  Traffic fluctuation has so far been studied on unweighted networks. However
many real traffic systems are better represented as weighted networks, where
nodes and links are assigned a weight value representing their physical
properties such as capacity and delay. Here we introduce a general random
diffusion (GRD) model to investigate the traffic fluctuation in 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 weight of individual links. We
obtain analytical solutions that characterise the relation between the average
traffic and the fluctuation through nodes and links. Our analysis is supported
by the results of numerical simulations. We observe that the value ranges of
the average traffic and the fluctuation, through nodes or links, increase
dramatically with the level of heterogeneity in link weight. This highlights
the key role that link weight plays in traffic fluctuation and the necessity to
study traffic fluctuation on weighted networks.
