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Multi-Class, Multi-Server Queueing Inventory System with Batch Service

Author

Listed:
  • Khamis A. K. ALMaqbali

    (Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
    These authors contributed equally to this work.)

  • Varghese C. Joshua

    (Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
    These authors contributed equally to this work.)

  • Achyutha Krishnamoorthy

    (Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
    Department of Mathematics, Central University of Kerala, Kasaragod 671316, India
    These authors contributed equally to this work.)

Abstract

In this paper, we consider a queueing inventory system with batch arrival and batch service processes. Customers arrive in batches of sizes 1 , 2 , … , k , according to a marked compound Poisson process. We call a batch of customers as belonging to j when there are j individual customers in that batch. The service facility has waiting rooms for each category of customers and also a room to serve them. Except for category 1, all other customers have finite waiting rooms. The service room has only a limited number of seats. These seats are arranged in such a fashion that customers belonging to category j have groups of seats, each with j seats for j = 1 , 2 , … , k . Customers are taken for service according to the availability of seats designated to each category. A category j customer can be taken for service only if j items are available in the inventory. The service time of customers of category j is exponentially distributed with parameter depending on j for j = 1 , 2 , … , k . The number of seats available in the service room for each category of customers is restricted to a finite number. The replenishment for items follows the ( s , S ) policy: fill up to S at the time of replenishment. Lead time follows an exponential distribution. We analyze the system in the equilibrium state. Performance characteristics are evaluated and a number of numerical illustrations are provided.

Suggested Citation

  • Khamis A. K. ALMaqbali & Varghese C. Joshua & Achyutha Krishnamoorthy, 2023. "Multi-Class, Multi-Server Queueing Inventory System with Batch Service," Mathematics, MDPI, vol. 11(4), pages 1-29, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:830-:d:1059785
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    References listed on IDEAS

    as
    1. K. Sikdar & S. K. Samanta, 2016. "Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 553-583, September.
    2. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
    3. Monita Baruah & Kailash C. Madan & Tillal Eldabi, 2014. "A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-12, January.
    4. Khamis A. K. Al Maqbali & Varghese C. Joshua & Ambily P. Mathew & Achyutha Krishnamoorthy, 2023. "Queueing Inventory System in Transport Problem," Mathematics, MDPI, vol. 11(1), pages 1-36, January.
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