Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 365-392
doi:10.1155/S1048953300000320
Abstract
We study MX/G/1 nonpreemptive and preemptive-resume priority queues
with/without vacations under random order of service (ROS) discipline
within each class. By considering the conditional waiting times given the
states of the system, which an arbitrary message observes upon arrival, we
derive the Laplace-Stieltjes transforms of the waiting time distributions
and explicitly obtain the first two moments. The relationship for the
second moments under ROS and first-come first-served disciplines extends
the one found previously by Takacs and Fuhrmann for non-priority single
arrival queues.