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Markov Process for Service Facility systems with perishable inventory and analysis of a single server queue with reneging – Stochastic Model

by M. Geetha Rani, C. Elango
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 44 - Number 15
Year of Publication: 2012
Authors: M. Geetha Rani, C. Elango
10.5120/6340-8619

M. Geetha Rani, C. Elango . Markov Process for Service Facility systems with perishable inventory and analysis of a single server queue with reneging – Stochastic Model. International Journal of Computer Applications. 44, 15 ( April 2012), 18-23. DOI=10.5120/6340-8619

@article{ 10.5120/6340-8619,
author = { M. Geetha Rani, C. Elango },
title = { Markov Process for Service Facility systems with perishable inventory and analysis of a single server queue with reneging – Stochastic Model },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 44 },
number = { 15 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 18-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume44/number15/6340-8619/ },
doi = { 10.5120/6340-8619 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:35:39.356789+05:30
%A M. Geetha Rani
%A C. Elango
%T Markov Process for Service Facility systems with perishable inventory and analysis of a single server queue with reneging – Stochastic Model
%J International Journal of Computer Applications
%@ 0975-8887
%V 44
%N 15
%P 18-23
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we develop a supply network model for a service facility system with perishable inventory (on hand) by considering a two dimensional stochastic process of the form (L, X) = , where L (t) is the level of the on hand inventory and X (t) is the number of customers at time t. The inter-arrival time to the service station is assumed to be exponentially distributed with mean 1/?. The service time for each customer is exponentially distributed with mean 1/ µ. The maximum inventory level is S and the maximum capacity of the waiting space is N. The replenishment process is assumed to be (S-1, S) with a replenishment of only one unit at any level of the inventory. Lead time is exponentially distributed with parameter ?. The items are replenished at a rate of ? whose mean replenishment time is 1/?. Item in inventory is perishable when it's utility drops to zero or the inventory item become worthless while in storage. Perishable of any item occurs at a rate of ?. Once entered a queue, the customer may choose to leave the queue at a rate of ? if they have not been served after a certain time (reneging). The steady state probability distributions for the system states are obtained. A numerical example is provided to illustrate the method described in the model.

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Index Terms

Computer Science
Information Sciences

Keywords

Markov Process Service Facility System Stochastic Model Inventory Control Queue-inventory Model Equilibrium Distribution

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