Flow interaction based propagation model and bursty influence behavior analysis of Internet flows

QoS (quality of service) fluctuations caused by Internet bursty flows influence the user experience in the Internet, such as the increment of packet loss and transmission time. In this paper, we establish a mathematical model to study the influence propagation behavior of the bursty flow, which is helpful for developing a deep understanding of the network dynamics in the Internet complex system. To intuitively reflect the propagation process, a data flow interaction network with a hierarchical structure is constructed, where the neighbor order is proposed to indicate the neighborhood relationship between the bursty flow and other flows. The influence spreads from the bursty flow to each order of neighbors through flow interactions. As the influence spreads, the bursty flow has negative effects on the odd order neighbors and positive effects on the even order neighbors. The influence intensity of bursty flow decreases sharply between two adjacent orders and the decreasing degree can reach up to dozens of times in the experimental simulation. Moreover, the influence intensity increases significantly when network congestion situation becomes serious, especially for the 1st order neighbors. Network structural factors are considered to make a further study. Simulation results show that the physical network scale expansion can reduce the influence intensity of bursty flow by decreasing the flow distribution density. Furthermore, with the same network scale, the influence intensity in WS small-world networks is 38.18% and 18.40% lower than that in ER random networks and BA scale-free networks, respectively, due to a lower interaction probability between flows. These results indicate that the macro-structural changes such as network scales and styles will affect the inner propagation behaviors of the bursty flow.