Waiting time analysis for \(\text{M}^X/\text{G}/1\) priority queues with/without vacations under random order of service discipline (Q5932231)

The authors investigate nonpreemptive and preemptive-resume priority queues with single and multiple vacations, and those without vacations under random order of service. Arrivals in batches of customers with equal priority according to independent Poisson processes are assumed. There are altogether nine types of queues, and for all of these explicit results for the first two moments of the waiting time distribution in steady state are derived. In numerical examples these moments are plotted as functions of the traffic intensity.