Performance Analysis of the Random Early Detection Algorithm

In this paper we consider a finite queue with its arrivals controlled by the Random Early Detection (RED) algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of TCP sources is locally considered stationary renewal or MMPP with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. But computing the performance indices for this system becomes computationally prohibitive. Thus in the latter half of the paper we approximate the dynamics of the average queue length process asymptotically via an ODE. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.