Journal of Mathematical Sciences

, Volume 92, Issue 3, pp 3930–3939 | Cite as

Stability and performance analysis of rate-based feedback flow controlled ATM networks

  • V. Sharma
  • J. Kuri
Article
  • 11 Downloads

Abstract

Motivated by the ABR class of service in ATM networks, we study a continuous-time queueing system with a feedback control of the arrival rate of some of the sources. The feedback regarding the queue length or the total workload is provided at regular intervals (variations on it, especially the EPRCA algorithm, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single bottleneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing the continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow, and lower delay jitter than any open-loop policy.

Keywords

Service Time Stationary Distribution Queue Length Propagation Delay Sojourn Time 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Asmussen,Applied Probability and Queues, Wiley, New York (1987).Google Scholar
  2. 2.
    E. Altman and T. Basar,Optimal Rate Control for High-Speed Telecommunication Networks, Preprint (1995).Google Scholar
  3. 3.
    E. Altman, F. Baccelli, and J.-C. Bolot,Discrete Time Analysis of Adaptive Rate Control Mechanisms, Preprint (1995).Google Scholar
  4. 4.
    B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tammer,Nonlinear Parametric Optimization, Birkhauser Verlag, Basel (1983).Google Scholar
  5. 5.
    P. Billingsley,Convergence of Probability Measures, Wiley, New York (1968).Google Scholar
  6. 6.
    F. Bonomi and K. W. Fendick, “The rate based flow control framework for the available bit rate ATM service”, in:IEEE Network, March/April (1995), pp. 25–39.Google Scholar
  7. 7.
    F. Bonomi, D. Mitra, and J. B. Seery, “Adaptive algorithms for feedback-based flow control in high speed wide-area ATM networks”,IEEE JSAC,13, 1267–1282 (1995).Google Scholar
  8. 8.
    A. A. Borovkov,Stochastic Processes in Queueing Theory, Springer, New York (1976).Google Scholar
  9. 9.
    A. Brandt, P. Franken, and B. Lisek,Stochastic Stationary Models, Wiley, New York (1990).Google Scholar
  10. 10.
    D. M. Chiu and R. Jain, “Analysis of the increase and decrease algorithms for congestion avoidance in computer networks,” in:Computer Networks and ISDN Systems, Vol. 17 (1989), pp. 1–84.Google Scholar
  11. 11.
    B. W. Conolly and C. Langaris, “On a new formula for the transient state probabilities forM|M| 1 queues and computational implications”,J. Appl. Probab.,30, 237–246 (1993).MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    S. N. Ethier and T. G. Kurtz,Markov Processes, Characterization and Convergence, Wiley, New York (1986).Google Scholar
  13. 13.
    K. W. Fendick, M. A. Rodrigues, and A. Weiss, “Analysis of a rate based feedback control strategy for long haul data transport”,Performance Evaluation,16, 67–84 (1992).MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    K. W. Fendick and M. A. Rodrigues, “Asymptotic analysis of adaptive rate control for diverse sources with delayed feedback”,IEEE Trans. Inf. Theor.,40, 2008–2025 (1994).MATHCrossRefGoogle Scholar
  15. 15.
    V. V. Kalashnikov,Mathematical Methods in Queueing Theory, Kluwer, Dordrecht (1994).Google Scholar
  16. 16.
    K. Kawahara, Y. Oie, and H. Miyahara, “Performance analysis of reactive congestion control for ATM networks”,IEEE JSAC,13, 651–660 (1995).Google Scholar
  17. 17.
    S. Keshav, “A control theoretic approach to flow control,” in:Proceedings ACM, SIGCOMM'91 (1991), pp. 3–15.Google Scholar
  18. 18.
    A. Mukherjee and J. C. Strikwerda, “Analysis of dynamic congestion control protocols. A Fokker-Planck approximation,” in:Proceedings ACM, SIGCOMM'91 (1991), pp. 159–169.Google Scholar
  19. 19.
    R. S. Pazhyannur and R. Agrawal, “Feedback based flow control of B-ISDN/ATM networks”,IEEE JSAC,13, 1252–1266 (1995).Google Scholar
  20. 20.
    W. A. Rosenkrantz, “Some martingales associated with queueing and storage processes”,Z. Wahrscheinlichkeits-theor. verw. Geb.,58, 205–222 (1981).MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    K.-Y. Siu and H.-Y. Tzeng, “Intelligent congestion control for ABR service in ATM networks,” in:Proceedings ACM, SIGCOMM'95 (1995), pp. 81–106.Google Scholar
  22. 22.
    O. P. Sharma,Markovian Queues, Harwood, New York (1990).Google Scholar
  23. 23.
    V. Sharma, “Reliable estimation via simulation”,Queueing Systems,19, 169–192 (1995).MATHCrossRefGoogle Scholar
  24. 24.
    V. Sharma and R. Mazumdar, “Stability and performance of some window and credit based flow controlled in the presence of background traffic” (submitted).Google Scholar
  25. 25.
    S. Shenker, “A theoretical analysis of feedback flow control”, in:Proceedings ACM, SIGCOMM'90 (1990), pp. 156–165.Google Scholar
  26. 26.
    V. Sumita, “On conditional passage time of birth-death processes”,J. Appl. Probab.,21, 10–21 (1984).MATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Y. T. Wang and B. Sengupta, “Performance analysis of a feedback congestion control policy”, in:Proceedings ACM, SIGCOMM'91 (1991), pp. 149–157.Google Scholar
  28. 28.
    N. Yin and M. G. Hluchyj, “On closed-loop rate control for ATM cell relay networks”, in:INFOCOM'94 (1994). pp. 99–108.Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. Sharma
    • 1
  • J. Kuri
    • 2
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Department de Génie Electrique et de Genie InformatiqueEcole PolytechniqueMontrealCanada

Personalised recommendations