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Infinite Server Queueing-Inventory Models

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Abstract

In this paper, we study an \(MAP/M/\infty \) queue associated with an inventory system. The inventory is replenished according to an (s, S)-policy. The (self) service and lead times are assumed to be exponentially distributed. No arriving customer is allowed to enter into the system (of infinite capacity) when there is no inventory available for servicing the customer. Thus, every customer in service is attached with an inventory at the time of entering into the system. We employ an algorithmic approach for the computation of various quantities of interest and derive some explicit expressions in some cases. An illustrative example and an optimization problem are presented.

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Acknowledgements

Dhanya Shajin and A. Krishnamoorthy: Research supported by Kerala State Council for Science, Technology and Environment (No. 001/KESS/2013/CSTE) in Department of Mathematics, Cochin University of Science and Technology, Cochin-682022, Kerala, India.

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Authors and Affiliations

  1. Departments of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI, 48504, USA

    S. R. Chakravarthy

  2. Department of Mathematics, S. N. College, Chempazhanthy, Thiruvananthapuram, Kerala, 695587, India

    Dhanya Shajin

  3. Department of Mathematics, CMS College, Kottayam, Kerala, 686001, India

    A. Krishnamoorthy

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  1. S. R. Chakravarthy
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  2. Dhanya Shajin
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  3. A. Krishnamoorthy
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Correspondence to A. Krishnamoorthy.

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Chakravarthy, S.R., Shajin, D. & Krishnamoorthy, A. Infinite Server Queueing-Inventory Models. J Indian Soc Probab Stat 21, 43–68 (2020). https://doi.org/10.1007/s41096-019-00072-9

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