The dynamical behaviors of groups of airspace sectors are not trivial to be analyzed withoutappropriate theoretical tools. In this paper, we suggest a discrete model based on cellular automata to express the air traffic dynamics and complexity in the controlled airspace. Discrete time simulations have been performed with random selected scenarios of traffic and with independent sector parameters to investigate the impact of availability of local sectors on the whole state of the airspace. Obtained results show the existence of a traffic threshhold that leads to an experimental saturation of airspace. In the test scenario of 900 sectors with fly overtime ranging from 5 to 10 minutes, and sector capacity ranging from 13 to 17 aircraft per time unit, the resulting traffic threshold was 18000 flights.