Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

Abstract

The time delay-induced instability in an Internet congestion control model is investigated. The star topology is considered, and the link bandwidth ratio and the control gain are selected as the tunable parameters for congestion suppression. The stability switch boundary is obtained by the eigenvalue analysis for the linearized system around the equilibrium. To investigate the oscillatory congestion when the equilibrium becomes unstable, the center manifold reduction and the normal form theory are used to study the periodic oscillation induced by the delay. The theoretical analysis and numerical simulation show that the ratio between bandwidths of the trunk link and the regular link, rather than these bandwidths themselves, is crucial for the stability of the congestion control system. The present results demonstrate that it is not always effective to increase the link bandwidth ratio for stabilizing the system, and for some certain delays, adjusting the control gain is more efficient.

Criteria for minimization of spectral abscissa of time-delay systems

“…Time delays are usually inevitable in control applications when digital controllers and digital filters are used, and they are also very common in human-machine interaction systems because humans need time to respond. Time-delay systems are a kind of infinite dimensional systems described by delay differential equations [1][2][3][4][5][6] . No matter how small the delay is, the evolution of a time-delay system is determined by the state defined over an interval of the time, not by a single state for the delay-free systems.…”

“…When SA is negative, the smaller the value of σ is, the faster the solution of the time-delay system decays to the equilibrium. Thus, SA can be regarded as a representative of the decaying rate for characterizing stability [5,[12][13] . In the case when SA exhibits a change from decreasing to increasing behavior in a given range of a parameter, the proposed time-delay control improves the stability of the time-delay system.…”