Modeling and understanding the dynamic features of urban mobility is a key issue for the development of governance policies for sustainable mobility in future smart cities. The possibility of collecting large datasets at an individual level opened a fruitful research field for Complex Systems Physics. We show that the application of Statistical Physics allows us to explain the power law distribution of human mobility in the framework of a Maximum Entropy Principle (MEP) assuming the existence of a multilayer structure for transport systems. The congestion formation on an urban road network is another fundamental problem and the quantification of the congestion degree for a city has been considered by various authors. Different models have been proposed and the simulation results suggest the existence of universal features for the transition to global congested states on a road network.

We cope with the question if simple transport models on graphs can reproduce universal features of congestion formation and the existence of control parameters is still an open problem using a reductionist approach to this problem. We study simple transport models by means of random processes on a graph assuming that each node has a finite transport capacity and it has a finite capacity. The dynamics is realized by a random walk on graphs according to given transition rates (link weights) and a displacement is possible if the number of particles in the destination nodes is smaller than their maximal capacity. We study the properties the particle stationary distributions on the graph and the possibility of applying the MEP to characterize the stationary distributions and to understand the congestion transition. This research activity is related to the project of a digital twin for the city of Bologna.