Priority queues with batch Poisson arrivals

This paper studies batch arrival M^X/G/1 priority queues without and with (multiple or single) vacations. Applying the delay busy cycle analysis, the authors explicitly derive the Laplace-Stieltjes transforms and the first two moments of the waiting time distributions for the nonpreemptive (head-of-the-line) and preemptive resume priority queues. Conservation laws for batch arrival systems are also mentioned. The results in this paper cover many previous results as special cases.