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Analysis of an M/G/1 queue with vacations and multiple phases of operation

Author

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  • Jianjun Li

    (Nanjing University of Science and Technology)

  • Liwei Liu

    (Nanjing University of Science and Technology)

  • Tao Jiang

    (Nanjing University of Science and Technology)

Abstract

This paper deals with an M / G / 1 queue with vacations and multiple phases of operation. If there are no customers in the system at the instant of a service completion, a vacation commences, that is, the system moves to vacation phase 0. If none is found waiting at the end of a vacation, the server goes for another vacation. Otherwise, the system jumps from phase 0 to some operative phase i with probability $$q_i$$ q i , $$i = 1,2, \ldots ,n.$$ i = 1 , 2 , … , n . In operative phase i, $$i = 1,2, \ldots ,n$$ i = 1 , 2 , … , n , the server serves customers according to the discipline of FCFS (First-come, first-served). Using the method of supplementary variables, we obtain the stationary system size distribution at arbitrary epoch. The stationary sojourn time distribution of an arbitrary customer is also derived. In addition, the stochastic decomposition property is investigated. Finally, we present some numerical results.

Suggested Citation

  • Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:1:d:10.1007_s00186-017-0606-0
    DOI: 10.1007/s00186-017-0606-0
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    References listed on IDEAS

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    1. U. Yechiali & P. Naor, 1971. "Queuing Problems with Heterogeneous Arrivals and Service," Operations Research, INFORMS, vol. 19(3), pages 722-734, June.
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    6. Noam Paz & Uri Yechiali, 2014. "An M/M/1 Queue In Random Environment With Disasters," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-12.
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    Cited by:

    1. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    2. Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.
    3. Sherif I. Ammar & Yousef F. Alharbi & Yiqiang Q. Zhao, 2023. "Analysis of Vacation Fluid M / M /1 Queue in Multi-Phase Random Environment," Mathematics, MDPI, vol. 11(21), pages 1-14, October.

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