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We study (batch arrival) M'/G/~ queues withlwithout 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 mements under ROS and first-come first-served disciplines is shown to be precisely the same as that found by TakAcs and Fuhrmann for (single arrival) M / G / l queues.

WAITING TIME ANALYSIS OF M^X/G/1 QUEUES WITH/WITHOUT VACATIONS UNDER RANDOM ORDER OF SERVICE DISCIPLINE