On the functional form of the speed-density relationship-I: General theory

In this work a functional form for the speed-density relationship is presented. This functional form is made up of a nondimensional spacing, the equivalent spacing and of a function, the generating function, whose argument is the equivalent spacing. This functional form is derived by means of two different arguments. The first argument is based on the set of properties that the volume-speed-density relationsips should satisfy. The second one arises when applying a dimensional analysis to a generic car-following model. Finally, several examples of generating functions are shown.