We study(batch arrival)MX/G/1 queues without vacations under random order of service(ROS)discipline.By considering the conditional waiting times given the states of the system when an arbitrary message arrives,we derive the Laplace-Stieltjes transforms of the waiting time distributions and explicitly obtain their first two moments.The relationship for the second moments under ROS and first-come first-served disciplones is shown to be precisely the same as that found by Takacs and Fuhrmann for(single arrival)M/G/1 queues
