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

doi:10.1007/s10483-019-2411-9

摘要/Abstract

摘要： 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.

关键词: local strictly pseudocontractive, local strongly accretive, uniformly smooth Banach space, Hopf bifurcation, delayed differential equation, normal form, Internet congestion control, stability

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.

Key words: local strictly pseudocontractive, local strongly accretive, uniformly smooth Banach space, delayed differential equation, Internet congestion control, Hopf bifurcation, stability, normal form

中图分类号:

34K20

Sainan WANG, Shu ZHANG, Jian XU. Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(1): 25-48.

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