Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-07T18:47:29.708Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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