Stability and Performance of Compound TCP With a Proportional Integral Queue Policy

The increase in queueing delays in the Internet motivates the study of transmission control protocol (TCP) and queue management policies. This paper studies Compound TCP with a Proportional–Integral (PI) policy for queue management at the Internet routers. A nonlinear fluid model for the Compound TCP-PI system is considered. For this model, a sufficient condition for local stability, which yields some design guidelines, is derived. Fragility analysis of this model highlights that even marginal variations in the PI parameters may induce instability. Next, a regime where the integral component, of the PI policy, operates over a small time-scale is considered. For a fluid model befitting this regime, the necessary and sufficient condition for local stability is derived. It is explicitly shown that, when this condition is violated, the system undergoes a Hopf bifurcation, which would lead to limit cycles. Furthermore, a detailed local bifurcation analysis is conducted to characterize the type of the Hopf bifurcation and determine the orbital stability of the limit cycles. Packet-level simulations corroborate the analytical insight. The analysis and simulations demonstrate some drawbacks of the PI policy. Following this, a simple threshold-based queue policy, which has desirable stability properties, is proposed for queue management at routers. Furthermore, a simulation-based performance evaluation reveals that this policy outperforms PI. Through a combination of theory and simulations, it is shown that the threshold-based policy can ensure system stability, while ensuring reduced queueing delays.