Relationship between queue length and waiting time in a stationary discrete-time queue

The authors consider a discrete-time single-server queue with batch arrivals. Assuming that the arrival process of batches is renewal and using the point process approach, they present a relationship between characteristics of queue-length and waiting-time distributions. This relationship enables us to obtain a distributional form of Little’s law (DFLL) for a multi-class priority queueing system with the head-of-the-line or preemptive-resume rule, assuming a batch Bernoulli input process for each class.