Analysis and Design of AQM based on Receding Horizon Control in Stabilizing TCP

In this paper, we propose a uni ed mathematical framework based on receding horizon control for analyzing and designing AQM (Active Queue Management) algorithms in stabilizing a given TCP (Transfer Control Protocol) algorithm. The proposed framework is based on a dynamical system of the given TCP and minimization of a linear quadratic cost on the transients in queue length, aggregate rate, jitter in the aggregate rate, and congestion measure. We derive the receding horizon AQMs that stabilize the linearized dynamical system with minimum cost. Conversely, we show that any AQM with an appropriate structure solves the same optimal control problem with appropriate weighting matrix. We interpret existing AQMs such as RED (Random Early Detection), REM (Random Exponential Marking), PI (Proportional-Integral) and AVQ (Adaptive Virtual Queue) as di erent approximations of the optimal AQM, and discuss the impact of these approximations on performance. We illustrate our results through simulation examples.