Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 4, Pages 399-419
The queue with queue length dependent service times
1Korea University, Department of Mathematics, A nam-dong Sungbuk-gu, Seoul 136- 701, Korea
2Mokpo National University, Department of Mathematics, Muan-gu, Chonnam 534- 729, Korea
3Changwon National University, Department of Statistics, 9 Sarimdong, Changwon 641-773, Korea
4University of Adelaide, Department of Applied Mathematics, Adelaide 5005, SA, Australia
Received 1 January 1999; Revised 1 December 2000
Copyright © 2001 Bong Dae Choi 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 deal with the queue where service times depend on the queue
length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the
transient queue length distribution at time and its limiting distribution
and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.