Modelling of Road Traffic

This chapter explores mathematical models of road traffic dynamics, emphasizing both continuum and microscopic perspectives. The discussion begins with the kinematic theory of traffic flow, which treats vehicles as a compressible fluid, enabling the analysis of density, flux, and wave propagation. Applications include the effects of traffic lights, mechanisms of congestion formation, conditions for the formation of the first shock, and the impact of road narrowing. A research-oriented case study investigates the feasibility of establishing a green wave in infinity street. The framework is extended through generalizations of kinetic theory, incorporating more complex driver behaviors (for instance, adjustment of the speed) and heterogeneous conditions. Complementing this, individual car models capture vehicle-level dynamics, particularly highlighting the role of instabilities in queues through the introduction of a delay term.