Discrete Event Dynamic Systems

, Volume 17, Issue 3, pp 405–421 | Cite as

Insensitive Traffic Models for Communication Networks



We present a survey of traffic models for communication networks whose key performance indicators like blocking probability and mean delay are independent of all traffic characteristics beyond the traffic intensity. This insensitivity property, which follows from that of the underlying queuing networks, is key to the derivation of simple and robust engineering rules like the Erlang formula in telephone networks.


Traffic modeling Communication networks Bandwidth sharing Insensitivity Kelly–Whittle queuing networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ben Fredj S, Bonald T, Proutière A, Régnié G, Roberts JW (2001) Statistical bandwidth sharing: a study of congestion at flow level. In: Proceedings of ACM SIGCOMM, San Diego, 27–31 August 2001Google Scholar
  2. Berger AW, Kogan Y (2000) Dimensioning bandwidth for elastic traffic in high-speed data networks. IEEE/ACM Trans Netw 8-5:643–654CrossRefGoogle Scholar
  3. Bertsekas D, Gallager R (1987) Data networks. Prentice Hall, Englewood CliffsGoogle Scholar
  4. Bonald T (2006a) The Erlang model with non-Poisson call arrivals. In: Proceedings of ACM SIGMETRICS / IFIP performance, Saint-Malo, 26–30 June 2006Google Scholar
  5. Bonald T (2006b) Throughput performance in networks with linear capacity constraints. In: Proceedings of CISS, Princeton University, Princeton, 22–24 March 2006Google Scholar
  6. Bonald T, Massoulié L, Proutière A, Virtamo J (2006) A queueing analysis of max-min fairness, proportional fairness and balanced fairness. Queueing Syst 53:65–84MATHCrossRefGoogle Scholar
  7. Bonald T, Proutière A (2002) Insensitivity in processor-sharing networks. Perform Eval 49:193–209MATHCrossRefGoogle Scholar
  8. Bonald T, Virtamo J (2005) A recursive formula for multi-rate systems with elastic traffic. IEEE Commun Lett 9:753–755CrossRefGoogle Scholar
  9. Cohen JW (1957) The generalized Engset formula. Phillips Telecommun Rev 18:158–170Google Scholar
  10. Delbrouck LEN (1983) On the steady state distribution in a service facility with different peakedness factors and capacity requirements. IEEE Trans Commun 11:1209–1211CrossRefGoogle Scholar
  11. Dziong Z, Roberts JW (1987) Congestion probabilities in a circuit-switched integrated services network. Perform Eval 7-4:267–284CrossRefGoogle Scholar
  12. Engset TO (1998) On the calculation of switches in an automatic telephone system. In: Myskja A, Espvik O (eds) Tore Olaus Engset: the man behind the formula. Tapir Academic Press, Trondheim (first appeared as an unpublished report in Norwegian)Google Scholar
  13. Enomoto O, Miyamoto H (1973) An analysis of mixtures of multiple bandwidth traffic on time division switching networks. In: Proceedings of the 7th International Teletraffic Congress, Stockholm, 1973Google Scholar
  14. Erlang AK (1948) Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. In: Brockmeyer E, Halstrom HL, Jensen A (eds) The life and works of A.K. Erlang. The Copenhagen Telephone Company, Copenhagen (first published in Danish)Google Scholar
  15. Gimpelson LA (1965) Analysis of mixtures of wide and narrow-band traffic. IEEE Trans Commun Technol 13-3:258–266CrossRefGoogle Scholar
  16. Heyman DP, Lakshman TV, Neidhardt AL (1997) A new method for analysing feedback-based protocols with applications to engineering Web traffic over the Internet. In: Proceedings of ACM SIGMETRICS, Seattle, 15–18 June 1997Google Scholar
  17. Hordijk A, van Dijk N (1982) Adjoint processes, job local balance and insensitivity of stochastic networks. In: Bulletin of the 44th session of the international statistical institute, vol 50. International Statistical Institute, Voorburg, pp 776–788Google Scholar
  18. Kaufman JS (1981) Blocking in a shared resource environment. IEEE Trans Commun 29:1474–1481CrossRefGoogle Scholar
  19. Kelly FP (1979) Reversibility and stochastic networks. Wiley, New YorkMATHGoogle Scholar
  20. Kelly FP (1991) Loss networks. Ann Appl Probab 1:319–378MATHGoogle Scholar
  21. Kelly FP, Maulloo A, Tan D (1998) Rate control for communication networks: shadow prices, proportional fairness and stability. J Oper Res Soc 49:237–252MATHCrossRefGoogle Scholar
  22. Massoulié L (2007) Structural properties of proportional fairness: stability and insensitivity. Ann Appl Probab 17-3:809–839CrossRefGoogle Scholar
  23. Massoulié L, Roberts JW (2000) Bandwidth sharing and admission control for elastic traffic. Telecommun Syst 15:185–201.MATHCrossRefGoogle Scholar
  24. Roberts JW (1981) A service system with heterogeneous user requirement. In: Pujolle G (ed) Performance of data communications systems and their applications. North-Holland, Amsterdam, pp 423–431Google Scholar
  25. Serfozo RF (1999) Introduction to stochastic networks. Springer, Berlin Heidelberg New YorkMATHGoogle Scholar
  26. Sevastyanov BA (1957) An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theory Probab Appl 2:104–112CrossRefGoogle Scholar
  27. Stevens WR (1994) TCP/IP illustrated, vol 1: the protocols. Addison-Wesley, ReadingMATHGoogle Scholar
  28. van Dijk NM (1988) On Jackson’s product form with “jump-over” blocking. Oper Res Lett 7:233–235MATHCrossRefGoogle Scholar
  29. Whitt W (1985) Blocking when service is required from several facilities simultaneously. AT&T Technol 64-8:1807–1856Google Scholar
  30. Whittle P (1985) Partial balance and insensitivity. J Appl Probab 22:168–176MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Orange LabsParisFrance

Personalised recommendations