IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4581-d1276458.html
   My bibliography  Save this article

Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System

Author

Listed:
  • Kathirvel Jeganathan

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

  • Thanushkodi Harikrishnan

    (Guru Nanak College (Autonomous), University of Madras, Chennai 600042, India)

  • Kumarasankaralingam Lakshmanan

    (Department of Mathematics, St. Joseph University, Chümoukedima 797115, India)

  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku, AZ 1141, Azerbaijan)

  • Janos Sztrik

    (Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

This article deals with the queuing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged with another junior server. The approaching junior servers await their turn in a finite waiting area with a capacity of c for consultation. Concerning this, we study the performance of junior servers approaching the senior server in the retrial queuing-inventory model with the two finite waiting halls dedicated to the primary customers and the junior servers for consultation. We formulate a level-dependent QBD process and solve its steady-state probability vector using Neuts and Rao’s truncation method. The stability condition of the system is derived and the R matrix is computed. The optimum total cost has been obtained, and the sensitivity analyses, which include the expected total cost, the waiting time of customers in the waiting hall and orbit, the number of busy servers, and a fraction of the successful retrial rate of the model, are computed numerically.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4581-:d:1276458
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4581/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4581/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. C. Suganya & B. Sivakumar, 2019. "MAP/PH (1), PH (2)/2 finite retrial inventory system with service facility, multiple vacations for servers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(3), pages 265-295.
    2. 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.
    3. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    4. 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.
    5. Anoop Nair & M. Jacob & A. Krishnamoorthy, 2015. "The multi server M/M/(s,S) queueing inventory system," Annals of Operations Research, Springer, vol. 233(1), pages 321-333, October.
    6. Gabi Hanukov & Tal Avinadav & Tatyana Chernonog & Uri Yechiali, 2021. "A multi-server system with inventory of preliminary services and stock-dependent demand," International Journal of Production Research, Taylor & Francis Journals, vol. 59(14), pages 4384-4402, July.
    7. Hanukov, Gabi, 2022. "A service system where junior servers approach a senior server on behalf of customers," International Journal of Production Economics, Elsevier, vol. 244(C).
    8. Dhanya Shajin & Achyutha Krishnamoorthy & Agassi Z. Melikov & Janos Sztrik, 2022. "Multi-Server Queuing Production Inventory System with Emergency Replenishment," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    9. Chakravarthy, Srinivas R., 2014. "A multi-server queueing model with server consultations," European Journal of Operational Research, Elsevier, vol. 233(3), pages 625-639.
    10. M. Abdul Reiyas & K. Jeganathan, 2023. "A classical retrial queueing inventory system with two component demand rate," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 47(4), pages 508-533.
    11. Jeganathan, K. & Abdul Reiyas, M., 2020. "Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 273-304.
    12. A. Krishnamoorthy & R. Manikandan & Dhanya Shajin, 2015. "Analysis of a Multiserver Queueing-Inventory System," Advances in Operations Research, Hindawi, vol. 2015, pages 1-16, January.
    13. J. Artalejo & A. Krishnamoorthy & M. Lopez-Herrero, 2006. "Numerical analysis of(s, S) inventory systems with repeated attempts," Annals of Operations Research, Springer, vol. 141(1), pages 67-83, January.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    4. 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.
    5. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    6. K. Jeganathan & M. Abdul Reiyas & S. Selvakumar & N. Anbazhagan & S. Amutha & Gyanendra Prasad Joshi & Duckjoong Jeon & Changho Seo, 2022. "Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility," Mathematics, MDPI, vol. 10(12), pages 1-22, June.
    7. Mohammad Saffari, 2022. "Periodic inventory management when demand stochastically depends on shelf-stock," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1489-1501, December.
    8. 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.
    9. 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.
    10. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    11. Arpita Roy & Shib Sankar Sana & Kripasindhu Chaudhuri, 2018. "Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model," Annals of Operations Research, Springer, vol. 260(1), pages 481-500, January.
    12. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    13. P., Vijaya Laxmi & M.L., Soujanya, 2015. "Perishable inventory system with service interruptions, retrial demands and negative customers," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 102-110.
    14. Setareh Boshrouei Shargh & Mostafa Zandieh & Ashkan Ayough & Farbod Farhadi, 2024. "Scheduling in services: a review and bibliometric analysis," Operations Management Research, Springer, vol. 17(2), pages 754-783, June.
    15. Gabi Hanukov & Michael Hassoun & Oren Musicant, 2021. "On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    16. Wang, Fong-Fan, 2023. "An efficient optimization procedure for location-inventory problems with (S-1, S) policy and retrial demands," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 664-688.
    17. Jalili Marand, Ata & Li, Hongyan & Thorstenson, Anders, 2019. "Joint inventory control and pricing in a service-inventory system," International Journal of Production Economics, Elsevier, vol. 209(C), pages 78-91.
    18. Sha, Yue & Zhang, Junlong & Cao, Hui, 2021. "Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 290(3), pages 886-900.
    19. Han-Wen Tuan & Kuo-Chen Hung & Gino K. Yang, 2021. "Inventory Model with Fixed Shelf Life under Generalized Non-Increasing Demand," Mathematics, MDPI, vol. 9(21), pages 1-15, October.
    20. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.

    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:22:p:4581-:d:1276458. 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.