Full Text:   <1735>

CLC number: TP393

On-line Access: 

Received: 2009-04-17

Revision Accepted: 2009-09-05

Crosschecked: 2009-12-30

Cited: 1

Clicked: 4054

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE C 2010 Vol.11 No.3 P.214-226


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

Author(s):  Behrooz REZAIE, Mohammad-Reza JAHED MOTLAGH, Siavash KHORSANDI, Morteza ANALOUI

Affiliation(s):  Deparment of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran; more

Corresponding email(s):   brezaie@iust.ac.ir

Key Words:  Internet congestion control, Global stability, Nonlinear time-delay system, Time-varying delay

Share this article to: More <<< Previous Article|

Behrooz REZAIE, Mohammad-Reza JAHED MOTLAGH, Siavash KHORSANDI, Morteza ANALOUI. Global stability analysis of computer networks with arbitrary topology and time-varying delays[J]. Journal of Zhejiang University Science C, 2010, 11(3): 214-226.

@article{title="Global stability analysis of computer networks with arbitrary topology and time-varying delays",
author="Behrooz REZAIE, Mohammad-Reza JAHED MOTLAGH, Siavash KHORSANDI, Morteza ANALOUI",
journal="Journal of Zhejiang University Science C",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Global stability analysis of computer networks with arbitrary topology and time-varying delays
%A Behrooz REZAIE
%A Mohammad-Reza JAHED MOTLAGH
%A Morteza ANALOUI
%J Journal of Zhejiang University SCIENCE C
%V 11
%N 3
%P 214-226
%@ 1869-1951
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C0910216

T1 - Global stability analysis of computer networks with arbitrary topology and time-varying delays
A1 - Behrooz REZAIE
A1 - Mohammad-Reza JAHED MOTLAGH
A1 - Siavash KHORSANDI
A1 - Morteza ANALOUI
J0 - Journal of Zhejiang University Science C
VL - 11
IS - 3
SP - 214
EP - 226
%@ 1869-1951
Y1 - 2010
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C0910216

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Alpcan, T., Basar, T., 2005. A globally stable adaptive congestion control scheme for Internet-style networks with delay. IEEE/ACM Trans. Netw., 13(6):1261-1274.

[2] Deb, S., Srikant, R., 2003. Global stability of congestion controllers for the Internet. IEEE Trans. Automat. Control, 48(6):1055-1060.

[3] Fan, M., Zou, X., 2004. Global asymptotic stability of a class of nonautonomous integro-differential systems and applications. Nonl. Anal., 57(1):111-135.

[4] Fan, X., Arcak, M., Wen, J.T., 2004. Robustness of network flow control against disturbances and time-delay. Syst. Control Lett., 53(1):13-29.

[5] Gao, H., Lam, J., Wang, C., Guan, X.P., 2005. Further results on local stability of REM algorithm with time-varying delays. IEEE Commun. Lett., 9(5):402-404.

[6] Guo, S.T., Liao, X.F., Li, C.D., Yang, D.G., 2007. Stability analysis of a novel exponential-RED model with heterogeneous delays. Comput. Commun., 30(5):1058-1074.

[7] Hale, J.K., Lunel, S.M.V., 1993. Introduction to Functional Differential Equations. Springer-Verlag, New York, USA.

[8] Johari, R., Tan, D., 2001. End-to-end congestion control for the Internet: delays and stability. IEEE/ACM Trans. Netw., 9(6):818-832.

[9] Kelly, F.P., 2000. Models for a self-managed Internet. Phil. Trans. Roy. Soc. A: Math. Phys. Eng. Sci., 358(1773):2335-2348.

[10] Kelly, F.P., Maulloo, A.K., Tan, D.K.H., 1998. Rate control in communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc., 49(3):237-252.

[11] Liu, S., Basar, T., Srikant, R., 2005. Exponential-RED: a stabilizing AQM scheme for low- and high-speed TCP protocols. IEEE/ACM Trans. Netw., 13(5):1068-1081.

[12] Long, C.N., Wu, J., Guan, X.P., 2003. Local stability of REM algorithm with time-varying delays. IEEE Commun. Lett., 7(3):142-144.

[13] Low, S.H., Lapsley, D.E., 1999. Optimization flow control: I. basic algorithm and convergence. IEEE/ACM Trans. Netw., 7(6):861-874.

[14] Low, S.H., Paganini, F., Doyle, J.C., 2002. Internet congestion control. IEEE Control Syst. Mag., 22(1):28-43.

[15] Massoulie, L., 2002. Stability of distributed congestion control with heterogeneous feedback delays. IEEE Trans. Automat. Control, 47(6):895-902.

[16] Mazenc, F., Niculescu, S.I., 2003. Remarks on the Stability of a Class of TCP-like Congestion Control Models. Proc. IEEE Conf. on Decision and Control, p.5591-5594.

[17] Paganini, F., 2002. A global stability result in network flow control. Syst. Control Lett., 46(3):165-172.

[18] Paganini, F., Wang, Z., Doyle, J.C., Low, S.H., 2005. Congestion control for high performance, stability and fairness in general networks. IEEE/ACM Trans. Netw., 13(1):43-56.

[19] Papachristodoulou, A., Doyle, J.C., Low, S.H., 2004. Analysis of Nonlinear Delay Differential Equation Models of TCP/AQM Protocols Using Sums of Squares. Proc. IEEE Conf. on Decision and Control, p.4684-4689.

[20] Peet, M., Lall, S., 2007. Global stability analysis of a nonlinear model of Internet congestion control with delay. IEEE Trans. Automat. Control, 52(3):553-559.

[21] Ranjan, P., Abed, E.H., La, R.J., 2004. Nonlinear instabilities in TCP-RED. IEEE/ACM Trans. Netw., 12(6):1079-1092.

[22] Ranjan, P., La, R.J., Abed, E.H., 2006. Global stability conditions for rate control with arbitrary communication delays. IEEE/ACM Trans. Netw., 14(1):94-107.

[23] Shakkottai, S., Srikant, R., 2004. Mean FDE models for Internet congestion control under a many-flows regime. IEEE Trans. Inf. Theory, 50(6):1050-1072.

[24] Slotine, J.J.E., Li, W., 1991. Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs, NJ, p.123.

[25] Srikant, R., 2004. The Mathematics of Internet Congestion Control. Birkhauser, Cambridge, MA, p.40-47.

[26] Tan, L., Zhang, W., Peng, G., Chen, G., 2006. Stability of TCP/RED systems in AQM routers. IEEE Trans. Automat. Control, 51(8):1393-1398.

[27] Tian, Y.P., 2005a. A general stability criterion for congestion control with diverse communication delays. Automatica, 41(7):1255-1262.

[28] Tian, Y.P., 2005b. Stability analysis and design of the second-order congestion control for networks with heterogeneous delays. IEEE/ACM Trans. Netw., 13(5):1082-1093.

[29] Vinnicombe, G., 2000. On the Stability of End-to-End Congestion Control for the Internet. Technical Report No. CUED/F-INFENG/TR.398, University of Cambridge, Cambridge, UK, p.1-6.

[30] Wang, Z., Paganini, F., 2006. Boundedness and global stability of a nonlinear congestion control with delays. IEEE Trans. Automat. Control, 51(9):1514-1519.

[31] Wen, J.T., Arcak, M., 2004. A unifying passivity framework for network flow control. IEEE Trans. Automat. Control, 49(2):162-174.

[32] Ying, L., Dullerud, G.E., Sirkant, R., 2006. Global stability of Internet congestion controllers with heterogeneous delay. IEEE/ACM Trans. Netw., 14(3):579-591.

[33] Zhang, Y., Loguinov, D., 2008. Local and global stability of delayed congestion control system. IEEE Trans. Automat. Control, 53(10):2356-2360.

[34] Zhang, Y., Kang, S.R., Loguinov, D., 2007. Delay-independent stability and performance of distributed congestion control. IEEE/ACM Trans. Netw., 15(4):838-851.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE