Mathematical modelling of traffic flows on controlled roads

A model of transient single-lane traffic flows is proposed, taking into account the basic components used to control road traffic (traffic lights and “sleeping policemen”), which is radically different from those traditionally considered in continuum mechanics. The model takes into account the main property of traffic flows, namely, the property of self-organisation, and enables the conditions required to ensure maximum carrying capacity to be described correctly both qualitatively and quantitatively, as well as the occurrence and evolution of “travelling traffic jams” on roads, as well as the effect of road traffic control units.