| Article ID: | iaor20013667 |
| Country: | Japan |
| Volume: | 43 |
| Issue: | 4 |
| Start Page Number: | 455 |
| End Page Number: | 468 |
| Publication Date: | Dec 2000 |
| Journal: | Journal of the Operations Research Society of Japan |
| Authors: | Takagi Hideaki, Takahashi Yutaka, Hasegawa Toshiharu, Kawasaki Norikazu, Hong Sung-Jo |
| Keywords: | queues: applications |
We study (batch arrival) MX/G/1 queues with/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 disciplines is shown to be precisely the same as that found by Takács and Fuhrmann for (single arrival) M/G/1 queues.