Reducing selfish routing inefficiencies using traffic lights

In this paper we equip congestion games with traffic lights, modelled as junction-based waiting cycles, therefore enabling more realistic route planning strategies. Using the SUMO simulator, we show that our modelling choices coincide with realistic routing behaviours, in particular, that drivers' decisions about route choices are based on the proportion of red light time for their direction of travel. Drawing upon the experimental results, we show that the effects of the notorious Braess' paradox can be avoided in theory and significantly reduced in practice, by allocating the appropriate traffic light cycles along a transport network. 1 Introduction Congestion games are the standard framework of algorithmic game theory employed to study the equilibria of traffic flows [ Roughgarden, 2005 ] . They are non-cooperative games of perfect information where self-interested actors choose sets of available resources, e.g., roads, and where the cost of each resource depends on its overall usage. A well-known phenomenon occurring in these games is Braess' paradox [ Braess, 1968 ], i.e., the existence of traffic networks that suffer from the increase of total cost when the cost of an available resource strictly decreases. While Braess' paradox is an important mathematical result, its existence relies on rather constraining modelling assumptions, as congestion games abstract away from a number of important features of real-world road networks. Notably, their cost functions assume no clashes between antagonistic traffic flows which, in the real-world, are typically resolved by interdependent control mechanisms such as traffic lights. Contact Author Traffic lights are themselves an important object of research in Artificial Intelligence, as understanding their best configuration is paramount for the branch of AI concerned with optimising traffic [ Chouhan and Banda, 2018; Laszka et al., 2016; Lopez et al., 2018; Pol and Oliehoek, 2016 ] . However, their effect on the traffic flow equilibria is yet to be understood.