Adaptive drivers in a model of urban traffic

– We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers’ behavioral parameters via numerical simulations and mean-field analytical arguments. In particular, we identify a phase transition between a lowand a high-density phase. In the latter, inductive drivers may surprisingly behave worse than randomly selecting drivers. After the seminal works [1, 2, 3], models of vehicular traffic have enjoyed a continuously increasing interest among physicists (see e.g. the excellent reviews [4, 5, 6]), and substantial progress has been achieved in understanding the origin of many empirically observed features. In several cases, traffic models have also revealed deep connections to important out-of-equilibrium systems in statistical mechanics. The celebrated NaSch cellular automaton [2, 7], for instance, is a close relative of the totally asymmetric simple exclusion process (TASEP) [8], and of the KPZ-class of surface growth models [9, 10]. Urban traffic has also been extensively studied. Remarkable examples are BML models [1, 5], where vehicles are bound to travel on a lattice, representing the network of streets, with their time-evolution governed by TASEP-like rules. Typically, increasing the density of vehicles, a sharp transition occurs from an unjammed regime with finite average velocity to a jammed state where cars are blocked in a single large cluster spanning the entire lattice. In these cellular-automaton type of models, the dynamics of drivers does not pursue an explicit goal, like minimizing traveling times. Here we introduce a different class of models. We postulate that each driver has a finite set of feasible routes for going between two points in a city and that, on each day, he/she tries to choose the least crowded one using a simple learning process [11]. Our principal aim is to investigate whether – and in which traffic conditions – inductive drivers behave more efficiently than purely random ones. A similar question arises in the Minority Game (MG) [12], and this affinity constitutes the starting point of our analysis. More precisely, upon increasing the density of vehicles we find a transition from a phase where drivers are unevenly distributed over streets to one where streets are equally trafficked. In this latter phase, depending on their learning rates, inductive drivers can behave worse than randomly selecting drivers because of crowd effects.