IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i4d10.1007_s11009-020-09823-9.html
   My bibliography  Save this article

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

Author

Listed:
  • S. K. Samanta

    (National Institute of Technology Raipur)

  • R. Nandi

    (National Institute of Technology Raipur)

Abstract

This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions at other various time epochs are also derived based on prearrival epoch probabilities. A simple approach has been developed to compute the waiting-time distribution of an arriving customer. We also carried out closed-form analytical expression for the service batch size distribution of an arriving customer. Some numerical results are provided in the form of tables for a variety of interarrival-time distributions and model parameters to understand the system behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09823-9
    DOI: 10.1007/s11009-020-09823-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09823-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09823-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. 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.
    4. Steven M. Brown & Thomas Hanschke & Ingo Meents & Benjamin R. Wheeler & Horst Zisgen, 2010. "Queueing Model Improves IBM's Semiconductor Capacity and Lead-Time Management," Interfaces, INFORMS, vol. 40(5), pages 397-407, October.
    5. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.
    6. Winfried K. Grassmann & Michael I. Taksar & Daniel P. Heyman, 1985. "Regenerative Analysis and Steady State Distributions for Markov Chains," Operations Research, INFORMS, vol. 33(5), pages 1107-1116, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abhijit Datta Banik & Souvik Ghosh & M. L. Chaudhry, 2020. "On the optimal control of loss probability and profit in a GI/C-BMSP/1/N queueing system," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 144-162, March.
    2. S. Pradhan & U.C. Gupta & S.K. Samanta, 2016. "Queue-length distribution of a batch service queue with random capacity and batch size dependent service: M / G r Y / 1 $M/{G^{Y}_{r}}/1$," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 329-343, June.
    3. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    4. Yongxi Cheng & Ding-Zhu Du & Yinfeng Xu, 2014. "A Zig-Zag Approach for Competitive Group Testing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 677-689, November.
    5. 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.
    6. 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.
    7. Gopinath Panda & Veena Goswami, 2023. "Analysis of a Discrete-time Queue with Modified Batch Service Policy and Batch-size-dependent Service," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    8. James J. Kim & Douglas G. Down & Mohan Chaudhry & Abhijit Datta Banik, 2022. "Difference Equations Approach for Multi-Server Queueing Models with Removable Servers," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1297-1321, September.
    9. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    10. Yongxi Cheng & Ding-Zhu Du & Feifeng Zheng, 2015. "A new strongly competitive group testing algorithm with small sequentiality," Annals of Operations Research, Springer, vol. 229(1), pages 265-286, June.
    11. 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.
    12. Bar-Lev, Shaul K. & Boxma, Onno & Kleiner, Igor & Perry, David & Stadje, Wolfgang, 2017. "Recycled incomplete identification procedures for blood screening," European Journal of Operational Research, Elsevier, vol. 259(1), pages 330-343.
    13. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.
    14. 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.
    15. Pala, Ali & Zhuang, Jun, 2018. "Security screening queues with impatient applicants: A new model with a case study," European Journal of Operational Research, Elsevier, vol. 265(3), pages 919-930.
    16. 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.
    17. Tijms, H.C. & Coevering, M.C.T. van de, 1990. "How to solve numerically the equilibrium equations of a Markov chain with infinitely many states," Serie Research Memoranda 0046, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    18. A. Banik & U. Gupta, 2007. "Analyzing the finite buffer batch arrival queue under Markovian service process: GI X /MSP/1/N," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 146-160, July.
    19. A. D. Banik & M. L. Chaudhry, 2017. "Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 140-151, February.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09823-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.