Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

Abstract

We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.

Analysis of a Congestion Model in a Wireless Access Network with One Bottleneck Router and N TCP Flows

“…In [12], the mathematical model for wireless access networks, with one bottleneck router and 1  n identical TCP flows that pass through the router, is analyzed. In this case, for…”

“…In the recent times, the wireless access network has paid great attention, because it is applied in different fields, especially to the Internet. The congestion control in wireless access network is important in the success of the wireless network technology [12]. According to [3], congestion control is an algorithm which allocates available resources to competing sources efficiently in order to avoid congestion collapse.…”

“…In [3], the communication time delay is a bifurcating parameter and the behavior of the system is investigated. In [2]− [12], the local stability of the equilibrium point is studied in different congestion control models. Also, the Hopf bifurcation is examined when there is a single link and a single communication delay.…”