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

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