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Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.

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Title: Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.
Authors: Tongyu Xu1 15194908257@163.com, Zhanyou Ma2 mzhy55@ysu.edu.cn, Ying Sun1 S1041942326@163.com
Source: IAENG International Journal of Applied Mathematics. May2025, Vol. 55 Issue 5, p1419-1427. 9p.
Subjects: Setup time, Consumers, Vacations, Probability theory, Queuing theory
Abstract: This paper considered a repairable MX/G/1 queueing system with the gated service, setup time and multiple adaptive vacation rules. Customers arrive according to Markov flow. The system has a main queue and an infinite buffer queue separated by a gate. After the customers arrival, they enter the buffer and wait for service in order. Before each service period begins, the system has a random setup period. After the setup period ends, the system opens the gate and customers waiting in the buffer zone enter the main queue according to the original order to receive the service. This paper uses tools such as the intuitive total probability decomposition theorem, regeneration cycle method, PGF and LST transform to analyze the system's queue length and waiting time. The probabilities for the server being in the states of general service, idle, setup, and vacation are presented individually. [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.)
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  Label: Title
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  Data: Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.
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  Data: <searchLink fieldCode="AR" term="%22Tongyu+Xu%22">Tongyu Xu</searchLink><relatesTo>1</relatesTo><i> 15194908257@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhanyou+Ma%22">Zhanyou Ma</searchLink><relatesTo>2</relatesTo><i> mzhy55@ysu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ying+Sun%22">Ying Sun</searchLink><relatesTo>1</relatesTo><i> S1041942326@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>. May2025, Vol. 55 Issue 5, p1419-1427. 9p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Setup+time%22">Setup time</searchLink><br /><searchLink fieldCode="DE" term="%22Consumers%22">Consumers</searchLink><br /><searchLink fieldCode="DE" term="%22Vacations%22">Vacations</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper considered a repairable MX/G/1 queueing system with the gated service, setup time and multiple adaptive vacation rules. Customers arrive according to Markov flow. The system has a main queue and an infinite buffer queue separated by a gate. After the customers arrival, they enter the buffer and wait for service in order. Before each service period begins, the system has a random setup period. After the setup period ends, the system opens the gate and customers waiting in the buffer zone enter the main queue according to the original order to receive the service. This paper uses tools such as the intuitive total probability decomposition theorem, regeneration cycle method, PGF and LST transform to analyze the system's queue length and waiting time. The probabilities for the server being in the states of general service, idle, setup, and vacation are presented individually. [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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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 9
        StartPage: 1419
    Subjects:
      – SubjectFull: Setup time
        Type: general
      – SubjectFull: Consumers
        Type: general
      – SubjectFull: Vacations
        Type: general
      – SubjectFull: Probability theory
        Type: general
      – SubjectFull: Queuing theory
        Type: general
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      – TitleFull: Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.
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            NameFull: Tongyu Xu
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            NameFull: Zhanyou Ma
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              M: 05
              Text: May2025
              Type: published
              Y: 2025
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