Hopf Bifurcation of the Wireless Network Congestion Model with State-Dependent Round Trip Delay

Abstract

In this paper, the bifurcation analysis software, DDE-BIFTOOL, is employed to analyze the Hopf bifurcation of the wireless network congestion model with state-dependent round trip delay. Hopf bifurcations are investigated for the four typical work conditions. The corresponding stable and unstable bifurcating periodic solutions are quantitatively and qualitatively verified by nonlinear simulation software, WinPP, respectively, which agree with those of DDE-BIFTOOL very well. The results imply that the channel loss probabilities [Formula: see text] and [Formula: see text] can play a more important role than the speed of the network, i.e. the related link bandwidth [Formula: see text]. For larger [Formula: see text] and [Formula: see text] in Cases 3 and 4, the smaller [Formula: see text] and [Formula: see text] can induce Hopf bifurcation. This will result in the loss of stability and performance degradation. So [Formula: see text] and [Formula: see text] should be set smaller to avoid congestion, providing a sound theoretical basis and instructions for the congestion control of the wireless network.