We consider a discrete time queueing system where the service of a customer may start at the moment of arrival or at moments differing from it by the multiples of a given cycle time. One finds the distribution of waiting time and its mean value. These results give possibility for the numerical optimization of cycle length. The original model was raised in connection with the landing process of airplanes, but it appears to be an exact model to describe the functioning of a node at the transmission of optical signals.