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

  • Tao Jiang
  • Liwei Liu
  • Yuanyuan Zhu


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.


Israeli queue Multi-phase random environment Matrix analytic method Spectral expansion method 

Mathematics Subject Classification (2010)

60K25 90B22 


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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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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.College of Economics and ManagementShandong University of Science and TechnologyQingdaoChina
  2. 2.School of ScienceNanjing University of Science and TechnologyNanjingChina

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