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

Abstract

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.internet congestion control, high-dimensional system, Hopf bifurcation, time-varying delay, method of multiple scales Citation:Zhang S, Xu J. Oscillation control for n-dimensional congestion control model via time-varying delay.

Suppression of Regenerative Chatter in a Plunge-Grinding Process by Spindle Speed

“…(27), {2C^a3/2g^ + 1) £e^r''(«)'^'ds, and Cel»'«'^ are periodical or linear functions of time [38]. By contrast, e^^^' is an exponential function of time.…”

“…In the analysis of the SSV control, the method adopted is based on the method of multiple scales (MMS) [38]. Generally, the fundamental idea of this method is transforming a complex problem into a group of simple problems.…”

“…That means this method can be used to investigate regenerative chatter vibrations as well [37]. Recently, this method was modified by Zhang and Xu [38]; thereafter, it is adopted to analyze dynamical systems with time-varying delays. Correspondingly, the SSV control can be theoretically studied by the method proposed by Zhang and Xu [38,39].…”