We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time intervals. Minimising the total delay of both streets gives rise to the optimum signalisation of traffic lights. We propose some traffic responsive signalisation algorithms which are based on the concept of cut-off queue length and cut-off density.

We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated and the delay experienced by the traffic at each individual street is evaluated. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalization schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic-light signalization schemes.

We propose a two dimensional probabilistic cellular automata for the description of traffic flow in a small city network composed of two intersections. The traffic in the network is controlled by a set of traffic lights which can be operated both in fixed-time and a traffic responsive manner. Vehicular dynamics is simulated and the total delay experienced by the traffic is evaluated within specified time intervals. We investigate both decentralized and centralized traffic responsive schemes and in particular discuss the implementation of the green-wave strategy. Our investigations prove that the network delay strongly depends on the signalisation strategy. We show that in some traffic conditions, the application of the green-wave scheme may destructively lead to the increment of the global delay.