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Discrete-Time Geo/Geo/1 Queueing System Associated with (s, S) Inventory Policy

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  • S. K. Samanta

    (National Institute of Technology Raipur)

  • A. Verma

    (National Institute of Technology Raipur)

Abstract

This paper investigates a discrete-time Geo/Geo/1 queueing-inventory system with (s,S) inventory policy. Assume that demand occurs to the system according to the Bernoulli process and every demand needs single item for service. The service time is assumed to be geometric distribution. An external vendor replenishes the items and the replenishment of items requires positive random time which follows geometric distribution. There are a limited number of places available for demands to wait. We obtain the joint probability distributions for the number of demands and the inventory position at the outside observer’s and random epochs. We compute the waiting time distribution for an arrival demand who are able to join the queue. Various performance measures are obtained to establish a suitable cost function for the system. Moreover, numerical experiments are used to highlight the minimum value of the cost function with respect to the optimal parameter values. We validate the accuracy of discrete-time results through a simulation study. It is demonstrated that the results from this paper tend toward their continuous-time counterpart in the limiting case.

Suggested Citation

  • S. K. Samanta & A. Verma, 2025. "Discrete-Time Geo/Geo/1 Queueing System Associated with (s, S) Inventory Policy," Methodology and Computing in Applied Probability, Springer, vol. 27(3), pages 1-28, September.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:3:d:10.1007_s11009-025-10184-4
    DOI: 10.1007/s11009-025-10184-4
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    References listed on IDEAS

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    1. Qingzhe Xu & Jianjun Li & Liwei Liu & Lixue Guo, 2024. "A Queueing-Inventory System with Modified Delayed Vacation under Bernoulli Schedule," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-22, December.
    2. Maike Schwarz & Hans Daduna, 2006. "Queueing systems with inventory management with random lead times and with backordering," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 383-414, December.
    3. Frank N. Gouweleeuw & Henk C. Tijms, 1998. "Computing Loss Probabilities in Discrete-Time Queues," Operations Research, INFORMS, vol. 46(1), pages 149-154, February.
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