Infinite Server Queueing-Inventory Models

Document Type

Article

Publication Date

2020

Publication Title

Journal of the Indian Society for Probability and Statistics

Abstract

In this paper, we study an MAP/M/∞" role="presentation" style="box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">MAP/M/∞MAP/M/∞ 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.

First Page

43

Last Page

68

DOI

10.1007/s41096-019-00072-9

ISSN

E-ISSN: 2364-9569

Rights

© 2019 Journal of the Indian Society for Probability and Statistics

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