Scalable Modeling and Performance Evaluation of Dynamic RED Router using Fluid-Flow Approximation

In recent years, AQM (Active Queue Management) mechanisms, which support the end-to-end congestion control mechanism of TCP (Transmission Control Protocol), have been widely studied in the literature. AQM mechanism is a congestion controller at a router for suppressing and stabilizing its queue length (i.e., the number of packets in the buffer) by actively discarding arriving packets. Although a number of AQM mechanisms have been proposed, behaviors of those AQM mechanisms other than RED (Random Early Detection) have not been fully investigated. In this paper, using fluid-flow approximation, we analyze steady state behavior of DRED (Dynamic RED), which is designed with a control theoretic approach. More specifically, we model several network components such as congestion control mechanism of TCP, DRED router, and link propagation delay as independent SISO (Single-Input Single-Output) continuous-time systems. By interconnecting those SISO models, we obtain a continuous-time model for the entire network. Unlike other fluid-based modeling approaches, our analytic approach is scalable; our analytic approach is scalable in terms of the number of TCP connections and DRED routers since both input and output of all continuous-time systems are uniformly defined as a packet transmission rate. By performing steady-state analysis, we derive TCP throughput, average queue length of DRED router, and packet loss probability. Through several numerical examples, we quantitatively show that DRED has an intrinsic problem in high-speed networks; i.e., DRED cannot stabilize its queue length when the bottleneck link bandwidth is high. We also validate accuracy of our analytic approach by comparing analytic results with simulation ones.