Detrended Fluctuation Analysis Of Traffic Data

Complex networks can be used to describe of systems from nature to society, thus there has been a quickly growing interest since the discoveries on scale-free properties. At present understanding and controlling of traffic congestion on network is a hot topic. However, the communication in the traffic does not always march/go freely. Therefore, sustaining its normal and efficient functioning is a basic requirement. To model realistic situation where different nodes in a network may have different capabilities, the message or packet creation and delivering rates at a node are assumed to depend on the degree of the node. In this article, we analyze the correlation of traffic data for three typical routing strategies by the detrended fluctuation analysis (DFA) and find that degree of correlation of the data can be divided into three regions, i.e., weak, medium, and strong correlation . The DFA scalings are constants in both the regions of weak and strong correlation but monotonously increase in the region of medium correlation. Our results suggest that it is better to consider the traffic on complex networks as three phases, i.e., the free, buffer, and congestion phase, than just as two phases believed before, i.e., the free and congestion phase.