This paper proposed a packet drop probability function with an adjustable nonlinearity parameter in random early detection (RED) for active queue management of a router to control network congestion. We investigated the effect of nonlinearity on the average queue size, average throughput, average retransmission rate, average round-trip time, and fairness index for two widely used loss-based congestion control algorithms: Reno and CUBIC. Simulations were performed with Tail-Drop and the original RED to clarify the effect of nonlinearity under different traffic loads. The results showed that the RED with a nonlinear function did not aggravate the network performance statistics because achieved high throughput while maintaining a low-queuing delay, such as the original RED with a linear function under the extremely heavy traffic condition. Under the light and the heavy traffic conditions, increasing the bending degree of the nonlinear function accomplished high throughput by preventing excessive discarding of packets.
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.
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