Predicting network congestion by extending betweenness centrality to interacting agents.

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We present a simple model to predict network activity at the edge level by extending a known approximation method to compute betweenness centrality with a repulsive mechanism to prevent unphysical densities. By taking into account the strong interaction effects often observed in real phenomena, we aim to obtain an improved measure of edge usage during rush hours as traffic congestion patterns emerge in urban networks. In this approach, the network is iteratively populated by agents following dynamically evolving fastest paths who are progressively attracted towards uncongested parts of the network as the global traffic volume increases. Following the transition of the network state from empty to saturated, we study the emergence of congestion and the progressive disruption of global connectivity due to a relatively small fraction of crowded edges. We assess the predictive power of our model by comparing the speed distribution against a large experimental data set for the London area with remarkable results, which also translate into a qualitative similarity of the congestion maps. Also, percolation analysis confirms the quantitative agreement of the model with the real data for London. We perform simulations for seven other topologically different cities to obtain the Fisher critical exponent τ that shows no common functional dependence on the traffic level. The critical exponent γ, studied to assess the power-law decay of spatial correlation, is found to be inversely proportional to the number of vehicles for both real and simulated traffic. This simulation approach seems particularly fit to describe qualitative and quantitative properties of the network loading process, culminating in peak-hour congestion, by using only topological and geographical network features.