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Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control

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  • Xiaohan Wu

    (Harbin Institute of Technology
    Southern University of Science and Technology)

  • Anyue Chen

    (Southern University of Science and Technology
    University of Liverpool)

Abstract

This paper aims to provide several further results for a queueing model recently discussed by Chen et al. (Queueing Syst 95:331–378, 2020), i.e. the Markovian bulk-arrival and bulk-service queue incorporating the general state-dependent control. We use an alternative method which is based on the resolvent decomposition theorem to obtain the important results for this model in this paper, including the important questions regarding equilibrium behaviour, queue length behaviour, hitting time and busy period distributions. Furthermore, a set of interesting examples are also provided in the last section.

Suggested Citation

  • Xiaohan Wu & Anyue Chen, 2023. "Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 19-52, June.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:1:d:10.1007_s11134-022-09870-8
    DOI: 10.1007/s11134-022-09870-8
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    References listed on IDEAS

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    1. Anyue Chen & Xiaohan Wu & Jing Zhang, 2020. "Markovian bulk-arrival and bulk-service queues with general state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 331-378, August.
    2. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
    3. M. Balasubramanian & R. Arumuganathan, 2011. "Steady state analysis of a bulk arrival general bulk service queueing system with modified M-vacation policy and variant arrival rate," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 11(4), pages 383-407.
    4. S. Jeyakumar & B. Senthilnathan, 2016. "Steady state analysis of bulk arrival and bulk service queueing model with multiple working vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(3), pages 375-394.
    5. M. Haridass & R. Arumuganathan, 2011. "Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(1), pages 56-77.
    6. Fakinos, D., 1991. "The relation between limiting queue size distributions at arrival and departure epochs in a bulk queue," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 327-329, April.
    7. Rajesh Kumar & Souvik Ghosh & Abhijit Datta Banik, 2021. "Numerical study on transient behaviour of finite bulk arrival or service queues with multiple working vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 18(3), pages 384-403.
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