A note on the distributional Little’s law for discrete-time queues with D-MAP arrivals and its application

For a class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process), we present a distributional Little’s law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue as an example, we demonstrate how this relation can be utilized to get the desired distribution of the number of customers. Sample numerical results are presented at the end.