The Burstiness Behavior of Regulated Flows in Networks

  • Yu Ying
  • Ravi Mazumdar
  • Catherine Rosenberg
  • Fabrice Guillemin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3462)


In this paper we study the impact of statistical multiplexing on leaky-bucket regulated traffic streams as they pass through the network. In particular we show that the burstiness of a flow is randomized as it transits through the nodes with mean equal to its initial burstiness value at the ingress. We then show that the random burstiness for a single flow converges to a constant equal to the initial value at the ingress when the flow is multiplexed with a large number of sources. The results do not depend on independence or homogeniety between flows. We conclude by providing some simulation results that confirm the theory.


Sample Path Peak Rate Input Stream Burst Size Stable Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Anick, D., Mitra, D., Sondhi, M.: Stochastic theory of a data handling system with multiple sources. Bell System Technical Journal 61(8), 1871–1894 (1982)MathSciNetGoogle Scholar
  2. 2.
    Leland, W., Taqqu, M., Willinger, W., Wilson, D.: On the Self-Similar Nature of Ethernet Traffic. IEEE/ACM Trans. on Networking 2(1), 1–15 (1994)CrossRefGoogle Scholar
  3. 3.
    Roberts, J.W.: Traffic Theory and the Internet. IEEE Communications Magazine, 94–99 (January 2001)Google Scholar
  4. 4.
    Cruz, R.: A calculus for network delay, Part I: Network elements in isolation. IEEE Trans. Inform. Theory 37(1), 114–131 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cruz, R.: A calculus for network delay, Part II: Network analysis. IEEE Trans. Inform. Theory 37(1), 132–141 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Le Boudec, J.-Y., Thiran, P.: Network calculus. In: Thiran, P., Le Boudec, J.-Y. (eds.) Network Calculus. LNCS, vol. 2050, p. 3. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Chang, C.S.: Performance Guarantees in communication networks. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  8. 8.
    Firoiu, V., Le Boudec, J.-Y., Towsley, D., Zhang, Z.-L.: Theories and models for Internet quality of service. Proceedings of the IEEE 90(9), 1565–1591 (2002)CrossRefGoogle Scholar
  9. 9.
    Cholvi, V., Echague, J., Leboudec, J.-Y.: Worst case burstiness increase due to FIFO multiplexing. In: Proceedings of Performance 2002, Rome, Italy (September 2002)Google Scholar
  10. 10.
    Massoulie, L., Busson, A.: Stochastic majorization of aggregates of leaky bucket constrained traffic streams (2001) (Preprint)Google Scholar
  11. 11.
    Guillemin, F., Likhanov, N., Mazumdar, R., Rosenberg, C.: Extremal traffic and bounds on the mean delay of multiplexed regulated traffic streams. In: Proc. of INFOCOM 2002, N.Y., June 2002, pp. 985–993 (2002)Google Scholar
  12. 12.
    Guillemin, F., Likhanov, N., Mazumdar, R., Rosenberg, C., Ying, Y.: Buffer overflow bounds for multiplexed regulated traffic streams. In: Proc. ITC 18. Elsevier Science, Berlin (2003)Google Scholar
  13. 13.
    Vojnovic, M., Le Boudec, J.-Y.: Stochastic analysis of some expedited forwarding networks. In: Proc. of IEEE INFOCOM 2002, New York, NY (June 2002)Google Scholar
  14. 14.
    Yaron, O., Sidi, M.: Performance and stability of communication networks via robust exponential bounds. IEEE/ACM Trans. Networking 1(3), 372–385 (1993)CrossRefGoogle Scholar
  15. 15.
    Starobinski, D., Sidi, M.: Stochastically bounded burstiness for communication networks. IEEE Tran. Information Theory 46(1), 206–212 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Wischik, D.: The output of a switch, or, effective bandwidths for networks. Queueing Systems 32, 383–396 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Eun, D., Shroff, N.B.: Simplification of Network Analysis in Large-Bandwidth Systems. In: Proc. of IEEE INFOCOM 2003, San Francisco, CA (March 2003)Google Scholar
  18. 18.
    Abendroth, D., Killat, U.: Intelligent Shaping: Well shaped throughout the entire network. In: Proc. of INFOCOM 2002, N.Y. (June 2002)Google Scholar
  19. 19.
    Lau, W.-c., Li, S.-q.: Traffic distortion and inter-source cross-correlation in highspeed integrated networks. Computer Networks and ISDN Systems 29, 811–830 (1997)CrossRefGoogle Scholar
  20. 20.
    Konstantopoulos, T., Last, G.: On the dynamics and performance of stochastic fluid systems. Journal of Applied Probability 37, 652–667 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Ying, Y., Mazumdar, R., Rosenberg, C., Guillemin, F.: Analysis of the burstiness of multiplexed regulated traffic flows in networks. Technical Report, Purdue UniversityGoogle Scholar
  22. 22.
    Baccelli, F., Bremaud, P.: Elements of Queueing Theory. Springer, Heidelberg (2003)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yu Ying
    • 1
  • Ravi Mazumdar
    • 2
  • Catherine Rosenberg
    • 2
  • Fabrice Guillemin
    • 3
  1. 1.Dept. of ECEPurdue UniversityWest LafayetteU.S.A
  2. 2.Dept. of ECEUniversity of WaterlooWaterlooCanada
  3. 3.France Telecom R&D DAC/CPNLannionFrance

Personalised recommendations