Fluid model for window-based congestion control mechanism

We study the stability of two queueing delay-based congestion control algorithms, the (p, 1)-proportionally fair algorithm and the global optimization algorithm. We linearize the systems around the intended operating point and show that these algorithms are stable within a range of feedback delay. Based on these linearized systems we study the impact of various (cascade) compensators on the system. We show that the PID control improves the transient behavior of the system. We simulate both the linearized system and non-linear system and illustrate the validity of the analysis and improvement in the system behavior with compensators.