The mean queue content of discrete-time queues with zero-regenerative arrivals

This letter investigates a single-server discrete-time queuing system with single-slot service times. For a broad class of arrival processes, a closed-form expression for the mean queue content in steady state is obtained. Apart from being stationary-ergodic, the arrival process adheres to a regeneration property when there are no arrivals in a slot. Well-studied arrival processes such as autoregressive arrival processes and M/G/∞M/G/∞-input or train arrival processes adhere to this property.