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

Abstract

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.