On acceleration of traffic flow

The paper contributes to the derivation and analysis of accelerations in freeway traffic flow models. First, a solution based on fluid dynamics and on pure mathematical manipulations is given to express accelerations. The continuous-time acceleration is then approximated by a discrete-time equivalent. By applying continues time microscopic and macroscopic traffic flow velocity definitions, spatial and material derivatives are used to describe the continuous-time and exact changes in the velocity vector field. A forward-difference Euler method is proposed to discretized the acceleration both in time and space. For applicability purposes the use of average quantities is proposed. The finite-difference approximation by space-mean speed is shown to be consistent, and its solution is convergent to the original continuous-time form. As an alternative, the acceleration obtained from a second-order macroscopic freeway model by means of physical interpretation [1] is analyzed and found to be an appropriate discrete approximations. Comparative remarks as well as future research questions conclude the paper.