An extension of the square root law of TCP

Using probabilistic scaling methods, we extend the square root law of TCP to schemes which may not be of the AIMD type. Our results offer insight in the relationship between throughput and loss rate, and the time scale on which losses take place. Similar results are shown to hold in scenarios where dependencies between losses occur.

[1]  Sally Floyd,et al.  HighSpeed TCP for Large Congestion Windows , 2003, RFC.

[2]  Volker Wihstutz,et al.  BOOK REVIEW of "Markov Chains and Stochastic Stability" by S.P. Meyn and R.L. Tweedie , 1997 .

[3]  Eitan Altman,et al.  Analysis of MIMD congestion control algorithm for high speed networks , 2005, Comput. Networks.

[4]  V'ictor Rivero.  Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case , 2009 .

[5]  Teunis Ott,et al.  Transport Protocols in the TCP Paradigm and their Performance , 2005, Telecommun. Syst..

[6]  Sally Floyd,et al.  Connections with multiple congested gateways in packet-switched networks part 1: one-way traffic , 1991, CCRV.

[7]  Teunis J. Ott,et al.  Asymptotic Behavior of a Generalized TCP Congestion Avoidance Algorithm , 2007, Journal of Applied Probability.

[8]  V. Jacobson,et al.  Congestion avoidance and control , 1988, CCRV.

[9]  Eitan Altman,et al.  State-dependent M/G/1 type queueing analysis for congestion control in data networks , 2002, Comput. Networks.

[10]  Vern Paxson,et al.  End-to-end Internet packet dynamics , 1997, SIGCOMM '97.

[11]  Donald F. Towsley,et al.  Modeling TCP Reno performance: a simple model and its empirical validation , 2000, TNET.

[12]  Tom Kelly,et al.  Scalable TCP: improving performance in highspeed wide area networks , 2003, CCRV.

[13]  Eitan Altman,et al.  Performance analysis and stochastic stability of congestion control protocols , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[14]  F. Guillemin,et al.  A Markovian analysis of additive-increase multiplicative-decrease algorithms , 2002, Advances in Applied Probability.

[15]  D. Gamarnik,et al.  Validity of heavy traffic steady-state approximations in generalized Jackson networks , 2004, math/0410066.

[16]  Deepak Bansal,et al.  Binomial congestion control algorithms , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[17]  Matthew Mathis,et al.  The macroscopic behavior of the TCP congestion avoidance algorithm , 1997, CCRV.

[18]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

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

[20]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[21]  Philippe Robert,et al.  AIMD algorithms and exponential functionals , 2004 .

[22]  Richard J. Gibbens,et al.  Fixed-Point Models for the End-to-End Performance Analysis of IP Networks , 2000 .

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