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

Author

Listed:
  • Anyue Chen

    (The Southern University of Science and Technology
    The University of Liverpool)

  • Xiaohan Wu

    (The Southern University of Science and Technology)

  • Jing Zhang

    (The Chinese University of Hong Kong)

Abstract

We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:95:y:2020:i:3:d:10.1007_s11134-020-09660-0
    DOI: 10.1007/s11134-020-09660-0
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Anyue Chen & Junping Li & Xiaohan Wu & Jing Zhang, 2021. "Decay parameter for general stopped Markovian bulk-arrival and bulk-service queues," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 305-344, December.
    3. Yuan, Xuchuan & Brian Hwarng, H., 2023. "Examining the dynamics of reactive capacity allocation through a chaos lens," European Journal of Operational Research, Elsevier, vol. 308(2), pages 912-928.
    4. Alexander Zeifman & Yacov Satin & Ivan Kovalev & Rostislav Razumchik & Victor Korolev, 2020. "Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method," Mathematics, MDPI, vol. 9(1), pages 1-20, December.

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