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Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit

Author

Listed:
  • Rasmi K

    (National Institute of Technology Calicut)

  • Jacob M J

    (National Institute of Technology Calicut)

  • Alexander Dudin

    (Belarusian State University)

  • A. Krishnamoorthy

    (Department of Mathematics, CMS College
    Central University of Kerala)

Abstract

In this paper, we consider a queueing inventory model with K service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (s, S) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.

Suggested Citation

  • Rasmi K & Jacob M J & Alexander Dudin & A. Krishnamoorthy, 2024. "Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit," Methodology and Computing in Applied Probability, Springer, vol. 26(1), pages 1-15, March.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:1:d:10.1007_s11009-023-10071-w
    DOI: 10.1007/s11009-023-10071-w
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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. 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.
    3. 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.
    4. V. Mushko & M. Jacob & K. Ramakrishnan & A. Krishnamoorthy & A. Dudin, 2006. "Multiserver queue with addressed retrials," Annals of Operations Research, Springer, vol. 141(1), pages 283-301, January.
    Full references (including those not matched with items on IDEAS)

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