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Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule

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  • J. Medhi

    (Gauhati University, India)

Abstract

This paper relates to a queueing system with Poisson input and exponential service time, service taking place in batches under a "general bulk service rule." (A batch will contain no fewer than "a" and no more than "b" units.) The object of this paper is to study the waiting time distribution of such a bulk service system under steady state and also to indicate how the moments of the distribution can be obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:7:p:777-782
    DOI: 10.1287/mnsc.21.7.777
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    Cited by:

    1. Rapoport, Amnon & Stein, William E. & Mak, Vincent & Zwick, Rami & Seale, Darryl A., 2010. "Endogenous arrivals in batch queues with constant or variable capacity," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1166-1185, December.
    2. Yusei Koyama & Ayane Nakamura & Tuan Phung-Duc, 2024. "Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers," Mathematics, MDPI, vol. 12(18), pages 1-27, September.
    3. Dieter Claeys & Koenraad Laevens & Joris Walraevens & Herwig Bruneel, 2010. "Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 1-23, August.
    4. Suryadeepto Nag & Siddhartha P. Chakrabarty & Sankarshan Basu, 2021. "Single Event Transition Risk: A Measure for Long Term Carbon Exposure," Papers 2107.06518, arXiv.org, revised May 2022.
    5. S. K. Samanta & R. Nandi, 2021. "Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP (a,b) / 1 / ∞ $^{\text {(a,b)}}/1/\infty $ Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1461-1488, December.
    6. 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.
    7. Lin, Yu-Hsin & Lee, Ching-En, 2001. "A total standard WIP estimation method for wafer fabrication," European Journal of Operational Research, Elsevier, vol. 131(1), pages 78-94, May.
    8. Mohan Chaudhry & Abhijit Datta Banik & Sitaram Barik & Veena Goswami, 2023. "A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input," Mathematics, MDPI, vol. 11(5), pages 1-26, February.
    9. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    10. Warren B. Powell, 1987. "Waiting‐time distributions for bulk arrival, bulk service queues with vehicle‐holding and cancellation strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 207-227, April.
    11. Ayane Nakamura & Tuan Phung-Duc, 2023. "Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size," Mathematics, MDPI, vol. 11(18), pages 1-22, September.
    12. Chen, Shih-Pin, 2005. "Parametric nonlinear programming approach to fuzzy queues with bulk service," European Journal of Operational Research, Elsevier, vol. 163(2), pages 434-444, June.

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