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Buffer content of a leaky-bucket system with long-range dependent input traffic

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Bárbara González-Arévalo  and
Gennady Samorodnitsky
Bárbara González-Arévalo
Affiliation:
Cornell University
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
∗∗Postal address: School of Operations Research and Industrial Engineering and Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA. Email address: [email protected]
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Abstract

The leaky bucket is a flow control mechanism that is designed to reduce the effect of the inevitable variability in the input stream into a node of a communication network. In this paper we study what happens when an input stream with heavy-tailed work sessions arrives to a server protected by such a leaky bucket. Heavy-tailed sessions produce long-range dependence in the input stream. Previous studies of single server fluid queues without flow control suggested that such long-range dependence can have a dramatic effect on the system performance. By concentrating on the expected time till overflow of a large finite buffer we show that leaky-bucket flow control does make the system overflow less often, but long-range dependence still makes its presence felt.

Keywords

Fluid queueflow controlleaky bucketfinite bufferheavy tailslong-range dependencetime until overflow

MSC classification

Primary: 90B15: Network models, stochastic
Secondary: 90B18: Communication networks 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 581 - 601
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

∗

Current address: Department of Mathematics, University of Louisiana at Lafayette, PO Box 41010, Lafayette, LA 70504-1010, USA

References

Altman, E., Avratchenkov, K., Barakat, C. and Núñez-Queija, R. (2002). State-dependent M/G/1 type queueing analysis for congestion control in data networks. Comput. Networks 39, 789–808.Google Scholar
Berger, A., and Whitt, W. (1992a). The Brownian approximation for rate-control throttles and the G/G/1/C queue. Discrete Event Dynamic Systems 2, 7–60.Google Scholar
Berger, A., and Whitt, W. (1992b). Comparison of multi-server queues with finite waiting rooms. Stoch. Models 8, 719–732.CrossRefGoogle Scholar
Berger, A., and Whitt, W. (1992c). The impact of a job buffer in a token-bank rate-control throttle. Stoch. Models 8, 685–717.Google Scholar
Berger, A., and Whitt, W. (1994). The pros and cons of a job buffer in a token-bank rate-control throttle. IEEE Trans. Commun. 42, 857–861.CrossRefGoogle Scholar
Borkovec, M., Dasgupta, A., Resnick, S., and Samorodnitsky, G. (2002). A single channel on/off model with TCP-like control. Stoch. Models 18, 333–367.CrossRefGoogle Scholar
Boxma, O., and Dumas, V. (1998). Fluid queues with long-tailed activity period distributions. Comput. Commun. 21, 1509–1529.CrossRefGoogle Scholar
Crovella, M., and Bestavros, A. (1996). Self-similarity in world wide web traffic: evidence and possible causes. Perf. Eval. Rev. 24, 160–169.Google Scholar
Cunha, C., Bestavros, A., and Crovella, M. (1995). Characteristics of www client-based traces. Tech. Rep. BU-CS-95-010, Boston University. Available at http://www.cs.bu.edu/techreports/.Google Scholar
Embrechts, P., and Veraverbeke, N. (1982). Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72.Google Scholar
Heath, D., Resnick, S., and Samorodnitsky, G. (1997). Patterns of buffer overflow in a class of queues with long memory in the input stream. Ann. Appl. Prob. 7, 1021–1057.Google Scholar
Heath, D., Resnick, S., and Samorodnitsky, G. (1999). How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails. Ann. Appl. Prob. 9, 352–375.Google Scholar
Jelenković, P., and Lazar, A. (1999). Asymptotic results for multiplexing subexponential on-off sources. Adv. Appl. Prob. 31, 394–421.Google Scholar
Jelenković, P. and Momčilović, P. (2003). Asymptotic loss probability in a finite buffer fluid queue with heterogeneous heavy-tailed on-off processes. Ann. Appl. Prob. 13, 576–603.Google Scholar
Leland, W., Taqqu, M., Willinger, W., and Wilson, D. (1994). On the self-similar nature of {E}thernet traffic (extended version). IEEE/ACM Trans. Networking 2, 1–15.Google Scholar
Misra, V., and Towsley, W. G. D. (1999). Stochastic differential equation modeling and analysis of TCP-windowsize behavior. In Proc. Performance'99, Istanbul, October 1999.Google Scholar
Paxson, V., and Floyd, S. (1994). Wide area traffic: the failure of {P}oisson modelling. IEEE/ACM Trans. Networking 3, 226–244.Google Scholar
Resnick, S., and Samorodnitsky, G. (1999). Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues. Queueing Systems 33, 43–71.Google Scholar
Vamvakos, S., and Anantharam, V. (1998). On the departure process of a leaky bucket system with long-range dependent input traffic. Queueing Systems 28, 191–214.CrossRefGoogle Scholar
Zwart, A., Borst, S., and Mandjes, M. (2001). Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows. In Proc. IEEE INFOCOM 2001 (Anchorage, AK, April 2001), Vol. 1, IEEE, New York, pp. 279–288.Google Scholar