Stability analysis and design of the second-order congestion control for networks with heterogeneous delays

This paper addresses the problem of the stability of congestion control for networks with heterogeneous round-trip communication delays. We present a frequency-domain approach to this problem. The approach is based on the analysis of the clockwise property of system transfer functions, generalized Nyquist stability criterion, and a recent lemma of Vinnicombe. We point out that a prerequisite for establishing decentralized stability criteria for distributed congestion control is that the Nyquist plots of time-delayed transfer functions corresponding to price (rate) dynamics at links (sources) satisfy clockwise property in certain frequency intervals. Based on the detailed investigation of global geometric properties of the frequency response of price dynamics at links, we derive sufficient conditions for the local asymptotic stability of a kind of the second-order active queue management algorithm-REM algorithm. A simple design procedure is also proposed for guaranteeing the asymptotic stability of the control algorithm.