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

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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.

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Acknowledgments

The authors would like to thank the editor and the referees for their valuable comments and helpful suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. College of Economics and Management, Shandong University of Science and Technology, Qingdao, 266590, China

    Tao Jiang

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Liwei Liu & Yuanyuan Zhu

Authors
  1. Tao Jiang
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  2. Liwei Liu
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  3. Yuanyuan Zhu
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Correspondence to Tao Jiang.

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Jiang, T., Liu, L. & Zhu, Y. Analysis of a Batch Service Polling System in a Multi-phase Random Environment. Methodol Comput Appl Probab 20, 699–718 (2018). https://doi.org/10.1007/s11009-017-9585-0

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  • DOI: https://doi.org/10.1007/s11009-017-9585-0

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