article

Asymptotic behavior of heterogeneous TCP flows and RED gateway

Authors:

Peerapol Tinnakornsrisuphap,

Richard J. LaAuthors Info & Claims

IEEE/ACM Transactions on Networking (TON), Volume 14, Issue 1

Pages 108 - 120

https://doi.org/10.1109/TNET.2005.863453

Published: 01 February 2006 Publication History

Abstract

We introduce a stochastic model of a bottleneck ECN/RED gateway under a large number of heterogeneous TCP flows, i.e., flows with diverse round-trip delays and session dynamics. We investigate the asymptotic behavior of the system and show that as the number of flows becomes large, the buffer dynamics and aggregate traffic simplify and can be accurately described by simple stochastic recursions independent of the number of flows, resulting in a scalable model. Based on the Central Limit analysis in the paper, we identify the sources of fluctuations in queue size and describe the relationship between the system parameters such as the marking function and variance of queue size. A closed-form approximation for the mean queue size as a function of system parameters is provided from a simple steady-state analysis. Numerical examples are provided to validate our results.

References

[1]

{1} E. Altman, K. Avrachenkov, and C. Barakat, "TCP in presence of bursty losses," in Proc. ACM SIGMETRICS, Santa Clara, CA, 2000, pp. 124-133.]]

[2]

{2} F. Baccelli, D. R. McDonald, and J. Reynier, "A mean-field model for multiple TCP connections through a buffer implementing RED," INRIA, Sophia Antipolis, France, Tech. Rep., Apr. 2002.]]

[3]

{3} M. E. Crovella and A. Bestavros, "Self-similarity in World Wide Web traffic: evidence and possible causes," in Proc. ACM SIGMETRICS, Philadelphia, PA, 1996, pp. 160-169.]]

[4]

{4} A. Durresi, M. Sridharan, C. Liu, M. Goyal, and R. Jain, "Multilevel early congestion notification," in Proc. 5th World Multiconf. Systemics, Cybernetics and Informatics, Orlando, FL, Jul. 2001, pp. 12-17.]]

[5]

{5} S. Floyd and V. Jacobson, "Random early detection gateways for congestion avoidance," IEEE Trans. Netw., vol. 1, no. 4, pp. 397-413, Aug. 1993.]]

[6]

{6} C. V. Hollot, V. Misra, D. Towsley, and W.-B. Gong, "A control theoretic analysis of RED," in Proc. IEEE INFOCOM, Apr. 2001, pp. 1510-1519.]]

[7]

{7} C. V. Hollot, Y. Liu, V. Misra, and D. Towsley, "Unresponsive flows and AQM performance," in Proc. IEEE INFOCOM, Apr. 2003, pp. 85-95.]]

[8]

{8} V. Jacobson, "Congestion avoidance and control," in Proc. ACM SIGCOMM , Aug. 1988, pp. 314-332.]]

[9]

{9} A. Kherani and A. Kumar, "Stochastic models for throughput analysis of randomly arriving elastic flows in the Internet," in Proc. IEEE INFOCOM , 2002, pp. 1014-1023.]]

[10]

{10} M. Mathis, J. Semske, J. Mahdavi, and T. Ott, "The macroscopic behavior of TCP congestion avoidance algorithm," Comput. Commun. Rev., vol. 27, no. 3, pp. 67-82, Jul. 1997.]]

[11]

{11} M. Mellia, I. Stoica, and H. Zhang, "TCP model for short lived flows," IEEE Commun. Lett., vol. 6, no. 2, pp. 85-87, Feb. 2002.]]

[12]

{12} J. Padhye, V. Firoiu, D. Towsley, and J. Kurose, "Modeling TCP Reno performance: a simple model and its empirical validation," IEEE/ACM Trans. Netw., vol. 8, no. 2, pp. 133-145, Apr. 2000.]]

[13]

{13} K. Park and W. Willinger, Eds., Self-Similar Network Traffic and Performance Evaluation. New York: Wiley, 2000.]]

[14]

{14} V. Paxson and S. Floyd, "Wide area traffic: the failure of Poisson modeling," IEEE/ACM Trans. Netw., vol. 3, no. 3, pp. 226-244, Jun. 1995.]]

[15]

{15} P. Ranjan, E. H. Abed, and R. J. La, "Nonlinear instabilities in TCP-RED," IEEE/ACM Trans. Netw., vol. 12, no. 6, pp. 1079-1092, Dec. 2004.]]

[16]

{16} S. Shakkottai and R. Srikant, "How good are deterministic fluid models of Internet congestion control?," in Proc. IEEE INFOCOM, Jun. 2002, pp. 497-505.]]

[17]

{17} P. Tinnakornsrisuphap and R. J. La, "Asymptotic behavior of heterogeneous TCP flows and RED gateways," Inst. Syst. Res., Univ. Maryland, College Park, MD, Tech. Rep., 2003.]]

[18]

{18} P. Tinnakornsrisuphap and R. J. La, "Limiting model of ECN/RED under a large number of heterogeneous TCP flows," Inst. Syst. Res., Univ. Maryland, College Park, MD, Tech. Rep., 2003.]]

[19]

{19} P. Tinnakornsrisuphap and R. J. La, "Characterization of queue fluctuations in probabilistic AQM mechanisms," ACM SIGMETRICS Perform. Eval. Rev., pp. 283-294, Jun. 2004.]]

[20]

{20} P. Tinnakornsrisuphap and A. M. Makowski, "Limit behavior of ECN/RED gateways under a large number of TCP flows," in Proc. IEEE INFOCOM, Apr. 2003, pp. 873-883.]]

[21]

{21} A. W. van der Vaart, Asymptotic Statistics. Cambridge, U.K.: Cambridge Univ. Press, 1998.]]

[22]

{22} L. Zhang, S. Shenker, and D. Clark, "Observations on the dynamics of a congestion control algorithm: the effects of two-way traffic," in Proc. ACM SIGCOMM, Sep. 1991, pp. 133-145.]]

Cited By

Pagano MSecchi R(2011)An introduction to modelling and performance evaluation for TCP networksNetwork performance engineering10.5555/1996629.1996659(571-593)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.5555/1996629.1996659
Wang XEun D(2007)Local and global stability of TCP-newReno/RED with many flowsComputer Communications10.1016/j.comcom.2006.11.00730:5(1091-1105)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1016/j.comcom.2006.11.007
La RRanjan P(2006)Technical CommuniqueAutomatica (Journal of IFAC)10.1016/j.automatica.2006.05.01842:10(1817-1820)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1016/j.automatica.2006.05.018

Index Terms

Asymptotic behavior of heterogeneous TCP flows and RED gateway

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cover image IEEE/ACM Transactions on Networking

IEEE/ACM Transactions on Networking Volume 14, Issue 1

February 2006

231 pages

ISSN:1063-6692

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IEEE Press

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Published: 01 February 2006

Published in TON Volume 14, Issue 1

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Cited By

Pagano MSecchi R(2011)An introduction to modelling and performance evaluation for TCP networksNetwork performance engineering10.5555/1996629.1996659(571-593)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.5555/1996629.1996659
Wang XEun D(2007)Local and global stability of TCP-newReno/RED with many flowsComputer Communications10.1016/j.comcom.2006.11.00730:5(1091-1105)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1016/j.comcom.2006.11.007
La RRanjan P(2006)Technical CommuniqueAutomatica (Journal of IFAC)10.1016/j.automatica.2006.05.01842:10(1817-1820)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1016/j.automatica.2006.05.018

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