Controllable Markov Jump Processes. II. Monitoring and Optimization of TCP Connections

  • A. V. BorisovEmail author
  • G. B. Miller
  • A. I. Stefanovich


The article considers the practical application of the analysis and estimation of the controlled Markov jump process states by continuous, discrete, and counting observations in the development of state monitoring algorithms for network connections operating under the Transmission Control Protocol (TCP). A specific feature of the applied problem is the physical heterogeneity of the channel providing the TCP connection under study: along with the wired section, there is a wireless “last mile” of the channel. The current state of the entire connection cannot be directly observed, and there is just indirect statistical information in the form of a flow of acknowledgements of successful packet transmission, as well as packet loss counting processes and timeouts. In this part of the work, not only the controlled stochastic dynamic observation system was used for the mathematical description of the TCP New Reno connection but also the developed high-precision algorithm for tracking this connection state according to the available statistical information. The numerical examples make it possible to define causes of channel losses, such as congestion in the wired section or signal attenuation in the wireless section, and as a result modify the TCP algorithm so as to significantly increase the bandwidth.



This work was supported by the Russian Foundation for Basic Research (grant no. 16-07-00677).


  1. 1.
    D. Kurose and K. Ross, Computer Networking: A Top-Down Approach, 7th ed. (Pearson, Upper Saddle River, NJ, 2016).Google Scholar
  2. 2.
    E. Altman, K. Avrachenkov, and C. Barakat, “TCP in presence of bursty losses,” Perform. Evaluat. 42, 129–147 (2000).CrossRefzbMATHGoogle Scholar
  3. 3.
    E. Yariv and N. Merhav, “Hidden Markov processes,” IEEE Trans. Inform. Theory 48, 1518–1569 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    A. V. Borisov and G. B. Miller, “Analysis and filtration of special discrete-time Markov processes. II. Optimal filtration,” Autom. Remote Control 66, 1125 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    A. V. Borisov, A. V. Bosov, and G. B. Miller, “Modeling and monitoring of VoIP connection,” Inform. Primen. 10 (2), 2–13 (2016).Google Scholar
  6. 6.
    G. Haßlinger and O. Hohlfeld, “The Gilbert-Elliott model for packet loss in real time services on the internet,” in Proceedings of the 14th GI/ITG Conference on Measurement, Modelling and Evaluation of Computer and Communication Systems MMB, Dortmund, Germany, 2008, pp. 269–283.Google Scholar
  7. 7.
    L. Kleinrock, Queueing Systems II: Computer Applications (Wiley Interscience, New York, 1976).zbMATHGoogle Scholar
  8. 8.
    D. P. Bertsekas and R. G. Gallager, Data Networks (Prentice-Hall, New Jersey, 1992).zbMATHGoogle Scholar
  9. 9.
    G. P. Basharin, Lectures on Mathematical Theory of Teletraffic (Ross. Univ. Druzhby Narodov, Moscow, 2004) [in Russian].Google Scholar
  10. 10.
    V. Misra, W. Gong, and D. F. Towsley, “Fluid-based analysis of network of AQM routers supporting TCP flows with an application to RED,” ACM SIGCOMM Comput. Commun. Rev. 30, 151–160 (2000).CrossRefGoogle Scholar
  11. 11.
    W. Whitt, Stochastic-Process Limits, An Introduction to Stochastic-Process Limits and their Application to Queues (Springer, New York, 2002).zbMATHGoogle Scholar
  12. 12.
    J. Domanska, A. Domanski, T. Czachorski, and J. Klamka, “Fluid flow approximation of time-limited TCP/UDP/XCP streams,” Bull. Polish Acad. Sci.: Tech. Sci. 62, 217–225 (2014).Google Scholar
  13. 13.
    H. Kushner, Heavy Traffic Analysis of Controlled Queueing and Communication Networks (Springer, New York, 2001).CrossRefzbMATHGoogle Scholar
  14. 14.
    W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, “On the self-similar nature of ethernet traffic,” IEEE/ACM Trans. Networking 2, 1–15 (1994).CrossRefGoogle Scholar
  15. 15.
    M. E. Crovella and A. Bestavros, “Self-similarity in world wide web traffic: evidence and possible causes,” IEEE/ACM Trans. Networking 5, 835–846 (1997).CrossRefGoogle Scholar
  16. 16.
    B. Tsybakov and N. Georganas, “Overflow and losses in a network queue with a selfsimilar input,” Queueing Syst. 35, 201–235 (2000).CrossRefzbMATHGoogle Scholar
  17. 17.
    T. Mikosch, S. Resnick, H. Rootzen, and A. Stegeman, “Is network traffic appriximated by stable Levy motion or fractional Brownian motion?,” Ann. Appl. Probab. 12, 23–68 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    E. Altman, T. Boulogne, R. El Azouzi, T. Jimenez, and L. Wynter, “A survey on networking games,” Comput. Operat. Res. 33, 286–311 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    K. J. R. Liu and B. Wang, Cognitive Radio Networking and Security: A Game-Theoretic View (Cambridge Univ. Press, Cambridge, 2010).CrossRefzbMATHGoogle Scholar
  20. 20.
    O. Habachi, R. El-Azouzi, and Y. A. Hayel, “Stackelberg model for opportunistic sensing in cognitive radio networks,” IEEE Trans. Wireless Commun. 12, 2148–2159 (2013).CrossRefGoogle Scholar
  21. 21.
    S. Liu, T. Basar, and R. Srikant, “TCP-Illinois: a loss and delay-based congestion control algorithm for high-speed networks,” Perform Evaluat. 65, 417–440 (2008).CrossRefGoogle Scholar
  22. 22.
    S. Mascolo and G. Racanelli, “Testing TCP westwood+ over transatlantic links at 10 gigabit/second rate,” in Proceedings of the 3rd International Workshop on Protocols for Fast Long-Distance Networks FLDNET05, Lyon, France, 2005.Google Scholar
  23. 23.
    C. Caini and R. Firrincieli, “TCP hybla: a TCP enhancement for heterogeneous networks,” Int. J. Satellite Commun. Networking 22, 547–566 (2004).CrossRefGoogle Scholar
  24. 24.
    S. Ha, I. Rhee, and L. Xu, “CUBIC: a new TCP-friendly high-speed TCP variant,” ACM SIGOPS Operat. Syst. Rev. 42 (5), 64–74 (2008).CrossRefGoogle Scholar
  25. 25.
    N. Cardwell, Y. Cheng, C. S. Gunn, S. H. Yeganeh, and V. Jacobson, “BBR: congestion-based congestion control,” ACM Queue 14 (5), 20–53 (2016).CrossRefGoogle Scholar
  26. 26.
    A. V. Borisov, G. B. Miller, and A. I. Stefanovich, “Controllable Markov jump processes. I. Optimum filtering based on complex observations,” J. Comput. Syst. Sci. Int. 57 (6) (2018, in press).Google Scholar
  27. 27.
    S. Floyd and V. Jacobson, “Random early detection gateways for congestion avoidance,” IEEE/ACM Trans. Networking 1, 397–413 (1993).CrossRefGoogle Scholar
  28. 28.
    B. M. Miller, K. E. Avrachenkov, K. V. Stepanyan, and G. B. Miller, “The problem of optimal stochastic data flow control based upon incomplete information,” Probl. Inform. Transmiss. 41, 150 (2005).CrossRefzbMATHGoogle Scholar
  29. 29.
    E. B. Dynkin, Markov Processes (Fizmatgiz, Moscow, 1959; Springer, Berlin, Heidelberg, 1965).Google Scholar
  30. 30.
    J. C. Cox and V. Smith, Recovery Theory (Sov. Radio, Moscow, 1967) [in Russian].Google Scholar
  31. 31.
    A. A. Borovkov, Asymptotic Methods in Queueing Theory, Probability and Mathematical Statistics (Fizmatlit, Moscow, 1980; Wiley, New York, 1984).Google Scholar
  32. 32. Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • A. V. Borisov
    • 1
    Email author
  • G. B. Miller
    • 1
  • A. I. Stefanovich
    • 1
  1. 1.Institute of Informatics Problems, Russian Academy of SciencesMoscowRussia

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