Maximum Entropy Principle and Data-Driven Markov Models For Transport Networks

The possibility to collect large data sets by the Information and Communication Technologies (ICT) allows to study the individual behaviors, but one has to take into account the restrictions imposed by privacy legislation, especially in Europe. The use of agent based models to simulate complex systems turns out to be difficult due to the need to measure the individual behavior. However, recent studies have pointed out some universal properties that characterize the development of congestion in a transport network, despite the characteristics of transport networks being different among different cities. These remarks open the possibility to develop a data driven reductionist approach using the maximum entropy principle of Statistical Mechanics. In this paper we illustrate the road map to build a data driven Markov process that allow to study the congestion formation on a transport system using a priori information, that are usually available in many European cities. Even if the justification of assumptions underlying the use of Markov stochastic systems to simulate the urban mobility would require further studies, we show some preliminary results on the city of Bologna (North Italy) that show the capacity of our model to reproduce the observed traffic flows.