  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.
