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Performance analysis and optimization of a retrial queue with working vacations and starting failures

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  • Dong-Yuh Yang
  • Chia-Huang Wu

Abstract

This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.

Suggested Citation

  • Dong-Yuh Yang & Chia-Huang Wu, 2019. "Performance analysis and optimization of a retrial queue with working vacations and starting failures," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 25(5), pages 463-481, September.
    • Handle: RePEc:taf:nmcmxx:v:25:y:2019:i:5:p:463-481
    DOI: 10.1080/13873954.2019.1660378
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    Cited by:

    1. Tang Tang & Lijuan Jia & Jin Hu & Yue Wang & Cheng Ma, 2022. "Reliability analysis and selective maintenance for multistate queueing system," Journal of Risk and Reliability, , vol. 236(1), pages 3-17, February.
    2. Tzu-Hsin Liu & Kuo-Ching Chiou & Chih-Ming Chen & Fu-Min Chang, 2024. "Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation," Mathematics, MDPI, vol. 12(8), pages 1-14, April.

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