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

Choi, Bong Dae; Kim, Yeong Cheol; Shin, Yang Woo; Pearce, Charles E. M.

doi:https://doi.org/10.1155/S104895330100034X

International Journal of Stochastic Analysis

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Volume 14 |Article ID 921703 | https://doi.org/10.1155/S104895330100034X

Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, Charles E. M. Pearce, "The MX/G/1 queue with queue length dependent service times", International Journal of Stochastic Analysis, vol. 14, Article ID 921703, 21 pages, 2001. https://doi.org/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, Korea

²Mokpo National University, Department of Mathematics, Muan-gu, Korea

³Changwon National University, Department of Statistics, 9 Sarimdong, Korea

⁴University of Adelaide, Department of Applied Mathematics, Australia

Received01 Jan 1999

Revised01 Dec 2000

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.

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Copyright © 2001 Hindawi Publishing Corporation. 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.

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