Wavelet Spectral Analysis of Packet Traffic Near Phase Transition Point from Free Flow to Congestion in Data Network Model

We have applied wavelet statistics to study packet traffic in a data communication network model of the packet switching type. Our focus is on the study of spectral properties of packet traffic near phase transition point (critical point) from free flow to congested states of the network model. We characterize the critical point by the level of packets production at sources in the packet switching network (PSN) model. In our model we consider different dynamic routing cost metrics (i.e., when the costs of transmission of packets from one router to another incorporate the information about how congested the routers are) and static routing cost metric (i.e., when the cost of transmission of packets from one router to another is constant over time). Using wavelets we study spectral properties of number of packets in transit from their sources to their destinations in PSN model for various routing algorithms and network connection topologies when source loads are close to the critical ones. We show that the wavelet power spectra is an important estimator of the changes occurring with the increase of source load values from sub-critical, through critical to supercritical ones and it is dependent on the routing algorithm.