Performance analysis of compound TCP with a Proportional Integral (PI) control policy

In this paper, we study the performance of Compound TCP with the classical Proportional Integral (PI) control policy implemented at routers. We first conduct a local stability analysis and derive the necessary and sufficient condition for local stability of the non-linear model of Compound with PI. We explicitly show that the system undergoes a Hopf bifurcation as it transits into instability, which would lead to the emergence of limit cycles in the queue size. We then use Poincaré normal forms and center manifold theory to provide an analytical basis to characterise the Hopf bifurcation and determine the orbital stability of the limit cycles. The analysis is complemented with numerical examples.