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Decay parameter for general stopped Markovian bulk-arrival and bulk-service queues

Author

Listed:
  • Anyue Chen

    (Southern University of Science and Technology
    University of Liverpool)

  • Junping Li

    (Central South University)

  • Xiaohan Wu

    (Harbin Institute of Technology)

  • Jing Zhang

    (Chinese University of Hong Kong-Shenzhen, and Shenzhen Institute of Artificial Intelligence and Robotics for Society)

Abstract

We consider the important decay parameter issue for a Markovian bulk-arrival and bulk-service queue which stops at reaching the first m states. The results obtained in this paper are a significant generalization of the ones obtained in Chen et al. (Queueing Syst 66:275–311, 2010). The exact value of the decay parameter is obtained. Based on the results obtained in this paper, we provide a practical method for calculating the decay parameter which is very effective. In some cases, the decay parameter can even be easily expressed explicitly. Some important key lemmas which also have their own interest are provided. The interesting and clear geometric interpretation of the decay parameter is explained. A few examples are provided to illustrate the results obtained in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:99:y:2021:i:3:d:10.1007_s11134-021-09712-z
    DOI: 10.1007/s11134-021-09712-z
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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.
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