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TRANSIENT BEHAVIOR OF PROCESSES IN THE TCP PARADIGM

Published online by Cambridge University Press:  27 May 2008

T. J. Ott  and
J. H. B. Kemperman
T. J. Ott
Affiliation:
WinlabRutgers UniversityNew Brunswick, NJ E-mail: ott@winlab.rutgers.edu
J. H. B. Kemperman
Affiliation:
Department of StatisticsRutgers UniversityNew Brunswick, NJ
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Abstract

This article derives the transient behavior of the stochastic process X(t) for which in earlier articles it was proven that for α<1, the process (X(t))1/(1−α) (approximately, under low drop probability or ECN marking probability) describes the behavior of the congestion windows in certain transport protocols in the so-called TCP paradigm. The transient distribution is found explicitly and is particularly transparent for moments like E[(X(t))k |X(0)]. The purpose of this article is to be part of the mathematical foundation when comparing the many protocols in the TCP paradigm.

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Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 431 - 471
Copyright
Copyright © Cambridge University Press 2008

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References

1Abramowitz, M. & Stegun, I.A. (1970). Handbook of mathematical functions Washington, DC: National Bureau of Standards.Google Scholar
2Altman, E., Avrachenkov, K. & Barakat, C. (2000). A stochastic model of TCP/IP with stationary random loss. ACM SigComm Computer Communications Review 30(4): 231–242.CrossRefGoogle Scholar
3Altman, E., Avrachenkov, K. & Barakat, C. (2002). TCP network calculus: The case of large delay-bandwidth product. In Proceeding of IEEE Infocom 2002.CrossRefGoogle Scholar
4Altman, E., Avrachenkov, K., Barakat, C., Kherani, A.A. & Prabhu, B.J. (2004). Analysis of scalable TCP. Proceedings IEEE HSNMC 2004, pp. 51–62.CrossRefGoogle Scholar
5Altman, E., Avrachenkov, K., Barakat, C. & Nunez-Queija, R. (2001). TCP modeling in the presence of nonlinear window growth. In Proceedings of ITC-17.CrossRefGoogle Scholar
6Altman, E., Avrachenkov, K., Kherani, A.A. & Prabhu, B.J. (2005). Performance analysis and stochastic stability of congestion control protocols. In Proceedings of IEEE Infocom 2005.CrossRefGoogle Scholar
7Altman, E., Avrachenkov, K. & Prabhu, B. (2005). Fairness in MIMD congestion control algorithms. In Proceedings of IEEE Infocom 2005.CrossRefGoogle Scholar
8Altman, E., Barakat, C. & Ramos, V.M. (2004). Analysis of AIMD protocols over paths with variable delay. In Proceedings IEEE Infocom 2004.CrossRefGoogle Scholar
9Altman, E., Jimenez, T. & Kofman, D. (2004). DPS queues with stationary ergodic service times and the performance of TCP in overload. In Proceedings IEEE Infocom 2004.CrossRefGoogle Scholar
10Baccelli, F., Chaintreau, F., de Vleeschauwer, D., & McDonald, D. (2004). A mean-fields analysis of short lived interacting TCP flows. New York: ACM.CrossRefGoogle Scholar
11Baccelli, F., McDonald, D. & Reynier, J. (2002). A mean-field model for multiple TCP connections through a buffer implementing RED. Performance Evaluation 49: 77–97.CrossRefGoogle Scholar
12Baras, J., Misra, A. & Ott, T.J. (1999). The window distribution of of multiple TCPs with random loss queues. In Proceedings of Globecomm 1999.Google Scholar
13Baras, J., Misra, A. & Ott, T.J. (2000). Generalized TCP congestion avoidance and its effect on bandwidth sharing and variability. In Proceedings of Globecomm 2000.Google Scholar
14Baras, J., Misra, A. & Ott, T.J. (2000). Using drop-biasing to stabilize the occupancy of random drop queues with TCP traffic. In Proceedings of ICCS 2000.Google Scholar
15Baras, J., Misra, A. & Ott, T.J. (2002). Predicting bottleneck bandwidth sharing by generalized TCP flows. Computer Networks 40(4): 557–576.Google Scholar
16Bohacek, S. (2003). A stochastic model of TCP and fair video transmission. In Proceedings Infocom 2003.CrossRefGoogle Scholar
17Budhiraja, A., Hernandez-Campos, F., Kulkarni, V.G. & Smith, F.D. (2004). Stochastic differential equation for TCP window size: Analysis and experimental validation. Probability in the Engineering and Information Sciences 18: 111–140.CrossRefGoogle Scholar
18Dumas, V., Guillemin, F. & Robert, Ph. (2002). A Markovian analysis of additive-increase, multiplicative decrease (AIMD) algorithms. Advances in Applied Probability 34(1): 85–111.CrossRefGoogle Scholar
19Floyd, S. (1994). TCP and explicit congestion notification. ACM Computer Communication Review 24(5): 10–23.CrossRefGoogle Scholar
20Floyd, S. (2006). Specifying alternate semantics for the explicit congestion notification (ECN) field. www.tools.ietf.org/html/rfc4774.CrossRefGoogle Scholar
21Gasper, G. & Rahman, M. (1990). Encyclopedia of mathematics and its applications Cambridge: Cambridge University Press.Google Scholar
22Guillemin, F, Robert, Ph & Zwart, B. (2004). AIMD algorithms and exponential functionate. Annals of Applied Probability 14(1): 90–117.CrossRefGoogle Scholar
23Kelly, C.T. (2003). Improving performance in high speed wide area networks. ACM SigComm Computer Communication Review 32(2): 83–91.CrossRefGoogle Scholar
24Kelly, C.T. (2004). Engineering flow controls in the Internet. Ph.D. thesis, Cambridge University, Cambridge.Google Scholar
25Lakshman, T.V. & Madhow, U. (1997). The performance of TCP/IP for networks with high bandwidth-delay products and random loss. Transactions on Networking 5(3): 336–350.CrossRefGoogle Scholar
26Löpker, A.H. & van Leeuwaarden, J.S.H. (2007). Transient moments of the window size in TCP. Available from www.win.tue.nl/~leeuwaa/paper14.html.Google Scholar
27Marquez, R., Altman, E. & Sole-Alvarez, S. (2004). Modeling TCP and high speed TCP: A nonlinear extension to AIMD mechanisms. Proceedings IEEE HSNMC 2004, pp. 132–143.CrossRefGoogle Scholar
28Mathis, M., Semke, J., Mahdavi, J., & Ott, T. J. (1997). The macroscopic behavior of the TCP congestion avoidance algorithm. Computer Communications Review 27(3): 67–82.CrossRefGoogle Scholar
29Misra, V., Gong, W.B. & Towsley, D. (1999). Stochastic differential equation modeling and analysis of TCP-windowsize behavior. In Proceedings of IFIP WG 7.3 Performance 1999Google Scholar
30Misra, A. & Ott, T.J. (1999). The window distribution of idealized TCP congestion avoidance with variable packet loss. In Proceedings of IEEE Infocom 1999, pp. 1564–1572.CrossRefGoogle Scholar
31Misra, A. & Ott, T.J. (2001). Effect of exponential averaging on the variability of a RED queue. In Proceedings of ICC 2001.CrossRefGoogle Scholar
32Misra, A. & Ott, T.J. (2001). Jointly coordinating ECN and TCP for rapid adaptation to varying bandwidth. In Proceedings of Milcom 2001.CrossRefGoogle Scholar
33Misra, A. & Ott, T.J. (2003). Performance sensitivity and fairness of ECN-aware “modified TCP.” Journal of Performance Evaluation 53(3): 255–272.CrossRefGoogle Scholar
34Ott, T.J. (1999). ECN protocols and the TCP paradigm. Available from www.teunisott.com/Papers.Google Scholar
35Ott, T.J. (2005). Transport protocols in the TCP paradigm and their performance. Telecommunication Systems 30(4): 351–385.CrossRefGoogle Scholar
36Ott, T.J. (2006). Rate of convergence for the “square root formula” in the Internet transmission control protocol. Advances in Applied Probability 38(4): 1132–1154.Google Scholar
37Ott, T.J. (1999). On the Ornstein–Uhlenbeck process with delayed feedback. web.njit.edu/ott/Papers/DelOu.ps.Google Scholar
38Ott, T.J., Kemperman, J.H.B. & Mathis, M. (1996). The stationary behavior of idealized TCP congestion behavior. Available from www.teunisott.com/PapersGoogle Scholar
39Ott, T.J. & Swanson, J. (2006). Stationarity of some processes in Transport Protocols. In IFIP WG 7.3 MAMA Workshop.CrossRefGoogle Scholar
40Ott, T.J. & Swanson, J. (2007). Asymptotic behavior of a generalized TCP congestion avoidance algorithm. Journal of Applited probability 44: 618–635.CrossRefGoogle Scholar
41Padhye, J., Firoiu, V., Towsley, D. & Kurose, J. (1998). Modeling TCP throughput: A simple model and its empirical validation. In Proceedings ACM SigComm 1998.CrossRefGoogle Scholar
42Padhye, J., Firoiu, V., Towsley, D. & Kurose, J. (2000). Modeling of TCP RENO performance: A simple model and its empirical validation. IEEE/ACM Transactions on Networking 8(2): 133–445.CrossRefGoogle Scholar
43Ramakrishnan, K., Floyd, S. & Black, D. (2001). The addition of Explicit Congestion Notification (ECN) to IP. IETF RFC 3168, Sept. 2001.Google Scholar