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Mat. Teor. Igr Pril., 2019, Volume 11, Issue 3, Pages 95–120 (Mi mgta242)  

This article is cited in 1 scientific paper (total in 1 paper)

Queueing-inventory models with batch demands and positive service times

Srinivas Chakravarthy

Departments of Industrial and Manufacturing Engineering \& Mathematics Kettering University

Abstract: We consider queueing-inventory models in which customers arrive according to a point process and each customer demands for one or more items but not exceeding a pre-determined (finite) value, say, $N$. The demands of the customers require positive service times. Replenishments are based on $(s, S)$-type policy and the lead times are assumed to be random. We consider two models. In Model 1, any arriving customer finding the inventory level to be zero will be lost. In Model 2, the loss of customers occur in two ways. First, an arriving customer finding the inventory level to be zero with the server being idle will be lost, and secondly, the customers, if any, present at a service completion with zero inventory will all be lost. We assume that in both the models the demands may be met partially based on the requests and the available inventory levels at that time. The inventory level is reduced by the amount to meet (fully or partially) the requisite demand of the customer at the beginning of the service. Under the assumption that all underlying random variables are exponential, we perform the steady-state analysis of the models using the classical matrix-analytic methods. Illustrative examples comparing the two models are presented.

Keywords: queueing-inventory systems, algorithmic probability, batch demands, lead times, matrix-analytic methods.

Full text: PDF file (283 kB)
References: PDF file   HTML file
UDC: 519.217
BBK: 22.18
Received: 25.05.2018
Revised: 28.08.2019
Accepted:30.09.2019

Citation: Srinivas Chakravarthy, “Queueing-inventory models with batch demands and positive service times”, Mat. Teor. Igr Pril., 11:3 (2019), 95–120

Citation in format AMSBIB
\Bibitem{Cha19}
\by Srinivas~Chakravarthy
\paper Queueing-inventory models with batch demands and positive service times
\jour Mat. Teor. Igr Pril.
\yr 2019
\vol 11
\issue 3
\pages 95--120
\mathnet{http://mi.mathnet.ru/mgta242}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. R. Chakravarthy, A. Rumyantsev, “Analytical and simulation studies of queueing -inventory models with map demands in batches and positive phase type services”, Simul. Model. Pract. Theory, 103 (2020), 102092  crossref  isi  scopus
  • Математическая теория игр и её приложения
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