Oscillation control for n-dimensional congestion control model via time-varying delay  

作　　者：ZHANG Shu XU Jian 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

出　　处：《Science China(Technological Sciences)》2011年第8期2044-2053,共10页中国科学（技术科学英文版）

基　　金：supported by the State Key Program of National Natural Science Foundation of China (Grant No. 11032009);Shanghai Leading Academic Discipline Project (Grant No. B302)

摘　　要：Time delay or round trip time (RTT) is an important parameter in the model of Internet congestion control. On the one hand, the delay may induce oscillation via the Hopf bifurcation. In the present paper, a congestion control model of n dimensions is considered to study the delay-induced oscillation. By linear analysis of the n-dimensional system, the critical delay for the Hopf bifurcation is obtained. To describe the relation between the delay and oscillation analytically, the method of multiple scales (MMS) is employed to obtain the bifurcating periodic solution. On the other hand, it can be understood that the oscillation will increase the risk of congestion for the network system. To avoid the congestion derived from the oscillation, a new control scheme is proposed by perturbing the delay periodically. Particularly, according to our study, it is possible to control the oscillation by perturbing only one of the n delays. This provides a practical scheme for the oscillation control in the real network system. By MMS, the strengths of the perturbations are predicted analytically such that the oscillation disappears. To give an example, an eight-dimensional model is studied in detail. The analytical results are in good agreement with the numerical simulations.

关 键 词：internet congestion control high-dimensional system Hopf bifurcation time-varying delay method of multiple scales 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TP393[自动化与计算机技术—控制科学与工程]