Stability analysis of multiple-bottleneck networks

Authors:
Lijun Wang;Lin Cai;Xinzhi Liu;Xuemin (Sherman) Shen;Junshan Zhang
Affiliations:
Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada V8W 3P6;Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Electrical and Computer Engineering, University of Waterloo, 200 University Ave. W., Waterloo, ON, Canada N2L 3G1;Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287, United States
Venue:
Computer Networks: The International Journal of Computer and Telecommunications Networking
Year:
2009

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Abstract

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.