  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.
