ΣD-BMAP/D/1/K queuing system with priorities

We consider the case of discrete-time queuing system with preemptive priority discipline, which is fed by two discrete-time batch Markovian arrival processes (D-BMAP), and denoted in Kendall´s notation as D-BMAP+D-BMAP/D/1/K. We show that for late arrival system model with delayed access non-preemptive, preemptive-repeat and preemptive-resume priority disciplines are are similar and can be treated simultaneously. Given this system we obtain probability functions of the number of lost packets and the delay of the arrival for low priority arrival process. Applications of the proposed model are then considered.