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Sojourn-time Distribution for $$M/G^a/1$$ M / G a / 1 Queue with Batch Service of Fixed Size - Revisited

Author

Listed:
  • Veena Goswami

    (Kalinga Institute of Industrial Technology)

  • Mohan Chaudhry

    (Royal Military College of Canada)

  • Abhijit Datta Banik

    (Indian Institute of Technology)

Abstract

This paper presents an explicit and straightforward method for finding the sojourn-time distribution of a random customer in an $$M/G^a/1$$ M / G a / 1 queue with a fixed-size batch service. The exhibited process is much more straightforward than the approach discussed by Yu and Tang (Methodology and Computing in Applied Probability 20(4):1503–1514, 2018). We obtain two closed-form expressions for probability density functions by using the inside and outside roots of the underlying characteristic equation. Applying partial fractions and residue theorem, we determine an explicit form of sojourn-time distribution and evaluate the distribution function for any specific time. In illustrative examples, we compare the results obtained by both methods and find that the results match excellently.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09963-0
    DOI: 10.1007/s11009-022-09963-0
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    References listed on IDEAS

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    1. S. Pradhan & U. C. Gupta, 2019. "Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process," Annals of Operations Research, Springer, vol. 277(2), pages 161-196, June.
    2. Mohan L. Chaudhry, 1992. "Numerical Issues in Computing Steady-State Queueing-Time Distributions of Single-Server Bulk-Service Queues: M/Gb/1 and M/Gd/1," INFORMS Journal on Computing, INFORMS, vol. 4(3), pages 300-310, August.
    3. 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.
    4. J. Medhi, 1975. "Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule," Management Science, INFORMS, vol. 21(7), pages 777-782, March.
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