Approximation of velocity-density function for traffic flow model with obstacle problem in Jalan Merdeka Bandung

This paper discuss an approximation of velocity-density function in simple traffic flow model with obstacle problem on a single road line. The traffic flow model is described by a macroscopic model where the conservation of laws involved. The traffic flow model in this paper is based on two conditions which are the obstacle and free obstacle conditions. In order to obtain the relation between velocity and density parameters, then the observation procedure is executed. The observation data consists of the characteristics of traffic flow such as density and average speed of the vehicle. The data is obtained from direct observation in Jalan Merdeka Bandung, West Java, Indonesia. There are 8 (eight) velocity functions are obtained by using a polynomial function approximation method. In the result of linear velocity function, the velocity-density function v(ρ) = -50.72ρ + 45.08 is obtained with free obstacle problem. Meanwhile, with the present of obstacle problem, the function is shown v(ρ) = -15.73ρ + 21.09. Moreover, trough the numerical simulations, using velocity-density function with obstacle, the numerical result shows congestion occurs by a shock wave phenomenon in traffic flow simulation.