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Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server

Author

Listed:
  • N. Nithya

    (Department of Mathematics, Alagappa University, Karaikudi 630004, India
    These authors contributed equally to this work.)

  • N. Anbazhagan

    (Department of Mathematics, Alagappa University, Karaikudi 630004, India
    These authors contributed equally to this work.)

  • S. Amutha

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630003, India)

  • K. Jeganathan

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

  • Gi-Cheon Park

    (Department of International Affairs and Education, Gangseo University, Seoul 07661, Republic of Korea)

  • Gyanendra Prasad Joshi

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

  • Woong Cho

    (Department of Electronics, Information and Communication Engineering, Kangwon National University, Samcheok-si 25913, Gangwon State, Republic of Korea)

Abstract

In recent times, we have encountered new situations that have imposed restrictions on our ability to visit public places. These changes have affected various aspects of our lives, including limited access to supermarkets, vegetable shops, and other essential establishments. As a response to these circumstances, we have developed a continuous review retrial queueing–inventory system featuring a single server and controlled customer arrivals. In our system, customers arriving to procure a single item follow a Markovian Arrival Process, while the service time for each customer is modeled by an exponential distribution. Inventories are replenished according to the ( s , Q ) reordering policy with exponentially distributed lead times. The system controls arrival in the waiting space with setup time. The customers who arrive at a not allowed situation decide to enter an orbit of infinite size with predefined probability. Orbiting customers make retrials to claim a place in the waiting space, and their inter-retrial times are exponentially distributed. The server may experience essential interruption (emergency situation) which arrives according to Poisson process. Then, the server goes for an emergency vacation of a random time which is exponentially distributed. In the steady-state case, the joint probability of the number of customers in orbit and the inventory level has been found, and the Matrix Geometric Method has been used to find the steady-state probability vector. In numerical calculations, the convexity of the system and the impact of F-policy and emergency vacation in the system are discussed.

Suggested Citation

  • N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3560-:d:1219389
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    References listed on IDEAS

    as
    1. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    2. A. Krishnamoorthy & Sajeev S. Nair & Viswanath C. Narayanan, 2015. "Production inventory with service time and interruptions," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1800-1816, July.
    3. 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.
    4. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    5. Hilal Al Hamadi & N. Sangeetha & B. Sivakumar, 2015. "Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers," Annals of Operations Research, Springer, vol. 233(1), pages 3-23, October.
    6. N. Anbazhagan & Gyanendra Prasad Joshi & R. Suganya & S. Amutha & V. Vinitha & Bhanu Shrestha, 2022. "Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
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    Cited by:

    1. Kathirvel Jeganathan & Thanushkodi Harikrishnan & Kumarasankaralingam Lakshmanan & Agassi Melikov & Janos Sztrik, 2023. "Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System," Mathematics, MDPI, vol. 11(22), pages 1-31, November.

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