Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 365-392

Waiting time analysis for MX/G/1 priority queues with/without vacations under random order of service discipline

Norikazu Kawasaki,1 Hideaki Takagi,2 Yutaka Takahashi,3 Sung-Jo Hong,4 and Toshiharu Hasegawa5

1Sumitomo Electric Industries, Ltd., 2nd Engineering Department, Systems & Electronics Division, 1-1-3 Shimaya Konohana-ku, Osaka 554-0024, Japan
2University of Tsukuba, Institute of Policy and Planning Sciences, 1-1-1 Tennoudai, Tsukuba-shi, Ibaraki 305-8573, Japan
3Kyoto University, Department of Systems Science, Graduate School of Informatics, Yoshida-Honmachi Sakyo-ku, Kyoto 606-8501, Japan
4Dongguk University, Department of Industrial Engineering, 3-26 Pil-dong, Jung-gu, Seoul 100- 715, Korea
5Nanzan University, Department of Information Systems and Quantitative Sciences, Faculty of Business Administration, 18 Yamazato-cho Showa-ku, Nagoya 466-0824, Japan

Received 1 December 1999; Revised 1 August 2000

Copyright © 2000 Norikazu Kawasaki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.