Bursting-like motion induced by time-varying delay in an internet congestion control model

Time delay is an important parameter in the problem of internet congestion control. According to some researches, time delay is not always constant and can be viewed as a periodic function of time for some cases. In this work, an internet congestion control model is considered to study the time-varying delay induced bursting-like motion, which consists of a rapid oscillation burst and quiescent steady state. Then, for the system with periodic delay of small amplitude and low frequency, the method of multiple scales is employed to obtain the amplitude of the oscillation. Based on the expression of the asymptotic solution, it can be found that the relative length of the steady state increases with amplitude of the variation of time delay and decreases with frequency of the variation of time delay. Finally, an effective method to control the bursting-like motion is proposed by introducing a periodic gain parameter with appropriate amplitude. Theoretical results are in agreement with that from numerical method.