A Discrete-Time Queueing System with General Inverse order of serviceand priorities

In this paper we study an inverse order general discipline for the service times with priorities, where customers in the server and arriving customers to the system can draw for a place in the server and it the head of the queue, moreover the possibility of changes in its lengths is considered. We obtain equations for the stationary probability of the number of states in the system M|G|1|∞ with inverse general discipline for the service time and priorities, also an algorithm for the solution of this equations can be found. Besides, some variant of the system under study are given.