Workload of Queueing Systems with Autocorrelated Service Times

The queuing model with autocorrelated service times is studied with respect to workload, i.e., the time needed to serve all the customers in the queue. Specifically, new formulas for the probability density of workload, its tail, the average value, and entropy are derived and illustrated using numerical examples. Both time-dependent and steady-state cases are covered. It is also demonstrated that the average workload may reach surprisingly large values, exceeding several times the product of the average queue size and the average service time.