Abstract
This paper considers a fluid dynamic traffic flow model appended with a closure linear velocity-density relationship which provides a first order hyperbolic partial differential equation (PDE) and is treated as an initial boundary value problem (IBVP). We consider the boundary value in such a way that one side of highway treat like there is a traffic controller at that point. We present the analytic solution of the traffic flow model as a Cauchy problem. A numerical simulation of the traffic flow model (IBVP) is performed based on a finite difference scheme for the model with two sided boundary conditions and a suitable numerical scheme for this is the Lax-Friedrichs scheme. Solution figure from our scheme indicates a desired result that amplitude and frequency of cars density and velocity reduces as time grows. Also at traffic controller point, velocity and density values change as desired manner. In further, we also want to introduce anisotropic behavior of cars(to get more realistic picture) which has not been considered here. Doi: 10.12777/ijse.5.1.25-30 [How to cite this article: Sultana, N., Parvin, M. , Sarker, R., Andallah, L.S. (2013). Simulation of Traffic Flow Model with Traffic Controller Boundary. International Journal of Science and Engineering, 5(1),25-30. Doi: 10.12777/ijse.5.1.25-30]
Highlights
At present time we cannot deal our life not a single day without vehicles likes bus, car, taxi, rickshaw etc. for our communication
We develop a finite difference scheme for our traffic flow model as an (IBVP) which has been presented before numerical simulation section
We present an outline of mathematical modeling, a partial differential equation as a mathematical model for traffic flow
Summary
At present time we cannot deal our life not a single day without vehicles likes bus, car, taxi, rickshaw etc. for our communication. Vehicles in traffic flow are considered as particles in fluid; further the behavior of traffic flow is described by the method of fluid dynamics and formulated by hyperbolic partial differential equation This model is used to study traffic flow by collective variables such as traffic flow rate ( ) (flux) q(x,t) , traffic speed v x,t and traffic density ( ) r x,t , all of which are functions of space, x Î R and time t Î R +. In the paper (Haberman, 1977 and Klar et al, 1996) authors consider the LWR model This model describes traffic phenomena resulting from interaction of many vehicles by discussing the fundamental traffic variables like density, velocity and flow.
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