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A simple procedure to determine the queue length and waiting time distributions for queueing system.

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Title: A simple procedure to determine the queue length and waiting time distributions for queueing system.
Authors: Samanta, Sujit Kumar1 (AUTHOR) sksamanta.maths@nitrr.ac.in, Das, Kousik1 (AUTHOR) kousikdas1993@gmail.com
Source: Mathematical Methods of Operations Research. Dec2025, Vol. 102 Issue 2/3, p359-393. 35p.
Subjects: Queuing theory, Differential-difference equations, Distribution (Probability theory), Scientific method, Numerical analysis
Abstract: This paper presents a simple procedure for investigating the distributions of queue length at post-departure and random epochs as well as the waiting time of a random customer in an queueing system. A set of differential-difference equations generated with the remaining service time as the supplementary variable constitutes the foundation of this study. The approach suggested in this investigation does not require the formulation of a transition probability matrix, which is a traditional procedure for analyzing the queue length distribution at post-departure epoch. By applying the residue theorem and partial fraction technique, we are able to get closed-form expressions for the distributions of queue length at post-departure and random epochs as well as the waiting time of a random customer. We also present some numerical results to validate the accuracy of our findings and to support the validity of the analytical process. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Methods of Operations Research is the property of Springer Nature 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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DbLabel: Engineering Source
An: 192725529
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  Data: A simple procedure to determine the queue length and waiting time distributions for queueing system.
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  Data: <searchLink fieldCode="AR" term="%22Samanta%2C+Sujit+Kumar%22">Samanta, Sujit Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sksamanta.maths@nitrr.ac.in</i><br /><searchLink fieldCode="AR" term="%22Das%2C+Kousik%22">Das, Kousik</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kousikdas1993@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Methods+of+Operations+Research%22">Mathematical Methods of Operations Research</searchLink>. Dec2025, Vol. 102 Issue 2/3, p359-393. 35p.
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  Data: <searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink><br /><searchLink fieldCode="DE" term="%22Differential-difference+equations%22">Differential-difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+method%22">Scientific method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Label: Abstract
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  Data: This paper presents a simple procedure for investigating the distributions of queue length at post-departure and random epochs as well as the waiting time of a random customer in an queueing system. A set of differential-difference equations generated with the remaining service time as the supplementary variable constitutes the foundation of this study. The approach suggested in this investigation does not require the formulation of a transition probability matrix, which is a traditional procedure for analyzing the queue length distribution at post-departure epoch. By applying the residue theorem and partial fraction technique, we are able to get closed-form expressions for the distributions of queue length at post-departure and random epochs as well as the waiting time of a random customer. We also present some numerical results to validate the accuracy of our findings and to support the validity of the analytical process. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Mathematical Methods of Operations Research is the property of Springer Nature 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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        Value: 10.1007/s00186-025-00910-6
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      – Code: eng
        Text: English
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        PageCount: 35
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    Subjects:
      – SubjectFull: Queuing theory
        Type: general
      – SubjectFull: Differential-difference equations
        Type: general
      – SubjectFull: Distribution (Probability theory)
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      – SubjectFull: Scientific method
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      – SubjectFull: Numerical analysis
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      – TitleFull: A simple procedure to determine the queue length and waiting time distributions for queueing system.
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              Text: Dec2025
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              Y: 2025
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