Abstract:
Traffic congestion is a major challenge in the transport industry, affecting both the
economy and environment. Designing efficient and sustainable transport models
requires a multifaceted approach. One of these facets is extracting optimal trajectories
for each passenger type, a task well-addressed by the principles of optimal transport
theory. By leveraging optimal transport principles, we can model passenger flows in
networks to reduce congestion. However, recent research based on optimal transport
overlooks crucial factors such as environmental impacts, multilayer transport
network analysis, and fails to consider practical constraints such as road capacity
limitations.
In response to these gaps, this thesis introduces optimal transport-based methods
for modeling flows within multilayer transport networks, with a primary focus
on addressing congestion and optimizing traffic flow. Additionally, we extend the
application of optimal transport theory to tackle community detection problems
within networks. This broader scope allows us to not only enhance our understanding
of traffic dynamics but also explore diverse applications of optimal transport in
networks.
First, we propose efficient methods, based on optimal transport theory, for modeling
passenger flows within multilayer transport networks. Our approach generates both
distributed and single-trajectory flows for each passenger types, and shows how
these trajectories can alleviate traffic congestion and reduce CO2 emissions. Second,
to address the limitation of existing methods on realistic constraints in transport
network, we delve into a constrained framework. This framework accommodates
nonlinear and non-convex constraints within optimal transport problems, providing
a computationally efficient tool for minimizing congestion. As an application, we
consider real multilayer transport networks where each layer is associated with a
different transport mode, and show how the traffic distribution varies with relevant
quantities (such as transport regime, origin-destination pairs, imposed constraints,
etc.) across layers.
Lastly, we present an optimal transport-based approach for detecting communities in
networks. By incorporating the Ollivier-Ricci curvature, our model provides various
transport regimes that allow for better control of information flow between node
neighborhoods. The algorithm not only exhibits improved accuracy in identifying
communities, but also outperforms conventional OT-based methods, providing
deeper insights into geometric approaches to analyzing complex networks. Overall, the methods presented in this thesis enhance our understanding of traffic
dynamics within multilayer transport networks, provides valuable insights that
contribute to sustainable transport systems. By addressing congestion through
optimal transport-based approaches, we pave the way for more efficient and envi-
ronmentally friendly transport systems. Furthermore, extending the application
of optimal transport to community detection problems highlights its versatility in
analyzing complex networks beyond transportation networks.
Dynamics of networks