Controllability of complex flow networks

When left uncontrolled, complex flow networks are susceptible to negative externalities and tend not to be used to their full potential. This work focuses more specifically on the specific instance of transportation networks that are subject to constantly increasing demand. Control strategies, based on increasingly promising technological advancements, have been developed with the aim to exploit the full potential of the existing transportation infrastructure. To improve the current state of transportation networks, control strategies rely on control technologies to impact road users on networks and redirect them, such as to improve the situation by avoiding delays, for example. However, the problem of identifying the required controller numbers, types, and locations has received little attention in the current literature. Existing research works proposed approaches to the problem but often either do not provide complete control over the considered network or lack scalability, thus are not applicable on any type and size of networks.

In this dissertation, we aim at filling this gap by providing a general methodology and proposing various approaches to this problem. The first part of this work focuses specifically on studying the problem of fully controlling a transportation network and provides various approaches. Their capacity to actually impact and control transportation networks is assessed empirically, showing that the proposed approaches can fully control small networks.

The second part studies the problem of scalability and provides a new method that is proved to be able to provide an efficient set of pricing controllers while being scalable. This approach is later improved by integrating flow information and demonstrated to be more reliable in the specific case where the demand is irregularly distributed over the considered network, which is a common setting in real transportation networks. Additionally, the proposed methods are applied and tested over the network of Luxembourg, demonstrating the scalability of the approaches and their capacity to improve the current state of large realistic networks subject to heavy congestion.