A complex networks approach to traffic flow theory: measures and models

Abstract

In this thesis, we developed a research direction that combines the theoretical concepts of complex networks with practical needs and applications in the field of transportation engineering. As a first objective we analyzed the phenomenon of congestion propagation in a city trying to synthesize - hence reproduce - dynamical systems of complex nature in a well-established and elegant mathematical-physical structure. With this perspective, we identified in the reaction-diffusion-like system the most natural way to describe how congestion spreads in the road networks according to elementary diffusion mechanics (linear) and self-enhancement of traffic jam (non-linear). This analysis showed that models with a small number of parameters can reproduce dynamic network patterns without the need for very detailed and accurate input data. Another topic we dealt with was to indicate centrality measures expressively defined for congested road networks. Inspired by classical complex networks theory, we defined more suitable and exploitable indices in the field of transport and urban mobility that consider in a dynamic framework both the network topology and the spatial distribution and magnitude of congestion. For this scope, we proposed the definition of dynamical efficiency for single and multi-layer networks. Dynamical efficiency responds adequately to the need for classification of urban areas based on their accessibility and on the influence that traffic has, region-par-region, on the average travel time of passengers. This measure combines and exploits local information (average road speeds, functional type) with the complex structure of the road network and the opportunity for convenient alternative routes. Furthermore, by generalizing the dynamical efficiency definition in a multimodal environment, we are able to identify the most attractive intermodal exchange stations (for example, bus-metro, private car-public transport) and estimate their optimal capacity service. This opens up the workspace for innumerable engineering applications and accurate evaluations of the impact of high traffic demand in each transport system. Among the same lines, another chapter of this thesis concerns a measure of simplicity for paths and allows us to study an extended database of real trajectories and classify the drivers according to their priority path choice factors. Finally, we studied the congestion propagation under a topological perspective as an aggregation of connected components of congested links. By analyzing the distribution of their sizes and the average merging rate we are be able to (i) point out important premonitory signals that anticipate imminent traffic jam (namely morning and evening peak-hours), (ii) to visualize the most critical bottlenecks and (iii) to better understand the causal inference between components of congestion and the average network speed.