Exact solution for a two-type customers retrial system

Based on a real problem connected with the landing of aeroplanes we examine a special queuing system, where peculiar conditions prevail. In such systems a request for landing can be serviced upon arrival if the system is free. When other planes are using the runway or waiting to land, the entering plane has to start a circular manoeuvre and can put its further requests when it comes to the starting point of its trajectory. Because of possible fuel shortage it is natural to use the FIFO rule. The article describes a more generalized form of such a system. This serves two types of customers, but one of them is accepted only if the system is in free state. Together with generating functions of probabilities we also give the condition of ergodicity. Theory is underpinned by numerical investigation.