Physics of traffic Gridlock in a city: a study of the spreading of traffic jams on urban street networks (2016)
Abstract. Traffic congestion has profound and varied impacts on modern society, yet characterizing on a city scale the transition that gives rise to the congestion remains an elusive task. The challenge lies in understanding the role of the interplay between topology and spatial dynamics in this traffic phenomenon. In this thesis we combine cellular automata modelling with analysis tools from statistical physics to study the emergence of congestions at road (street), grid (neighbourhood) and network (city) levels. At street level, we shown for at least two traffic cellular automata that implementing a simple Monte Carlo exploration of the driving rules reproduces the fundamental diagram of a single road segment. Next, by applying tools of percolation theory, we unveiled the underlying mechanism of jamming process in the Biham-Middleton Levine model, i.e., a paradigmatic model for car traffic, both on square and honeycomb grids, solving a puzzle of more than a decade on the origin of the intermediate states of this model on square grids and pointing out the relevance of both asymmetry and the underlying grid on the model's behaviour. Finally, we used the origin-destination matrices obtained from mobile phone data to simulate car by car the traffic on the detailed road network of five large cities: Rio, Boston, San Francisco bay, Porto and Lisbon. We found at this network level that the characteristic recovery time the system takes to unload is proportional to the fraction of road infrastructure being used and the mean travel time on all trips. In addition, we study the emergence of congestion when the number of cars increases by keeping the trip distributions and street capacities unchanged. Our last findings strongly support the notion that the transitions to urban traffic gridlock resemble the direct percolation universality class and can be approached with the framework of non-equilibrium phase transitions. Our work illustrates the power of a computational description at the level of each car with the solid theoretical framework of statistical physics to analyze the origins and behaviour or vehicular traffic congestion.