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A study on the performance of a queuing system with heterogeneous arrivals and various types of breakdowns under multiple working vacations

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  • Lidiya P
  • K Julia Rose Mary

Abstract

The paper analyses the performance of a single server queue with heterogeneous arrivals and various types of breakdowns under multiple working vacations. Customers enter the queue according to a Poisson process with a rate that varies according to the types of customers. In both the regular busy and working during the vacation states, the server offers services with an exponential distribution. During peak times, the system may breakdown due to server unavailability, the system may breakdown at any time. The model considers systems with two types of breakdowns. In this model, batches of customers are served under the General Bulk Service Rule. The steady-state equations, the performance of measures for the systems, and particular cases of the described model are derived. Finally, in the form of tables and graphs, numerical results have been obtained.

Suggested Citation

  • Lidiya P & K Julia Rose Mary, 2024. "A study on the performance of a queuing system with heterogeneous arrivals and various types of breakdowns under multiple working vacations," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 125-140.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:4:p:125-140:id:8
    DOI: 10.37190/ord240408
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    References listed on IDEAS

    as
    1. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    2. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 5-28.
    3. 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.
    4. Kaustav Dutta & Amit Choudhury, 2023. "Frequentist inference on traffic intensity of M/M/1 queuing system," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(1), pages 21-34.
    5. Balasubramanian Sundar Rajan & V. Ganesan & Samikannu Rita, 2020. "Batch arrival Poisson queue with breakdown and repairs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 17(3), pages 424-435.
    6. Edvinas Greičius & Saulius Minkevičius, 2017. "Diffusion limits for the queue length of jobs in multi-server open queueing networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 71-84.
    7. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    8. Sudeep Kumar & Ritu Gupta, 2023. "Reliability analysis of N-policy vacation based FTC system subject to standby switching failures," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(2), pages 53-80.
    9. Amina Angelika Bouchentouf & Abdelhak Guendouzi & Houalef Meriem & Majid Shakir, 2022. "Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(2), pages 16-33.
    10. Manickam Vadivukarasi & Kaliappan Kalidass, 2022. "A discussion on the optimality of bulk entry queue with differentiated hiatuses," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(2), pages 137-150.
    11. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    12. Rakesh Kumar & Narendra Kumar Jain & Bhupernder Kumar Som, 2014. "Optimization of an M/M/1/N feedback queue with retention of reneged customers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 45-58.
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