Priority queues with batch Poisson arrivals (Q1178734)

The paper studies batch arrival \(M^ x/G/1\) priority queues without and with (multiple or single) vacations. Applying the delay busy cycle analysis, it explicitly derives 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 the paper cover previous results as special cases.