Delay-Dependent Stability Analysis for Large-Scale Multiple-Bottleneck Systems Using Singular Perturbation Approach

AIMD/RED (additive increase and multiplicative decrease/random early detection) systems with multiple- bottleneck links are becoming more and more common in the vast-scale Internet. In this paper, we develop a mathematical model of AIMD/RED systems with multiple bottlenecks and feedback delays, which can be brought into the frame of singularly perturbed systems. Stability properties of multiple- bottleneck systems are studied by applying the techniques for singularly perturbed systems. Delay-dependent LMI (Linear Matrix Inequalities) criteria for the stability of singularly perturbed AIMD/RED systems with multiple bottlenecks are obtained, and the existence of the sufficiently small parameters that guarantee the asymptotic stability of the system considered above is also demonstrated. Numerical results with Matlab and simulation results with NS-2 are given to validate the analytical results.