Traffic Fluctuations on Weighted Networks

Traffic fluctuation has so far been studied on unweighted networks. However, many real traffic systems are better represented and understood as weighted networks, where nodes and links are assigned some weight values representing their physical properties such as capacity and delay. Here, we introduce a general random diffusion (GRD) model to investigate the traffic fluctuations on weighted networks, where a random walk's choice of route is affected not only by the number of links a node has, but also by the weights of individual links. We obtain analytical solutions that characterize the relation between the average traffic and the fluctuations through nodes and links. Our analysis is supported by results of extensive numerical simulations. We observe that the value ranges of the average traffic and the fluctuations, through nodes or links, increase dramatically with the level of heterogeneity in link weights. This highlights the key role that link weight plays in traffic fluctuation and the necessity to study traffic fluctuations on weighted networks.