original paper on the Square Root Law for TCP. It then continues with more general

papers on protocols in the TCP Paradigm.

"Papers in the TCP Paradigm" is a sequence of papers attempting to construct a class of

Transport Protocols that are (much) better than TCP in efficiently using scarce network

resources, do a better job in quickly adapting to changing circumstances, do not

over-react to minor loss, yet keep the overall network stable, etc.

The papers below (in chronological order) give most of the mathematical background. I am

currently working on more protocol-specific issues. I estimate I will have to write about 4

more papers to complete the sequence.

The stationary behavior of ideal TCP Congestion Avoidance. (PDF)

August 1996. With J.H.B Kemperman and Matt Mathis.

This is often refered to as the "Square Root paper".

This material was presented at "Performance 96" in Lausanne, Oct 1996.

This paper was submitted to*ToN*and jeered out of the ballpark.

I was so angry about the weird referee reports that I did not re-submit.

Unpublished, but widely cited.The Macroscopic Behavior of the TCP Congestion Avoidance Algorithm. (PDF)

With Matt Matthis, Jeff Semke, and Jamshid Mahdavi.

*CCR 27(3)*July 1997 pp 67 - 82

This paper received the SigComm 2008 "Test of Time" award.ECN Protocols and the TCP Paradigm. (PDF)

This is the 1999 version of the next paper:Transport Protocols in the TCP Paradigm and their Performance. (PDF)

*Telecommunication Systems, 30:4,*pp 351-385, Springer 2005.Rate of convergence for the "Square Root Formula". (PDF)

*Adv. Appl. Prob. 38:4*pp 1132 - 1154 (Dec 2006).Rate of convergence for the "Square Root Formula", extended version. (PDF)

Extended version of the paper aboveStationarity and existence of moments for some processes in Transport Protocols. (PDF)

with Jason Swanson. Part of this material was presented at the MAMA

workshop, St Malo, France, June 2006. A shortened version appeared

in ACM Sigmetrics Performance Evaluation Review, Dec 2006.

This version contains more than the PER version.Asymptotic Behavior of a Generalized TCP Congestion Avoidance Algorithm. (PDF)

With Jason Swanson.

*J. Appl. Prob. 44,*pp 618-635, Sept 2007.

This paper proves the conjectures formulated in the "TCP Paradigm" papers above.The Transient Behavior of processes in the TCP Paradigm. (PDF)

With J.H.B.Kemperman.

*Probability in the Engineering and Informational Sciences 22(3)*pp 431 - 471 (July 2008)

- Ornstein-Uhlenbeck with Delayed Feedback , DRAFT, postscript
- Ornstein-Uhlenbeck with Delayed Feedback
, DRAFT, PDF

The purpose of this paper is to predict what values of the parameters in protocols

in the "TCP Paradigm" lead to instabilities in the Internet. I am looking for an

expert in classical control theory to be co-author of this paper.