Detection) have been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows and packets are lost. When the queue length reaches a certain threshold RED schemes drop/mark incoming packets with a probability that increases as the queue size increases. The objectives are an equitable distribution of packet loss, reduced delay and delay variation and improved network utilization. Here we model multiple connections maintained in the congestion avoidance

regime by the RED mechanism. The window sizes of each TCP session evolve like independent dynamical systems coupled by the queue length at the buffer. We introduce a mean-field approximation to one such RED system as the number of flows tends to infinity. The deterministic limiting system is described by a transport equation. The numerical solution of the limiting system is found to provide a good description of the evolution of the distribution of the window sizes, the average queue size, the average loss rate per connection and the total throughput.

He will be giving a follow-on seminar in the Probability Seminar Series:

Thursday Feb 20 at 3 PM in Room 269

Title: Mean-field convergence of distributed dynamical systems sharing a common resource

Abstract: Multiple TCP/IP connections multiplexed through a RED buffer are in fact dynamical systems which share a common resource - the buffer. We adapt the technique developed by Kurtz and Donnelly to prove mean-field convergence of the histogram of window sizes.

]]>Industrial and Systems Engineering

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