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Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

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  • Dong-Yuh Yang
  • Yi-Hsuan Chen
  • Chia-Huang Wu

Abstract

This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.

Suggested Citation

  • Dong-Yuh Yang & Yi-Hsuan Chen & Chia-Huang Wu, 2020. "Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns," International Journal of Production Research, Taylor & Francis Journals, vol. 58(10), pages 3036-3048, May.
    • Handle: RePEc:taf:tprsxx:v:58:y:2020:i:10:p:3036-3048
    DOI: 10.1080/00207543.2019.1624856
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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.

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