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.

Roundabouts play a crucial role, especially in the moderately populated areas and places which are largely residential and are in the vicinity of schools where traffic lights are not in place. Though roundabouts can significantly solve the congestion problem on intersection roads, the mobility and time delay depend on the capacity of vehicles. In high traffic moments, the congestion will affect the smooth traffic flow and the queue length on the secondary lane. According to systematic regulations, the cars from the secondary lane need to wait for the cars on the main lane to move forward so as to create a sufficient space to enter the roundabout. In addition, the incoming cars from the main lane have the priority to pass through the arm junction, and the cars on the secondary lane have to make sure these incoming cars are totally driven through the arm junction, before they can be allowed to enter the roundabout. Based on the phenomena mentioned, a long waiting time takes place on the secondary lane. Therefore, a waiting system needs to be installed to facilitate traffic flow on the secondary lane as well as to determine the number of cars crossing the arm junction from the incoming main lane to the outgoing main lane. The plots of Total Travel Time, Total Waiting Time and queue length with different parameters are simulated and discussed. Finally, the results presented in certain simulated situations, produced the tailback on the secondary lane and occasionally, eased the traffic flow due to the mentioned priority regulations.