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Cost optimization of a M/M/1/WV&MAV queueing system using Newton–Raphson and particle swarm optimization techniques

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  • Ramachandran Remya
  • Amina Angelika Bouchentouf
  • Kaliappan Kalidass

Abstract

This paper is concerned with the optimal control of a Markovian queueing system subjected to multiple adaptive vacation and working vacation policies. This system is applicable in diverse modern technologies, in particular in call centers. We establish the steady-state solution as well as important system characteristics by means of probability generating functions technique. We also construct the expected total cost for this model and develop a procedure to determine the optimal service rate that yields the minimum cost. Further, we carried out a comparative analysis to obtain the minimum cost using the Newton–Raphson method and particle swarm optimization (PSO) algorithm.

Suggested Citation

  • Ramachandran Remya & Amina Angelika Bouchentouf & Kaliappan Kalidass, 2024. "Cost optimization of a M/M/1/WV&MAV queueing system using Newton–Raphson and particle swarm optimization techniques," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 205-220.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:3:p:205-220:id:11
    DOI: 10.37190/ord2403011
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.
    4. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4.
    6. K. Kalidass & J. Gnanaraj & S. Gopinath & Ramanath Kasturi, 2014. "Transient analysis of an M/M/1 queue with a repairable server and multiple vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(2), pages 193-216.
    7. Wojciech M. Kempa & Rafał Marjasz, 2020. "Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(3), pages 447-455, March.
    8. S. Jeyakumar & E. Rameshkumar, 2019. "A study on M X / G ( a , b )/ 1 queue with server breakdown without interruption and controllable arrivals during multiple adaptive vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(2), pages 137-155.
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