On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals (Q1611999)

The paper deals with finite- and infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the late arrival system with delayed access as well as the early arrival system. Using simple arguments such as the balance equation, ``rate in equals rate out'', relationships among the stationary queue lengths at arrival, at departure, and at random epochs are derived. Such relationships hold for a broad class of discrete-time queues with D-BMAP arrivals.