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Convexity analysis and cost optimization of a retrial queue with Bernoulli vacation and delayed phase mending

Author

Listed:
  • Shweta Upadhyaya

    (Amity University)

  • Richa Sharma

    (JK Lakshmipat University)

  • Divya Agarwal

    (Amity University)

  • Geetika Malik

    (Amity University)

Abstract

A recurrent queueing system under multi-optional and state dependent arrivals has been explored wherein the customers/units join in cluster form. The service provided to the units is carried out in duet junctures. The server is unreliable and may collapse. Thereafter, it needs to be mended in d requisite phases. Delay in the mending procedure is also considered. Whenever the system is free of customers, then server either departs for a vacation with a certain probability or pursues to serve the next customer with the complimentary probability. Eminent results are derived by employing Embedded Markov Chain (EMC) approach. Further, convexity of expected system size is also discussed. Also, the results are verified via Adaptive Neuro Fuzzy Interface System (ANFIS). Lastly, cost optimization is carried out and optimal cost is compared via different methods, namely: Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Artificial Bee Colony (ABC) algorithm and Cuckoo Search Algorithm (CSA).

Suggested Citation

  • Shweta Upadhyaya & Richa Sharma & Divya Agarwal & Geetika Malik, 2023. "Convexity analysis and cost optimization of a retrial queue with Bernoulli vacation and delayed phase mending," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(5), pages 1671-1690, October.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:5:d:10.1007_s13198-023-01972-7
    DOI: 10.1007/s13198-023-01972-7
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    References listed on IDEAS

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    1. Shweta Upadhyaya & Chetna Kushwaha, 2020. "Performance prediction and ANFIS computing for unreliable retrial queue with delayed repair under modified vacation policy," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 17(4), pages 437-466.
    2. P. Rajadurai, 2019. "A study on M/G/1 preemptive priority retrial queue with Bernoulli working vacations and vacation interruption," International Journal of Process Management and Benchmarking, Inderscience Enterprises Ltd, vol. 9(2), pages 193-215.
    3. Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    4. Chandra Shekhar & Madhu Jain & Ather Aziz Raina & Javid Iqbal, 2018. "Reliability prediction of fault tolerant machining system with reboot and recovery delay," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(2), pages 377-400, April.
    5. P. Rajadurai & M.C. Saravanarajan & V.M. Chandrasekaran, 2018. "Cost optimisation analysis of retrial queue with K optional phases of service under multiple working vacations and random breakdowns," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 29(2), pages 193-222.
    6. P. Vijaya Laxmi & V. Goswami & K. Jyothsna, 2013. "Optimization of Balking and Reneging Queue with Vacation Interruption under -Policy," Journal of Optimization, Hindawi, vol. 2013, pages 1-9, June.
    7. Arie Harel & Paul H. Zipkin, 1987. "Strong Convexity Results for Queueing Systems," Operations Research, INFORMS, vol. 35(3), pages 405-418, June.
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