T. Luspay, B. Kulcsár, I. Varga, S.K. Zegeye, B. De Schutter, and M. Verhaegen, "On acceleration of traffic flow," Proceedings of the 13th International IEEE Conference on Intelligent Transportation Systems (ITSC 2010), Madeira Island, Portugal, pp. 741-746, Sept. 2010.
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 discretize 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 (see "Model-based traffic control for balanced reduction of fuel consumption, emissions, and travel time," by S.K. Zegeye, B. De Schutter, H. Hellendoorn, and E. Breunesse, Proceedings of the 12th IFAC Symposium on Transportation Systems, Redondo Beach, California, pp. 149-154, Sept. 2009) is analyzed and found to be an appropriate discrete approximation. Comparative remarks as well as future research questions conclude the paper.