Modeling of Traffic Flow on Roundabouts
Keywords:Traffic flow, Hyperbolic Conservation Laws, Godunov Method, CFL condition,
The aim of this research is to create the modeling of roundabouts. First of all, the three-arm roundabout is created for validation with the existing model. Then, the model is expanded to the four-arm roundabout. In the development of a modern intelligent transportation system, the effectiveness of dealing with the non-linear, time-varying and congested traffic flow is imperative in achieving traffic control and accuracy. In this paper, the roundabout is modelled as a circuit of 2×2 junction comprising a main lane and a secondary lane. The rotation of the roundabout is in the clockwise direction, as in the case of Malaysia. In mathematical modelling, the traffic flow is created, based on one-dimensional hyperbolic conservation laws which are represented by non-linear partial differential equations where the unknown variable is a conserved quantity. As a scheme used in the computation and analysis, the Godunov method computes the fluxes at the interfaces of each cell in order to advance the solution of a Riemann Problem. In addition, the Courant-Friedrichs-Levy (CFL) condition is proposed and used to ensure the stability and accuracy of the numerical algorithm where the time step is not a constant. The optimization on the roundabout for Total Travel Time and Total Waiting Time with several parameters is applied to generate numerous results which will assist in assessing the reasonableness of the roundabout. The comparison data of the three-arm roundabout with our model and the existing model are discussed. In comparison, our results show similar properties with higher readings than in other published papers because our calculations involved all arms and roads. In addition, the comparison data between three-arm and four-arm roundabouts are reasonable and logical. Lastly, our model is more flexible and realistic, as compared to the existing model.
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