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Analysis of a Batch Service Polling System in a Multi-phase Random Environment

Author

Listed:
  • Tao Jiang

    (Shandong University of Science and Technology)

  • Liwei Liu

    (Nanjing University of Science and Technology)

  • Yuanyuan Zhu

    (Nanjing University of Science and Technology)

Abstract

In this paper, we consider a single-server multi-queue polling system with unlimited-size batch service (so called ‘Israeli queue’) operating in a multi-phase random environment. The polling system consists of a service region and a waiting region, and the external environment evolves through time, i.e., when the external environment is in state i, after a period time, it stays in this state or makes a transition from this state to its adjacent ones. By using matrix analytic method and spectral expansion method, stationary probabilities are derived for computations of performance measures and the conditional waiting times of customers in waiting region. In addition, some numerical examples are presented to show the impact of parameters on performance measures.

Suggested Citation

  • Tao Jiang & Liwei Liu & Yuanyuan Zhu, 2018. "Analysis of a Batch Service Polling System in a Multi-phase Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 699-718, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9585-0
    DOI: 10.1007/s11009-017-9585-0
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    References listed on IDEAS

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    1. Winfried K. Grassmann, 2003. "The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-Dimensional Queueing Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 412-421, November.
    2. A. Krishnamoorthy & S. Jaya & B. Lakshmy, 2015. "Queues with interruption in random environment," Annals of Operations Research, Springer, vol. 233(1), pages 201-219, October.
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    Cited by:

    1. Chai, Xudong & Liu, Liwei & Chang, Baoxian & Jiang, Tao & Wang, Zhen, 2019. "On a batch matching system with impatient servers and boundedly rational customers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 308-328.

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