Stability analysis of multiple-bottleneck networks

A TCP/RED (Transmission Control Protocol/Random Early Detection) system with multiple-bottleneck links could be unstable even if its system parameters are set the same as those in a stable single-bottleneck system [D. Bauso, L. Giarre, G. Neglia, Active queue management stability in multiple bottleneck networks, IEEE ICC’04, vol. 4, June 2004, pp. 2267–2271]. In this paper, we study the stability of more general AIMD (Additive Increase and Multiplicative Decrease)/RED system with multiple bottlenecks that may incur non-negligible packet losses. We develop a general mathematical model to analyze network stability for both delay-free and delayed AIMD/RED systems. Sufficient conditions for the asymptotic stability of multiple-bottleneck systems with heterogeneous delays are derived by appealing to Lyapunov stability theory with Lyapunov–Razumikhin conditions, and these conditions can be easily assessed by using LMI (Linear Matrix Inequality) Toolbox. Numerical results with Matlab and simulation results with NS-2 are given to validate the analytical results.