A cellular automata model for urban traffic with multiple roundabouts

Urban transportation with multiple roundabouts is facing significant challenges such as traffic congestion, gridlock and traffic accidents. In order to understand these behaviors, we propose a two-dimensional cellular automata (CA) model, where all streets are two-way, with one lane in each direction. To allow the turning movement, a roundabout is designed for each intersection where four roads meet. The distance between each pair of roundabouts is configured with the parameter K while the turning behavior of drivers is modeled by a parameter γ. To study the impact of these different parameters on the urban traffic, several traffic metrics are considered such as traffic flow, average velocity, accident probability and waiting time at the entrance of roundabout. Our simulation results show that the urban traffic is in free flow state when the vehicle's density is low enough. However, when the density exceeds a critical density ρc, the urban traffic will be in gridlock state whenever γ is nonzero. In the case where γ=0, the urban traffic presents a phase transition between free flow and congested state. Furthermore, detailed analysis of the traffic metrics shows that the model parameters (γ, K) have a significant effects on urban traffic dynamics.