Traffic Fluctuations on Weighted Networks

TL;DR

This paper introduces a general random diffusion model to analyze traffic fluctuations on weighted networks, revealing how link weight heterogeneity significantly impacts traffic variability.

Contribution

The study develops an analytical framework for traffic fluctuation in weighted networks, extending previous unweighted models and highlighting the importance of link weights.

Findings

Traffic fluctuation increases with link weight heterogeneity.

Analytical solutions relate average traffic to fluctuation on nodes and links.

Numerical simulations support the analytical results.

Abstract

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.