
∗∗Postal address: Department of Mathematics, University of Essex, Colchester CO4 3SQ, UK. Email address: mazum@essex.ac.uk.
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Abstract

In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sources with heavy-tailed distributed ON periods, which are typical candidates for so-called ‘self-similar’ inputs, showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for the Markovian type of sources, which has important implications for statistical multiplexing. Numerical validation of the results against simulations are also reported.

Keywords

ATMfinite bufferscell loss asymptoticsBahadur–Rao theoremrate functionsheavy-tailed distributions

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60F10: Large deviations 60K25: Queueing theory 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 86 - 96
Copyright
Copyright © Applied Probability Trust 1999 

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