A recent paper gave an elementary analysis of the effect of control procedures on the flow of air traffic. It was shown that the average delay experienced by aircraft landing at an airport increases rapidly as the arrival rate approaches the maximum handling capacity of the airport. It is the object of the present paper to give a more rigorous treatment of the problem and to derive the distribution of delays under different traffic conditions.

The maximum handling capacity of an airport is the greatest rate at which aircraft can enter the airport with absolute safety. It is determined by the safe minimum separation between successive landings. An aircraft arriving in the central zone with less than the safe minimum separation is withheld from landing until the minimum interval has elapsed.

In the following it is generally assumed that aircraft cross the boundaries of the control zone from random directions with random separations, the mean arrival rate being constant. Aircraft which follow their predecessors too closely are assumed to be delayed for a minimum period so that none lands with an interval less than the safe minimum. As a simplification it is assumed that no aircraft takes off from the airport.