Published In: Pakistan Journal of Science

Abstract:

The Lighthil-Whitham-Richards (LWR) model characterizes traffic flow based on the conservation of vehicles. Changes in velocities are based on the changes in densities which is given by equilibrium velocity distributions. The LWR model is employed with target to attain the equilibrium velocity. In this paper, density behavior of the LWR model is investigated using different equilibrium velocity distributions. The numerical solution of LWR model is obtained by applying the first order upwind scheme (FOUS). The stability of the numerical scheme is achieved by the Courant-Friedrich-Lewy (CFL) conditions. The performance results show that the density behavior of LWR model is realistic and smooth with target to attain the Greenshields, Underwood and Northwestern equilibrium velocity. Whereas, with target to attain the Greenberg velocity, the density behavior of LWR model is not realistic, and the variations in density grow over time.