An Information Theoretic Approach for Systems with Parallel Distributions: Case Studying Internet Traffic

  • Charalabos Skianis
  • Lambros Sarakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3976)


The principle of Minimum Relative Entropy (MRE) is applied to characterize a ‘proportionality’ relationship between the state probabilities of infinite and finite capacity queues at equilibrium and thus, establish an information theoretic interpretation for the exact global balance solution of some finite capacity queues with or without correlated arrival processes. This result serves to establish the utility of the MRE inference technique and encourage its applicability to the analysis of more complex, and thus more realistic, queuing systems. The principles of Maximum Entropy (ME) and MRE are then employed, as least-biased methods of inference, towards the analysis of a Internet link carrying realistic TCP traffic, that exhibit this ‘proportionality’ relationship between a finite and infinite buffer system, as produced by a large number of connections. The analytic approximations are validated against exhaustive simulation experiments. Despite its simplicity, the methodology captures the behavior of the system under study both in the cases of finite and infinite buffers and finally and can easily be utilized for network management and design, capacity planning, and congestion control.


Congestion Control Bottleneck Link Queue Length Distribution Finite Buffer Information Theoretic Approach 
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.
    Crovella, M.E., Bestavros, A.: Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE/ACM Transactions on Networking 5(6), 835–846 (1997)CrossRefGoogle Scholar
  2. 2.
    Grossglauser, M., Bolot, J.: On the Relevance of Long Range Dependence in Network Traffic. IEEE/ACM Transactions on Networking 7(5), 629–640 (1999)CrossRefGoogle Scholar
  3. 3.
    Feldman, A., Gilbert, A., Huang, P., Willinger, W.: Data networks as cascades: Explaining the multifractal nature of Internet Wan tra.c. In: ACM SIGCOMM 1998, Vancouver, Canada, pp. 42–55 (1998)Google Scholar
  4. 4.
    Willinger, W., Paxson, V.: Where Mathematics meets the Internet. Notices of the American Mathematical Society 45(8), 961–970 (1998)MathSciNetMATHGoogle Scholar
  5. 5.
    Erramilli, A., Narayan, O., Willinger, W.: Experimental queuing analysis with long-range dependent packet traffic. IEEE/ACM Transactions on Networking 4(2), 209–223 (1996)CrossRefGoogle Scholar
  6. 6.
    Erramilli, A., Narayan, O., Neidhardt, A.: Performance Impacts of Multi-Scaling in Wide Area TCP/IP Traffic. In: IEEE INFOCOM 2000, Tel Aviv, Israel (2000)Google Scholar
  7. 7.
    Ribeiro, V., Riedi, R., Crouse, M., Baraniuk, R.: Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic. In: IEEE INFOCOM 2000, Tel Aviv, Israel (2000)Google Scholar
  8. 8.
    Vanichpun, S., Makowski, A.: Positive correlations and buffer occupancy: Lower bound via supermodular ordering. In: IEEE INFOCOM 2002, New York, NY (2002)Google Scholar
  9. 9.
    Cardwell, N., Savage, S., Anderson, T.: Modeling TCP Latency. In: IEEE INFOCOM 2000, Tel Aviv, Israel (2000)Google Scholar
  10. 10.
    Fredj, S.B., Bonald, T., Proutiere, A., Regnie, G., Roberts, J.: Statistical Bandwidth Sharing: A Study of Congestion at Flow Level. In: ACM SIGCOMM 2001, San Diego, USA, pp. 111–122 (2001)Google Scholar
  11. 11.
    Barakat, C., Thiran, P., Iannaccone, G., Diot, C., Owezarski, P.: A flow-based model for Internet backbone traffic. In: ACM Internet Measurement Workshop, Marseille, France (2002)Google Scholar
  12. 12.
    Garetto, M., Towsley, D.: Modeling, Simulation and Measurements of Queuing Delay under Long-tail Internet Traffic. In: SIGMETRICS 2003, San Diego, USA, pp. 47–57 (2003)Google Scholar
  13. 13.
    Appenzeller, G., Keslassy, I., McKeown, N.: Sizing router buffers. In: ACM SIGCOMM 2004, USA, pp. 281–292 (August/September 2004)Google Scholar
  14. 14.
    Benes, V.E.: Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York (1965)MATHGoogle Scholar
  15. 15.
    Ferdinand, A.E.: A Statistical Mechanical Approach to Systems Analysis. IBM Journal of Research and Development 14, 539–547 (1970)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Pinsky, E., Yemini, Y.: A Statistical Mechanics of Some Interconnection Networks. In: Performance 1984, pp. 147–158. North-Holland, Amsterdam (1984)Google Scholar
  17. 17.
    Jaynes, E.T.: Information Theory and Statistical Mechanics I. Physical Review 106, 620–630 (1957)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Jaynes, E.T.: Information Theory and Statistical Mechanics II. Physical Review 108, 171–190 (1957)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Shore, J.E., Johnson, R.W.: Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum-Cross Entropy. IEEE Trans. on Information Theory IT-26, 26–37 (1980)Google Scholar
  20. 20.
    Shore, J.E., Johnson, R.W.: Properties of Cross Entropy Minimisation. IEEE Trans. on Information Theory IT-27, 472–482 (1981)Google Scholar
  21. 21.
    Kouvatsos, D.D.: Maximum Entropy and the G/G/1/N Queue. Acta Informatica 23, 545–565 (1986)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Kouvatsos, D.D.: A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium. Journal of Oper. Research Society 39, 183–200 (1988)CrossRefMATHGoogle Scholar
  23. 23.
    Skianis, C., Kouvatsos, D.D.: Arbitrary Open Queueing Networks with Server Vacation Periods and Blocking. Special Issue on Queueing Networks and Blocking, Annals of Operations Research 79, 143–180 (1998)MathSciNetMATHGoogle Scholar
  24. 24.
    McCanne, S., Floyd, S.: Ns-2 network simulator,

Copyright information

© IFIP International Federation for Information Processing 2006

Authors and Affiliations

  • Charalabos Skianis
    • 1
    • 2
  • Lambros Sarakis
    • 2
  1. 1.Department of Information and Communication Systems EngineeringUniversity of the AegeanKarlovassiGreece
  2. 2.Institute of Informatics & TelecommunicationsNational Centre for Scientific Research Demokritos’AthensGreece

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