IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3560-d1219389.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3560/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3560/
    Download Restriction: no
    ---><---

    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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. V. Radhamani & B. Sivakumar & G. Arivarignan, 2022. "A Comparative Study on Replenishment Policies for Perishable Inventory System with Service Facility and Multiple Server Vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 229-265, March.
    2. Emre Berk & Ülkü Gürler & Saeed Poormoaied, 2020. "On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders," Annals of Operations Research, Springer, vol. 284(1), pages 81-98, January.
    3. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    4. 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.
    5. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    6. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    7. Yang Yang & Jianming Yao, 2021. "Resource integration optimization of convenience service platforms adopting dynamic service modes in new retail," Frontiers of Business Research in China, Springer, vol. 15(1), pages 1-19, December.
    8. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    9. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    10. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    11. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2020. "Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 133-152, October.
    12. 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.
    13. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    14. Kai Li & Yuqian Pan & Bayi Cheng & Bohai Liu, 2018. "The Setting and Optimization of Quick Queue," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 1014-1026, September.
    15. Agassi Melikov & Ramil Mirzayev & Sajeev S. Nair, 2022. "Double Sources Queuing-Inventory System with Hybrid Replenishment Policy," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    16. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    17. WonIl Lee & JaeWook Shin & BumYong Park, 2024. "The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    18. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.
    19. Subramanian Selvakumar & Kathirvel Jeganathan & Krishnasamy Srinivasan & Neelamegam Anbazhagan & Soojeong Lee & Gyanendra Prasad Joshi & Ill Chul Doo, 2023. "An Optimization of Home Delivery Services in a Stochastic Modeling with Self and Compulsory Vacation Interruption," Mathematics, MDPI, vol. 11(9), pages 1-34, April.
    20. T. Harikrishnan & K. Jeganathan & S. Selvakumar & N. Anbazhagan & Woong Cho & Gyanendra Prasad Joshi & Kwang Chul Son, 2022. "Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility," Mathematics, MDPI, vol. 10(15), pages 1-37, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3560-:d:1219389. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.