A topological approach for identifying pricing controller locations to ensure controllability of transportation networks

To use efficiently the infrastructure of transportation networks, control strategies have been developed with the aim to reduce negative externalities, such as congestion and pollutant emissions. Previous works demonstrated that the maximum performance achievable by traffic control policies depends on the number and location of controllers employed, which implies the need to determine a set of controllers capable of fully controlling the underlying transportation network. Various approaches have been explored in the literature to locate controllers on networks, however a gap remains in terms of scalability as the methods proposed often exhibit heavy computational complexity. In this paper we aim to propose an approach capable of locating pricing controllers on transportation networks that is scalable, such that it can be applied on large instances, such as city-sized or regional networks. For this purpose, we propose a topology-based approach, adapted from the sensor location problem, as both problems share similar characteristics. We validate our proposed approach by analyzing the performance of controller sets produced on a wide range of artificially generated network ensembles. The analysis we provide reveals that the method proposed, while being easily applicable on large instances, is capable to locate an efficient controller set, and to redirect flows on the network so as to reduce the total time spent by road users.