Possible Self-Organised Criticality and Dynamical Clustering of Traffic flow in Open Systems

We focus in this work on the study of traffic in open systems using a modified version of an existing cellular automaton model. We demonstrate that the open system is rather different from the closed system in its 'choice' of a unique steady-state density and velocity distribution, independently of the initial conditions, reminiscent of self-organised criticality. Quantities of interest such as average densities and velocities of cars, exhibit phase transitions between free flow and the jammed state, as a function of the braking probability R in a way that is very different from closed systems. Velocity correlation functions show that the concept of a dynamical cluster, introduced earlier in the context of granular flow is also relevant for traffic flow models.