Congestion in large balanced multirate links

In this paper we obtain approximations for various performance measures in a multirate link sharing bandwidth under an insensitive sharing mechanism called balanced fairness. Balanced fairness can be viewed as the large system limit of proportional fairness. For a large system, we obtain closed form expressions for the calculation of long run fraction of time that the system is congested, the probability that an arriving flow will not obtain its maximum bit rate and the average fraction of time that an arriving flow is not allocated its maximum bit rate while in the system. The techniques are based on local limit theorems for convolution measures.

[1]  Jorma T. Virtamo,et al.  A recursive formula for multirate systems with elastic traffic , 2005, IEEE Communications Letters.

[2]  Peter Whittle,et al.  Systems in stochastic equilibrium , 1986 .

[3]  Larry L. Peterson,et al.  Understanding TCP Vegas: a duality model , 2001, JACM.

[4]  Alexandre Proutière,et al.  Insensitive Bandwidth Sharing in Data Networks , 2003, Queueing Syst. Theory Appl..

[5]  T. V. Lakshman,et al.  A new method for analysing feedback-based protocols with applications to engineering Web traffic over the Internet , 1997, SIGMETRICS '97.

[6]  Catherine Rosenberg,et al.  A game theoretic framework for bandwidth allocation and pricing in broadband networks , 2000, TNET.

[7]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[8]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[9]  L. Massouli'e.  Structural properties of proportional fairness: Stability and insensitivity , 2007, 0707.4542.

[10]  J. Kaufman,et al.  Blocking in a Shared Resource Environment , 1981, IEEE Trans. Commun..

[11]  Yaakov Kogan,et al.  Dimensioning bandwidth for elastic traffic in high-speed data networks , 2000, TNET.

[12]  Laurent Massoulié,et al.  Bandwidth sharing and admission control for elastic traffic , 2000, Telecommun. Syst..

[13]  Laurent Massoulié,et al.  A queueing analysis of max-min fairness, proportional fairness and balanced fairness , 2006, Queueing Syst. Theory Appl..

[14]  R. Serfozo.  Introduction to Stochastic Networks , 1999 .

[15]  Anurag Kumar,et al.  Stochastic models for throughput analysis of randomly arriving elastic flows in the Internet , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[16]  R. Mazumdar,et al.  Blocking probabilities for large multirate erlang loss systems , 1993, Advances in Applied Probability.

[17]  François Baccelli,et al.  Elements Of Queueing Theory , 1994 .