**IMA Complex Systems Seminar**

**1:30, Thursday, March 18,
2004 **

Mean Field
Convergence of a rate model of multiple TCP connections through a buffer
implementing RED

Department of Mathematics and Statistics

585 King Edward Ave.

Ottawa, ON K1N 6N5

(Joint work with J. Reynier.) RED (Random Early Detection) have been suggested
when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the
buffer overflows by dropping or marking packets with a probability that
increases with the queue length. The
objectives are an equitable distribution of packet loss, reduced
synchronization together with reduced packet loss, delay, and delay variation.

Baccelli, McDonald and Reynier have proposed
a rate model for multiple TCP connections in the congestion avoidance regime multiplexed
through a bottleneck buffer implementing RED. The window sizes of each TCP
session evolve like independent dynamical systems coupled by the queue length
at the buffer. The key idea is to consider the histogram of window sizes as a
random measure coupled with the queue. Here we prove the conjecture made in the
earlier work that as the number of connections tends to infinity this system
converges to a deterministic mean- field limit comprising the window size
density coupled with a deterministic queue.