Efficiency in road networks

In order to answer the question as to whether road networks follow a self-organisation process, we need to be able to understand what principles of economy would this mechanism entail. It is therefore of interest to be able to explore the possible shape that a performance function would have for transportation systems. In this work, we tackle this issue by proposing a network generation model based on a single parameter alpha which is capable of creating any type of network from trees to quasi-surfaces and is shown to generate networks close to the real road networks under study. This is obtained through the definition of local and weighted versions of centrality measures. These centrality measures deal with distance-decay effects and nodes having different masses.
We set ourselves to determine the properties and different regimes of this alpha-model and we lay out a definition for the performance of a network taking into account factors such as robustness, construction cost, congestion and distance. We obtain the optimal alpha from the analysis of the space of possible performance functions, which is shown to have the highest agreement with the actual road network, giving an intuition on the self-organisational properties of the original network. We then confront the road network against the highest performance version of our alpha-model and define its efficiency as the ratio between the performance of the real road network and the idealised model.