A square root formula for the rate of non-persistent TCP flows

In this paper, we derive a closed form formula for the average rate attained by a non persistent TCP source which alternates between idle periods and download periods subject to a fixed packet loss probability. We also derive closed form expressions for the mean time to transfer a file and for the distribution of the transmission rate. Several distributions for the file sizes and idle times are considered including heavy tailed distributions. The formula for mean transmission rate is shown to boil down to the classical square root mean value formula for persistent flows when the average file size tends to infinity. The formulae are applied to predict bandwidth sharing among competing flows subject to active queue management.

[1]  Alexandre Proutière,et al.  Statistical bandwidth sharing: a study of congestion at flow level , 2001, SIGCOMM.

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

[3]  T. V. Lakshman,et al.  A new method for analyzing feedback-based protocols with applications to engineering Web traffic over the Internet , 2003, Comput. Commun..

[4]  Matthew Mathis,et al.  The stationary behavior of ideal TCP congestion avoidance , 1996 .

[5]  Thomas L. Saaty,et al.  Elements of queueing theory , 1961 .

[6]  Anurag Kumar,et al.  Performance Analysis of TCP with Nonpersistent Sessions , 2007 .

[7]  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.

[8]  James Aweya,et al.  DRED: a random early detection algorithm for TCP/IP networks , 2002, Int. J. Commun. Syst..

[9]  François Baccelli,et al.  A mean-field analysis of short lived interacting TCP flows , 2004, SIGMETRICS '04/Performance '04.

[10]  QUTdN QeO,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

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

[12]  Philippe Jacquet,et al.  Performance Evaluation of a Single Queue under Multi-User TCP/IP Connections , 2001 .

[13]  Van Jacobson,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

[14]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[15]  Thomas Bonald,et al.  Statistical bandwidth sharing: a study of congestion at flow level , 2001, SIGCOMM.

[16]  Zhen Liu,et al.  A bandwidth sharing theory for a large number of HTTP-like connections , 2002, IEEE/ACM Transactions on Networking.

[17]  François Baccelli,et al.  A mean-field model for multiple TCP connections through a buffer implementing RED , 2002, Perform. Evaluation.

[18]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .