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Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation

Author

Listed:
  • Subramani Palani Niranjan

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Suthanthira Raj Devi Latha

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Sorin Vlase

    (Department of Mechanical Engineering, Transilvania University of Brasov, Romania, B-dul Eroilor, 29, 500036 Brașov, Romania
    Technical Sciences Academy of Romania, B-dul Victoriei, 120, 010093 Bucharest, Romania)

Abstract

This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘ a ’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘ a ’. When returning from vacation, if threshold ‘ a ’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost.

Suggested Citation

  • Subramani Palani Niranjan & Suthanthira Raj Devi Latha & Sorin Vlase, 2024. "Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3535-:d:1519468
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    References listed on IDEAS

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    1. Wei Wang & Yindong Ji & Zhonghao Zhao & Haodong Yin, 2024. "Simulation Optimization of Station-Level Control of Large-Scale Passenger Flow Based on Queueing Network and Surrogate Model," Sustainability, MDPI, vol. 16(17), pages 1-34, August.
    2. Nobel, Rein D. & Tijms, Henk C., 1999. "Optimal control for an MX/G/1 queue with two service modes," European Journal of Operational Research, Elsevier, vol. 113(3), pages 610-619, March.
    3. James J. Kim & Douglas G. Down & Mohan Chaudhry & Abhijit Datta Banik, 2022. "Difference Equations Approach for Multi-Server Queueing Models with Removable Servers," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1297-1321, September.
    4. Carlos Chaves & Abhijit Gosavi, 2022. "On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study," Operational Research, Springer, vol. 22(5), pages 5205-5229, November.
    5. Saber Shiripour & Milad Hematian & Nezam Mahdavi-Amiri, 2023. "A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms," Operational Research, Springer, vol. 23(3), pages 1-52, September.
    6. Deena Merit C.K. & Haridass M. & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Energy Efficiency in a Base Station of 5G Cellular Networks using M/G/1 Queue with Multiple Sleeps and N-Policy," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-28, June.
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