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



David McDonald

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.