Time-related analysis of small world and scale-free transportation networks.

Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web are only a few examples of Small World and Scale-free complex networks, i.e. systems composed by a large number of highly interconnected dynamical units. During the last ten years these kinds of systems have been the subject of many studies related to comprehend their common structural properties and their dynamics. Small World and Scale-free networks are supposed to be very stable and robust structures in case of failures or deliberate attacks on the system. Moreover, due to their well-known properties, they allow to model several real networks in order to find the key elements for a complete and efficient communication activity between nodes. This thesis introduced a new mathematical tool developed by the author called Time=net.work. The latter has got the purpose to extend the above mentioned complex networks theories to transportation systems under a new time-related point of view. Analysis have been taken firstly on Berlin Transportation Network and then to several other test cases. The relative results help in finding statistical properties about the connectivity and the structure of such system both topologically and considering the travel time and the frequency of the scheduled services. This is a new approach on robustness of transportation networks which allows to find which and how many nodes have to assurance their functionality in order to provide a desired Level of Service in case of failures or deliberate attacks.