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Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process

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  • S. Pradhan

    (Indian Institute of Technology)

  • U. C. Gupta

    (Indian Institute of Technology)

Abstract

This paper considers an infinite-buffer batch-service queue with Markovian arrival process, generally distributed and batch-size-dependent service time. We obtain a bivariate vector generating function of queue length and server content distribution at departure epoch of a batch. The complete joint distribution of queue length, server content and phase of the arrival process at departure epoch is extracted in terms of roots of the associated characteristic equation. By employing these probability vectors we also perceive the joint distribution at arbitrary and pre-arrival epochs. Our analytic procedure and results are demonstrated using some numerical examples for phase-type as well as deterministic service time distributions with high and low values of model parameters. The occurrence of multiple roots are also investigated in case of phase-type service time distribution. Finally, we also investigate the influence of correlation of the arrival process on the behavior of the system performance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:277:y:2019:i:2:d:10.1007_s10479-017-2476-5
    DOI: 10.1007/s10479-017-2476-5
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    1. Bar-Lev, Shaul K. & Parlar, Mahmut & Perry, David & Stadje, Wolfgang & Van der Duyn Schouten, Frank A., 2007. "Applications of bulk queues to group testing models with incomplete identification," European Journal of Operational Research, Elsevier, vol. 183(1), pages 226-237, November.
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    3. Yu, Miaomiao & Alfa, Attahiru Sule, 2015. "Algorithm for computing the queue length distribution at various time epochs in DMAP/G(1, a, b)/1/N queue with batch-size-dependent service time," European Journal of Operational Research, Elsevier, vol. 244(1), pages 227-239.
    4. 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.
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    6. Bar-Lev, S.K. & Parlar, M. & Perry, D. & Stadje, W. & van der Duyn Schouten, F.A., 2007. "Applications of bulk queues to group testing models with incomplete identification," Other publications TiSEM 0b1bfa5e-c1e6-43ec-9684-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. 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.
    2. Dieter Fiems & Koen De Turck, 2023. "Analysis of Discrete-Time Queues with Branching Arrivals," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    3. Souvik Ghosh & A. D. Banik & Joris Walraevens & Herwig Bruneel, 2022. "A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service," 4OR, Springer, vol. 20(2), pages 241-272, June.
    4. Nitin Kumar & Umesh Chandra Gupta, 2022. "Markovian Arrival Process Subject to Renewal Generated Binomial Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2287-2312, December.
    5. 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.
    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. 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.
    8. Sergei Dudin & Olga Dudina, 2023. "Analysis of a Multi-Server Queue with Group Service and Service Time Dependent on the Size of a Group as a Model of a Delivery System," Mathematics, MDPI, vol. 11(22), pages 1-20, November.

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