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Front. Inform. Technol. Electron. Eng.  2010, Vol. 11 Issue (3): 214-226    DOI: 10.1631/jzus.C0910216
    
Global stability analysis of computer networks with arbitrary topology and time-varying delays
Behrooz REZAIE*,1, Mohammad-Reza JAHED MOTLAGH1, Siavash KHORSANDI2, Morteza ANALOUI3
1 Deparment of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran 2 Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran 15914, Iran 3 Deparment of Computer Engine
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Abstract  In this paper, we determine the delay-dependent conditions of global asymptotic stability for a class of multi-dimensional nonlinear time-delay systems with application to computer communication networks. A nonlinear delayed model is considered for a rate-based congestion control system of a heterogeneous network with arbitrary topology and time-varying delays. We propose a Lyapunov-based method to obtain a sufficient condition under which global asymptotic stability of the equilibrium is guaranteed. The main contribution of the paper lies in considering time variations of delays in a heterogeneous network which may be applicable in actual networks. Moreover, we obtain conditions for Internet-style networks with multi-source multi-link topology. We first prove the stability for a class of nonlinear time-delay systems. Then, we apply the results to a Kelly’s rate-based approximation of the congestion control system.

Key words： Internet congestion control      Global stability      Nonlinear time-delay system      Time-varying delay     
Received: 17 April 2009      Published: 01 March 2010
CLC:  TP393  
Fund:  Project  (No.  T500-11453)  supported  in  part  by  the  Iran  Telecom-munication Research Center, Iran
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Behrooz REZAIE
Mohammad-Reza JAHED MOTLAGH
Siavash KHORSANDI
Morteza ANALOUI
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Behrooz REZAIE, Mohammad-Reza JAHED MOTLAGH, Siavash KHORSANDI, Morteza ANALOUI. Global stability analysis of computer networks with arbitrary topology and time-varying delays. Front. Inform. Technol. Electron. Eng., 2010, 11(3): 214-226.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C0910216     OR     http://www.zjujournals.com/xueshu/fitee/Y2010/V11/I3/214


Global stability analysis of computer networks with arbitrary topology and time-varying delays

In this paper, we determine the delay-dependent conditions of global asymptotic stability for a class of multi-dimensional nonlinear time-delay systems with application to computer communication networks. A nonlinear delayed model is considered for a rate-based congestion control system of a heterogeneous network with arbitrary topology and time-varying delays. We propose a Lyapunov-based method to obtain a sufficient condition under which global asymptotic stability of the equilibrium is guaranteed. The main contribution of the paper lies in considering time variations of delays in a heterogeneous network which may be applicable in actual networks. Moreover, we obtain conditions for Internet-style networks with multi-source multi-link topology. We first prove the stability for a class of nonlinear time-delay systems. Then, we apply the results to a Kelly’s rate-based approximation of the congestion control system.

关键词： Internet congestion control,  Global stability,  Nonlinear time-delay system,  Time-varying delay 
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