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Single Server Queueing-inventory System with Impatient Customers and Hybrid Vacations.

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Title: Single Server Queueing-inventory System with Impatient Customers and Hybrid Vacations.
Authors: Shengli Lv1 qhdddlsl@163.com, Yangyang Zan2 zanyangyang0524@163.com, Siyuan Yin3 13591270853@163.com
Source: IAENG International Journal of Applied Mathematics. Dec2024, Vol. 54 Issue 12, p2679-2690. 12p.
Subjects: Matrix analytic methods, Geometric approach, Cost functions, Markov processes, Consumers, Queuing theory
Abstract: This paper investigates a single-server queuing inventory system with impatient customers and multiple vacation strategies, where the first vacation is a working vacation. After a customer completes the service, he or she will bring a product away with probability r or not to bring a product away with probability 1 - r. Based on the M/M/1 queuing model, we construct a three-dimensional Markov process to represent the number of customers, inventory level, and server state in the system. The steady-state conditions of the system are obtained by the Neuts-Rao truncation method. Using the matrix geometric solution method, the steady-state performance indicators are derived. In addition, the cost function is established to do optimization analysis of the system. Finally, numerical experiments are conducted to analyze the effects of variations in system parameters on the performance indicators, and to determine the optimal inventory strategy and minimum cost under specific system parameters. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Single Server Queueing-inventory System with Impatient Customers and Hybrid Vacations.
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  Data: <searchLink fieldCode="AR" term="%22Shengli+Lv%22">Shengli Lv</searchLink><relatesTo>1</relatesTo><i> qhdddlsl@163.com</i><br /><searchLink fieldCode="AR" term="%22Yangyang+Zan%22">Yangyang Zan</searchLink><relatesTo>2</relatesTo><i> zanyangyang0524@163.com</i><br /><searchLink fieldCode="AR" term="%22Siyuan+Yin%22">Siyuan Yin</searchLink><relatesTo>3</relatesTo><i> 13591270853@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Dec2024, Vol. 54 Issue 12, p2679-2690. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Matrix+analytic+methods%22">Matrix analytic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+approach%22">Geometric approach</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Consumers%22">Consumers</searchLink><br /><searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink>
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  Label: Abstract
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  Data: This paper investigates a single-server queuing inventory system with impatient customers and multiple vacation strategies, where the first vacation is a working vacation. After a customer completes the service, he or she will bring a product away with probability r or not to bring a product away with probability 1 - r. Based on the M/M/1 queuing model, we construct a three-dimensional Markov process to represent the number of customers, inventory level, and server state in the system. The steady-state conditions of the system are obtained by the Neuts-Rao truncation method. Using the matrix geometric solution method, the steady-state performance indicators are derived. In addition, the cost function is established to do optimization analysis of the system. Finally, numerical experiments are conducted to analyze the effects of variations in system parameters on the performance indicators, and to determine the optimal inventory strategy and minimum cost under specific system parameters. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
      – SubjectFull: Geometric approach
        Type: general
      – SubjectFull: Cost functions
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      – SubjectFull: Markov processes
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      – SubjectFull: Consumers
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      – SubjectFull: Queuing theory
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              M: 12
              Text: Dec2024
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              Y: 2024
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