Fixed point analysis of a first-order discrete model for the random early detection with nonlinearity

Abstract

In this paper, we propose a first-order discrete model for random early detection (RED) with nonlinearity, focusing on the average queue size in a router. The RED is a representative router-based algorithm for congestion control. Congestion is avoided by discarding packets at random using the packet drop probability function and the average queue size in RED. Our proposed model replaces the linear packet drop probability function of the original RED with a nonlinear function and can continuously change the nonlinearity strength, namely the bending degree of the nonlinear function. In other words, the model mathematically analyzes the influence of the nonlinearity strength in the packet drop probability function on the control of RED. Our simulation results showed the reproducibility of the model under three traffic conditions: light, heavy, and extremely heavy, by comparing the model and the network simulator-2. Furthermore, we performed a fixed point analysis on the steady-states to determine the average queue size. Consequently, the effect of the change in the nonlinearity strength on the average queue size was mathematically ensured.