Hostname: page-component-89b8bd64d-r6c6k Total loading time: 0 Render date: 2026-05-08T07:34:59.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Queueing systems for multiple FBM-based traffic models

Published online by Cambridge University Press:  17 February 2009

Mihaela T. Matache  and
Valentin Matache
Mihaela T. Matache
Affiliation:
Department of Mathematics, The University of Nebraska at Omaha, Omaha, NE 68182, USA: e-mail: dmatache@mail.unomaha.edu and vmatache@mail.unomaha.edu.
Valentin Matache
Affiliation:
Department of Mathematics, The University of Nebraska at Omaha, Omaha, NE 68182, USA: e-mail: dmatache@mail.unomaha.edu and vmatache@mail.unomaha.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A multiple fractional Brownian motion (FBM)-based traffic model is considered. Various lower bounds for the overflow probability of the associated queueing system are obtained. Based on a probabilistic bound for the busy period of an ATM queueing system associated with a multiple FBM-based input traffic, a minimal dynamic buffer allocation function (DBAF) is obtained and a DBAF-allocation algorithm is designed. The purpose is to create an upper bound for the queueing system associated with the traffic. This upper bound, called a DBAF, is a function of time, dynamically bouncing with the traffic. An envelope process associated with the multiple FBM-based traffic model is introduced and used to estimate the queue size of the queueing system associated with that traffic model.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 361 - 377
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Beran, J., Sherman, R., Taqqu, M. S. and Willinger, W., “Long-range dependence in variable-bit-rate video traffic”, IEEE Trans. Communications 43 (1995) 1566–1579.CrossRefGoogle Scholar
[2]Chang, C., “Stability, queue length, and delay of deterministic and stochastic queuing networks”, IEEE Trans. Aut. Control 39 (1994) 913–931.CrossRefGoogle Scholar
[3]Crovella, M. E. and Bestavros, A., “Self-similarity in world wide web traffic: Evidence and possible causes”, IEEE/ACM Trans. Networking 5 (1997) 835–846.CrossRefGoogle Scholar
[4]Dembo, A. and Zeitouni, O., Theory of large deviation techniques and applications (Jones and Bartlett, Boston, 1993).Google Scholar
[5]Duffield, N. G. and O'Connell, N., “Large deviations and overflow probabilities for the general single-server queue, with applications”, Math. Proc. Cambridge Philos. Soc. 118 (1995) 363–374.CrossRefGoogle Scholar
[6]Erramilli, A., Narayan, O. and Willinger, W., “Experimental queuing analysis with long-range dependent packet traffic”, IEEE/ACM Trans. Networking 4 (1996) 209–223.CrossRefGoogle Scholar
[7]Garrett, M. W. and Willinger, W., “Analysis, modeling and generation of self-similar VBR video traffic”, in Proceedings of ACM Sigcom '94, London, (ACM Press, New York, 1994), 269–280.CrossRefGoogle Scholar
[8]Leland, W. E., Taqqu, M. S., Willinger, W. and Wilson, D. V., “On the self-similar nature of Ethernet traffic”, in Proceedings of ACM Sigcom'93, San Francisco, (ACM Press, New York, 1993), 183–193.Google Scholar
[9]Leland, W. E., Taqqu, M. S., Willinger, W. and Wilson, D. V., “On the self-similar nature of Ethernet traffic (Extended version)”, IEEE/ACM Trans. Networking 2 (1994) 1–15.CrossRefGoogle Scholar
[10]Mayor, G. and Silvester, J., “Time scale analysis of an ATM queuing system with long-range dependent traffic”, in Proceedings of INFOCOM'97, (IEEE, Washington, 1997) 205–212.CrossRefGoogle Scholar
[11]Meier-Hellstern, K., Wirth, P. E., Yan, Y.-L. and Hoeflin, D. A., “Traffic models for ISDN data users: office automation application”, in Proceedings of 13th ITC, Copenhagen, Denmark, (Elsevier Science Publ., Amsterdam, 1991), 167–172.Google Scholar
[12]Norros, I., “A storage model with self-similar input”, Queuing Systems Theory Appl. 16 (1994) 387–396.CrossRefGoogle Scholar
[13]Paxson, V. and Floyd, S., “Wide-area traffic: the failure of Poisson modeling”, in Proceedings of ACM Sigcom'94, London, (ACM Press, New York, 1994), 257–268.CrossRefGoogle Scholar
[14]Roberts, J., Mocci, U. and Virtamo, J. (eds.), Broadband network traffic (Springer, Berlin, 1996).CrossRefGoogle Scholar
[15]Schwartz, M., Broadband integrated networks (Prentice-Hall, Euglewood-Cliffs, NJ, 1996).Google Scholar
[16]Willinger, W., Taqqu, M. S., Leland, W. E. and Wilson, D. V., “Self-similarity in high-speed packet traffic: Analysis and modelling of Ethernet traffic measurements”, Statist. Sci. 10 (1995) 67–85.CrossRefGoogle Scholar
[17]Willinger, W., Taqqu, M. S., Sherman, R. and Wilson, V., “Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level”, IEEE/ACM Trans. Networking 5 (1997) 71–86.CrossRefGoogle Scholar