Cellular Automata for a Traffic Roundabout

We propose a cellular automaton model for a typical traffic roundabout to regulate traffic flow from four different directions. In the four-way symmetrical case, the number of parameters reduce from sixteen to four. As these four parameters change, we observe three distinct traffic phases: free flow, congestion, and gridlock. As the inflow increases, free flow transits to congestion when the interweaving traffic is light. When the interweaving traffic is heavy, free flow transits directly to gridlock instead. The traffic interweave is characterized by a new parameter X. We present both numerical simulations and analytical discussions.