Optimization vs randomness for car traffic regulation A. Cascone (1) , R. Manzo (1) , B. Piccoli (2) , L. Rarit` a (2) (1) Department of Information Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy (2) Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Roma, Italy January 24, 2014 Abstract This paper focuses on the differences among the analytical optimization of traffic flow on a road network, modelled by a fluid - dynamic approach, and a dynamic random approach. In particular, two real urban networks are presented: Re di Roma Square, in Rome, and Via Parmenide crossing, in Salerno. With such two examples, it is possible to show that dynamic random simulations are not the right choice for the improvement of traffic conditions. 1 Introduction In this paper, we focus the attention on the urban traffic regulation through a random approach and an optimization algorithm for a fluid - dynamic model, introduced in [3]. The aim is to show that a dynamic random approach is absolutely not convenient in order to improve traffic conditions, as suggested in [15]. In particular, in [15], there is a discussion about the benefits due to the synchronization among a series of traffic lights using a cellular automata. The simulation of traffic flows are made through a different choice of signal period T and a time delay δ. Moreover, it is shown that a correct synchronization gives some improvements only when the traffic density is low. When the traffic demand surpasses a given saturation value, the synchronization is useless and also the use of a fixed T and a random delay δ, assigned to each traffic light, lets the throughput remain the same. The principal aim of this paper is to use network models, opposed to single roads, in order to verify the performances of traffic regulation algorithms. We show that an optimization approach outperforms a random one, even in heavy traffic conditions. Also, the use of random parameters for traffic regulation can lead to traffic conditions in which accidents are very frequent. The mathematical modelling of vehicular traffic requires, first of all, the choice of the scale of representation. There are many examples of models at any scale, from the microscopic to the macroscopic through the kinetic one. Each of them implies some technical approximations, and suffers therefore from related drawbacks, either analytical 1