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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    9. 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.
    10. Chakravarthy, Srinivas R., 2014. "A multi-server queueing model with server consultations," European Journal of Operational Research, Elsevier, vol. 233(3), pages 625-639.
    11. 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.
    12. 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.
    13. 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.
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