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Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

Author

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  • Miaomiao Yu

    (Sichuan University of Science and Engineering)

  • Yinghui Tang

    (Sichuan Normal University)

Abstract

This paper presents a simple algorithm for computing the cumulative distribution function of the sojourn time of a random customer in an M/GL/1 queue with bulk-service of exactly size L. Both theoretical and numerical aspects related to this problem were not discussed by Chaudhry and Templeton in their monograph (1983). Our analysis is based on the roots of the so-called characteristic equation of the Laplace-Stieltjes transform (LST) of the sojourn time distribution. Using the method of partial fractions and residue theorem, we obtain a closed-form expression of sojourn time distribution, from which we can calculate the value of the distribution function for any given time t ∈ [0, + ∞). Finally, to ensure the reliability of the analytical procedure, employing the work done by Gross and Harris (1985), an effective way to validate the correctness of our results along with some numerical examples are also provided.

Suggested Citation

  • Miaomiao Yu & Yinghui Tang, 2018. "Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1503-1514, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-018-9635-2
    DOI: 10.1007/s11009-018-9635-2
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    References listed on IDEAS

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    1. M. L. Chaudhry & Gagandeep Singh & U. C. Gupta, 2013. "A Simple and Complete Computational Analysis of MAP/R/1 Queue Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 563-582, September.
    2. Le-Duc, Tho & de Koster, Rene M.B.M., 2007. "Travel time estimation and order batching in a 2-block warehouse," European Journal of Operational Research, Elsevier, vol. 176(1), pages 374-388, January.
    3. Mohan L. Chaudhry & James J. Kim, 2016. "Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 237-257, February.
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    Cited by:

    1. Veena Goswami & Mohan Chaudhry & Abhijit Datta Banik, 2022. "Sojourn-time Distribution for $$M/G^a/1$$ M / G a / 1 Queue with Batch Service of Fixed Size - Revisited," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2897-2912, December.
    2. Srinivas R. Chakravarthy & Shruti & Alexander Rumyantsev, 2021. "Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1551-1579, December.

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