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Buffer overflow asymptotics for a buffer handling many traffic sources

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

Published online by Cambridge University Press:  14 July 2016

Costas Courcoubetis  and
Richard Weber
Costas Courcoubetis*
Affiliation:
University of Crete
Richard Weber*
Affiliation:
University of Cambridge
*
∗Postal address: Department of Computer Science, University of Crete, P.O. Box 1470 Heraklion, 71110 Greece.
∗∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

As a model for an ATM switch we consider the overflow frequency of a queue that is served at a constant rate and in which the arrival process is the superposition of N traffic streams. We consider an asymptotic as N → ∞ in which the service rate Nc and buffer size Nb also increase linearly in N. In this regime, the frequency of buffer overflow is approximately exp(–NI(c, b)), where I(c, b) is given by the solution to an optimization problem posed in terms of time-dependent logarithmic moment generating functions. Experimental results for Gaussian and Markov modulated fluid source models show that this asymptotic provides a better estimate of the frequency of buffer overflow than ones based on large buffer asymptotics.

Keywords

ATM SWITCHESBUFFER OVERFLOW ASYMPTOTICSEFFECTIVE BANDWIDTHSLARGE DEVIATIONSMARKOV MODULATED FLUID

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60F10: Large deviations 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling 90B10: Network models, deterministic 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 886 - 903
Copyright
Copyright © Applied Probability Trust 1996 

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