Optimised Traffic Flow at a Single Urban Crossrtoads: Dynamical Symmetry Breaking

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We propose a stochastic model for the intersection of two urban streets. The traffic state at the crossroads is controlled by a set of traffic lights, which periodically switch to red and green with a total period of T. Vehicular dynamics is simulated and total delay experienced by the traffic is evaluated within a definite time interval. Minimizing the delay give rises to the optimum signalization of traffic lights. It is shown that two different phases are identified. In the light traffic phase, the green times should be distributed to the streets on an equal basis. In the congested phase, minimizing the delay enforces us to break the symmetry between the roads by allocating the majority of green times to one of the roads. In contrast to our common sense, dividing the green times on an equal basis, leads to unfairness to drivers.