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A Queueing-Inventory System with Modified Delayed Vacation under Bernoulli Schedule

Author

Listed:
  • Qingzhe Xu

    (Nanjing University of Science and Technology)

  • Jianjun Li

    (Nanjing University of Science and Technology)

  • Liwei Liu

    (Nanjing University of Science and Technology)

  • Lixue Guo

    (Nanjing Agricultural University)

Abstract

In this paper, we consider a queueing-inventory system with modified delayed vacation under Bernoulli schedule. If the inventory is empty upon completion of the service, the server will take the modified delayed vacation. During the modified delayed vacation period, if the replenishment is completed, the customer will still be served as normal. After this period, the server will take Bernoulli schedule, where the server reverts to normal work with probability $$q(0\le q\le 1)$$ q ( 0 ≤ q ≤ 1 ) or takes multiple vacations with probability $$1-q$$ 1 - q . The customers arrive according to a Poisson process. Upon customer arrival, if the inventory is not empty, the customer accepts the service and leaves the system carrying a product. The service time, lead time, modified delayed vacation time and multiple vacations time are all assumed to be exponentially distributed. We derive the stability condition of the system and the matrix geometric solution of steady-state probabilities using an algorithm. Then performance measures of the system are derived. Finally, numerical results are presented to demonstrate the impact of system parameters on performance measures and the expected cost function.

Suggested Citation

  • Qingzhe Xu & Jianjun Li & Liwei Liu & Lixue Guo, 2024. "A Queueing-Inventory System with Modified Delayed Vacation under Bernoulli Schedule," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-22, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10117-7
    DOI: 10.1007/s11009-024-10117-7
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    References listed on IDEAS

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    1. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    2. I. Padmavathi & A. Shophia Lawrence & B. Sivakumar, 2016. "A finite-source inventory system with postponed demands and modified M vacation policy," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 41-62, March.
    3. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    Full references (including those not matched with items on IDEAS)

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