Modeling of Traffic Flow on Roundabouts

Abstract

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.

The fitting of roundabout model with gradient-based minimization

“…In this research, the model of roundabout is described in the paper as "Modeling of Traffic Flow on Roundabouts" [18]. Furthermore, the model has been modified with the coupling of waiting system in demand as in the paper "Modeling and Simulation of Roundabout with Waiting System" [19].…”

Modeling and Simulation on Roundabout with Waiting System

“…Firstly, based on our four-arm roundabout model, it is J n , n = 1, 2, 3, 4 where each arm is designed as a 2 × 2 circuit arm junction and the main lane, I and the secondary lane, r are described by arcs, and arm junctions by vertexes [3]. The main lane is partitioned by the arm junction I n , I n+1 , n = 1, 2, 3, 4, and the periodic boundary condition is I 5 = I 1 (Figs.…”

“…It also includes some fixed constants where f max = 0.66, ρ c = 0.66, and γ max r1 = 0.65. Lastly, the simulation on both the three-unit length and four-unit length circumferences of the roundabout with the total time and space step will be T = 50 and x = 0.1, respectively [3].…”

“…The calculations of Total Travel Time (TTT ) on the road network and Total Waiting Time (TWT ) at the entrance of the secondary road are the inputs for analysing the effectiveness of the waiting system. The equations are as follows [3],…”

“…First of all, the installation of a waiting system is on our four-arm roundabout model where this model is a modification and expansion of their three-arm roundabout model. Our model is more realistic and flexible [3]. The realistic parts of our model are the flow on each arm junction, either the main lane or the secondary lane is different, and the calculation of Total Travel Time and Total Waiting Time involves all the main lanes and secondary lanes.…”