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Analysis of a GIX/M/1 queue with two-stage vacation policy using shift operator method

Author

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  • Yufei Liu
  • Qingqing Ye
  • Junnai Yan

Abstract

In this paper, we investigate a GI X/M/1 queue with the two-stage vacation policy. The system will first enter a working vacation once the system becomes empty in the normal busy period, during which the service rate will be switched to a lower rate. After this working vacation, if the system is nonempty, the service rate will be switched to the normal rate immediately; otherwise, the system will enter multiple vacations during which the service rate reduces to zero until the system is nonempty after one vacation and a new normal busy period starts. The distinguishing feature of this paper is the use of a general algorithm for solving the difference equation based on the right shift operator method to obtain the queue length distribution at pre-arrival time and arbitrary time. Moreover, the sojourn time of arbitrary customer is analyzed. Finally, several typical numerical examples are provided to validate our computational algorithm.

Suggested Citation

  • Yufei Liu & Qingqing Ye & Junnai Yan, 2024. "Analysis of a GIX/M/1 queue with two-stage vacation policy using shift operator method," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(19), pages 6732-6761, October.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:19:p:6732-6761
    DOI: 10.1080/03610926.2023.2250488
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