Abstract. L. Lakatos introduced a queuing system in which the waiting time V of a customer is increased up to a value multiple of T. The model is motivated by a problem occurred in aviation. Indeed, T is just the aircraft round time of the emergency circle as soon as the runway is occupied. In the presented paper, a queuing system is considered in which V is increased up to the time T₁x+T₂y, where T₁ and T₂ are constant time intervals (round times of two emergency circles) whereas x and y are V-dependent integers (numbers of rounds). An ergodic theorem is proved for a proper embedded Markov chain. An algorithm is given to compute x and y given V.

Keywords: queuing systems, retrial systems, Lakatos systems, aircraft landing.