# American Institute of Mathematical Sciences

April  2018, 14(2): 743-757. doi: 10.3934/jimo.2017073

## Analysis of a batch service multi-server polling system with dynamic service control

 1 College of Economics and Management, Shandong University of Science and Technology, Qingdao, Shandong, 266590, China 2 Department of Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, China

* Corresponding author: Tao Jiang

Received  April 2016 Revised  September 2016 Published  April 2018 Early access  September 2017

This paper considers a multi-server polling system with batch service of an unlimited size, i.e., the so called "Israeli queue" with multi-server, where the service rate of each server switches between a low and a high value depending on the number of groups standing in front of the servers upon its service completion. By means of matrix geometric method and LU-type RG factorization of the infinitesimal generator in irreducible QBD process, the explicit closed-form of rate matrix $R$ and the steady state distribution of the queue length are respectively derived. In terms of the results, some stationary performance measures are obtained. In addition, some numerical examples are presented.

Citation: Tao Jiang, Liwei Liu. Analysis of a batch service multi-server polling system with dynamic service control. Journal of Industrial & Management Optimization, 2018, 14 (2) : 743-757. doi: 10.3934/jimo.2017073
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##### References:
$L_q$ versus $\lambda$ ($p = 0.6, \theta= 0.2, \mu_1=3$)
$L_q$ versus $\mu_1$ ($\lambda=3, p = 0.6, \theta= 0.2,$)
$L_q$ versus $p$ ($\lambda=3, \mu_1=3, \theta= 0.2,$)
$L_q$ versus $p$ ($\lambda=3, \mu_1=3, p= 0.6,$)
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