Maximum Entropy Approach to Data Driven Markov Models for Congestion Formation in Transport Networks

The possibility to collect large data sets by the Information and Communication Technologies 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 of knowing the individual behavior even to simulate collective effects. Recent studies have pointed out universal properties that characterize the development of congestion in a transport network, despite the dynamics of transport networks being different among different cities. These results 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 simulates the congestion formation on a transport network using apriori information, that are usually available in many European cities. Even if to justify the use of Markov systems to simulate the urban mobility would require further studies, we show some preliminary results of our approach on the real case of Bologna (a city in North Italy), that point out the capacity of our model to reproduce the observed traffic flows.