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Analysis of M / M /1/ N Stochastic Queueing—Inventory System with Discretionary Priority Service and Retrial Facility

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Listed:
  • K. Jeganathan

    (Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chepauk, Chennai 600005, India)

  • S. Vidhya

    (Department of Mathematics, Queen Mary’s College, Chennai 600005, India)

  • R. Hemavathy

    (Department of Mathematics, Queen Mary’s College, Chennai 600005, India)

  • N. Anbazhagan

    (Department of Mathematics, Alagappa University, Karaikudi 630003, India)

  • Gyanendra Prasad Joshi

    (Department of Computer Science and Engineering, Sejong University, Seoul 05006, Korea)

  • Chanku Kang

    (Department of Convergence Science, Kongju National University, Gongju 32588, Korea)

  • Changho Seo

    (Department of Convergence Science, Kongju National University, Gongju 32588, Korea)

Abstract

In this paper, we analyze a queueing–inventory system with two classes of customers, high priority (HP) and low priority (LP), under the discretionary priority discipline. The LP customers are served in two stages: preliminary service in stage-I and main service in stage-II. In contrast, HP customers require only the main service. Whenever the inventory level is less than the threshold level during the stage-I service of an LP customer, an arriving HP customer is allowed to interrupt the service of an LP customer by adopting the mixed-priority discipline. Otherwise, non-preemptive priority discipline is used in both stages. The interrupted LP customer moves to orbit and retries for the service whenever the server is free. The waiting hall of finite capacity is afforded for the HP customer only. The orbital search is provided for LP customers in orbit. The inventory is replenished following the ( s , Q ) ordering policy, with the lifetimes of the items being exponentially distributed. An expression for the stability condition is determined explicitly, and system performance measures are evaluated. Numerical examples are formulated for different sets of input values of the parameters.

Suggested Citation

  • K. Jeganathan & S. Vidhya & R. Hemavathy & N. Anbazhagan & Gyanendra Prasad Joshi & Chanku Kang & Changho Seo, 2022. "Analysis of M / M /1/ N Stochastic Queueing—Inventory System with Discretionary Priority Service and Retrial Facility," Sustainability, MDPI, vol. 14(10), pages 1-29, May.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:10:p:6370-:d:822213
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    References listed on IDEAS

    as
    1. Valentina I. Klimenok & Alexander N. Dudin & Vladimir M. Vishnevsky & Olga V. Semenova, 2022. "Retrial BMAP / PH / N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution," Mathematics, MDPI, vol. 10(2), pages 1-21, January.
    2. K. Jeganathan & S. Selvakumar & S. Saravanan & N. Anbazhagan & S. Amutha & Woong Cho & Gyanendra Prasad Joshi & Joohan Ryoo, 2022. "Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers," Mathematics, MDPI, vol. 10(7), pages 1-37, April.
    3. M. Amirthakodi & B. Sivakumar, 2019. "An inventory system with service facility and feedback customers," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 33(3), pages 374-411.
    4. K. Jeganathan & J. Kathiresan & N. Anbazhagan, 2016. "A retrial inventory system with priority customers and second optional service," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 808-834, December.
    5. I. Adiri & I. Domb, 1982. "A Single Server Queueing System Working under Mixed Priority Disciplines," Operations Research, INFORMS, vol. 30(1), pages 97-115, February.
    6. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan, 2021. "Joint optimization of condition-based and age-based replacement policy and inventory policy for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    7. N. Sangeetha & B. Sivakumar, 2020. "Optimal service rates of a perishable inventory system with service facility," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(4), pages 515-550.
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    Cited by:

    1. M. Nithya & Gyanendra Prasad Joshi & C. Sugapriya & S. Selvakumar & N. Anbazhagan & Eunmok Yang & Ill Chul Doo, 2022. "Analysis of Stochastic State-Dependent Arrivals in a Queueing-Inventory System with Multiple Server Vacation and Retrial Facility," Mathematics, MDPI, vol. 10(17), pages 1-29, August.

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