Symbolic Dynamical Model of Average Queue Size of Random Early Detection Algorithm

In this paper, a symbolic dynamical model of the average queue size of the random early detection (RED) algorithm is proposed. The conditions on both the system parameters and the initial conditions that the average queue size of the RED algorithm would converge to a fixed point are derived. These results are useful for network engineers to design both the system parameters and the initial conditions so that internet networks would achieve a good performance. Keywords⎯Transmission control protocol, random early detection algorithm, internet congestion problem, symbolic dynamics, Lyapunov stability.