Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 4, Pages 399-419
doi:10.1155/S104895330100034X

The MX/G/1 queue with queue length dependent service times

Bong Dae Choi,1 Yeong Cheol Kim,2 Yang Woo Shin,3 and Charles E. M. Pearce4

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.

Abstract

We deal with the MX/G/1 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 t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.