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

Tao Jiang (), Liwei Liu and Yuanyuan Zhu
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Tao Jiang: Shandong University of Science and Technology
Liwei Liu: Nanjing University of Science and Technology
Yuanyuan Zhu: Nanjing University of Science and Technology

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 2, 699-718

Abstract: 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.

Keywords: Israeli queue; Multi-phase random environment; Matrix analytic method; Spectral expansion method; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9585-0

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