Design of Feedback Controls Supporting TCP Based on the State–Space Approach
K.B. Kim · IEEE Transactions on Automatic Control · 2006
This paper investigates how to design feedback controls supporting transmission control protocol (TCP) based on the state-space approach for the linearized system of the well-known additive increase multiplicative decrease (AIMD) dynamic model. We formulate the feedback control design problem as state-space models without assuming its structure in advance. Thereby, we get three results that have not been observed by previous studies on the congestion control problem. 1) In order to fully support TCP, we need a proportional-derivative (PD)-type state-feedback control structure in terms of queue length (or RTT: round trip time). This backs up the conjecture in the networking literature that the AQM RED is not enough to control TCP dynamic behavior, where RED can be classified as a P-type AQM (or as an output feedback control for the linearized AIMD model). 2) In order to fully support TCP in the presence of delays, we derive delay-dependent feedback control structures to compensate for delays explicitly under the assumption that RTT, capacity and number of sources are known, where all existing AQMs including RED, REM/PI and AVQ are delay-independent controls. 3) In an attempt to interpret different AQM structures in a unified manner rather than to compare them via simulations, we propose a PID-type mathematical framework using integral control action. As a performance index to measure the deviation of the closed-loop system from an equilibrium point, we use a linear quadratic (LQ) cost of the transients of state and control variables such as queue length, aggregate rate, jitter in the aggregate rate, and congestion measure. Stabilizing gains of the feedback control structures are obtained minimizing the LQ cost. Then, we discuss the impact of the control structure on performance using the PID-type mathematical framework. All results are extended to the case of multiple links and heterogeneous delays.