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Buffer overflow asymptotics for a buffer handling many traffic sources

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

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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References

Anick, D., Mitra, D. and Sondhi, M. (1982) Stochastic theory of a data-handling system with multiple sources. Bell System Tech. T 61, 1872–1894.Google Scholar
Choudhury, G., Lucantoni, D. and Whitt, W. (1994a) Squeezing the most out of ATM. IEEE Trans. Commun. to appear CrossRefGoogle Scholar
Choudhury, G., Lucantoni, D. and Whitt, W. (1994b) On the effectiveness of effective bandwidths for admission control in ATM networks. In ITC 14. ed. Labetouille, J. and Roberts, J. Elsevier, Amsterdam. pp. 411–420.Google Scholar
Courcoubetis, C, Kesidis, G., Ridder, A., Walrand, J. and Weber, R. (1995) Admission control and routing in ATM networks using inferences from measured buffer occupancy. IEEE Trans. Commun. 43, 1778–1784.CrossRefGoogle Scholar
Courcoubetis, C. and Weber, R. (1995) Effective bandwidths for stationary sources. Prob. Eng. Inf. Sci. 7, 285–296.CrossRefGoogle Scholar
De Veciana, G. and Walrand, J. (1994) Effective bandwidths: call admission, traffic policing and filtering for ATM networks. Queueing Systems 20, 37–59.CrossRefGoogle Scholar
Duffield, N. (1996) Economies of scale in queues with sources having power-law large deviation scalings. J. Appl. Prob. 33, 840–857.CrossRefGoogle Scholar
Elwalid, A. and Mitra, D. (1993) Effective bandwidth of general Markovian traffic sources and admission control of high speed networks. IEEE/ACM Trans. Network. 1, 329–343.CrossRefGoogle Scholar
Gibbens, R. and Hunt, P. (1991) Effective bandwidths for the multi-type UAS channel. Queueing Systems 1, 17–28.CrossRefGoogle Scholar
Kelly, F. (1991) Effective bandwidths at multi-class queues. Queueing Systems 9, 5–16.CrossRefGoogle Scholar
Kesidis, G., Walrand, J. and Chang, C. (1993) Effective bandwidths for multiclass Markov fluids and other ATM sources. IEEE/ACM Trans. Network. 1, 424–428.CrossRefGoogle Scholar
Simonian, A. and Guilbert, J. (1994) Large deviations approximation for fluid queues fed by a large number of on-off sources. Preprint.CrossRefGoogle Scholar
Weiss, A. (1983) The large deviation of a Markov process which models traffic generation. Technical report. AT&T Bell Laboratories.Google Scholar
Whitt, W. (1993) Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues. Telecommun. Systems 2, 71–107.CrossRefGoogle Scholar