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Optimal design for a retrial queueing system with state-dependent service rate

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Abstract

This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Xuelu Zhang & Jinting Wang

  2. School of Science, Qilu University of Technology, Jinan, 250353, China

    Xuelu Zhang

  3. Department of Basic Courses, Shandong Women’s University, Jinan, 250002, China

    Qing Ma

Authors
  1. Xuelu Zhang
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  2. Jinting Wang
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  3. Qing Ma
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Corresponding author

Correspondence to Jinting Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71571014 and 71390334.

This paper was recommended for publication by Editor WANG Shouyang.

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Zhang, X., Wang, J. & Ma, Q. Optimal design for a retrial queueing system with state-dependent service rate. J Syst Sci Complex 30, 883–900 (2017). https://doi.org/10.1007/s11424-017-5097-9

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  • DOI: https://doi.org/10.1007/s11424-017-5097-9

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