IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v252y2017i1d10.1007_s10479-015-2060-9.html
   My bibliography  Save this article

Analysis of discrete-time queues with general service demands and finite-support service capacities

Author

Listed:
  • Michiel Muynck

    (Department of Telecommunications and Information Processing)

  • Sabine Wittevrongel

    (Department of Telecommunications and Information Processing)

  • Herwig Bruneel

    (Department of Telecommunications and Information Processing)

Abstract

In this paper, we study a non-classical discrete-time queueing model with variable service demands and variable service capacities. Specifically, we consider the case where the service capacities of the system, i.e., the numbers of work units that the system can perform during each slot, are independent from slot to slot and have an identical general distribution with finite support. New customers enter the system according to a general independent arrival process. The service demands of the customers, i.e., the numbers of work units of service that each customer requires from the system, are general independent. We present an analytical technique to analyze the behavior of this queueing system. The analysis leads to expressions for the probability generating functions and the moments of the unfinished work in the system, the queueing delay of an arbitrary customer and the number of customers in the system in steady state. We also derive approximations for the tail probabilities of the system content and the customer delay. Numerical results are included to illustrate the impact of the various model parameters on the system performance.

Suggested Citation

  • Michiel Muynck & Sabine Wittevrongel & Herwig Bruneel, 2017. "Analysis of discrete-time queues with general service demands and finite-support service capacities," Annals of Operations Research, Springer, vol. 252(1), pages 3-28, May.
  • Handle: RePEc:spr:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-2060-9
    DOI: 10.1007/s10479-015-2060-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2060-9
    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/s10479-015-2060-9?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. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    2. Laevens, Koenraad & Bruneel, Herwig, 1995. "Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers," European Journal of Operational Research, Elsevier, vol. 85(1), pages 161-177, August.
    3. Srinivas R. Chakravarthy, 2009. "Analysis Of A Multi-Server Queue With Markovian Arrivals And Synchronous Phase Type Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 85-113.
    4. Bruneel, Herwig, 1984. "A general model for the behaviour of infinite buffers with periodic service opportunities," European Journal of Operational Research, Elsevier, vol. 16(1), pages 98-106, April.
    5. Glock, C. H., 2010. "Batch sizing with controllable production rates," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57823, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    6. Giri, B. C. & Yun, W. Y. & Dohi, T., 2005. "Optimal design of unreliable production-inventory systems with variable production rate," European Journal of Operational Research, Elsevier, vol. 162(2), pages 372-386, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nitin Kumar & U. C. Gupta, 2020. "A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1293-1324, September.
    2. Nitin Kumar & U. C. Gupta, 2020. "Analysis of batch Bernoulli process subject to discrete-time renewal generated binomial catastrophes," Annals of Operations Research, Springer, vol. 287(1), pages 257-283, April.
    3. Michiel Muynck & Herwig Bruneel & Sabine Wittevrongel, 2020. "Analysis of a queue with general service demands and correlated service capacities," Annals of Operations Research, Springer, vol. 293(1), pages 73-99, October.
    4. Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.

    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. Herwig Bruneel & Sabine Wittevrongel & Dieter Claeys & Joris Walraevens, 2016. "Discrete-time queues with variable service capacity: a basic model and its analysis," Annals of Operations Research, Springer, vol. 239(2), pages 359-380, April.
    2. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2022. "Delay analysis of a discrete-time single-server queue with an occasional extra server," Annals of Operations Research, Springer, vol. 310(2), pages 551-575, March.
    3. AlDurgam, Mohammad & Adegbola, Kehinde & Glock, Christoph H., 2017. "A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate," International Journal of Production Economics, Elsevier, vol. 191(C), pages 335-350.
    4. H. Bruneel & W. Rogiest & J. Walraevens & S. Wittevrongel, 2015. "Analysis of a discrete-time queue with general independent arrivals, general service demands and fixed service capacity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 285-315, December.
    5. Dhahri, Akrem & Gharbi, Ali & Ouhimmou, Mustapha, 2022. "Integrated production-delivery control policy for an unreliable manufacturing system and multiple retailers," International Journal of Production Economics, Elsevier, vol. 245(C).
    6. Asif Iqbal Malik & Biswajit Sarkar, 2020. "Coordination Supply Chain Management Under Flexible Manufacturing, Stochastic Leadtime Demand, and Mixture of Inventory," Mathematics, MDPI, vol. 8(6), pages 1-32, June.
    7. Vinck, Bart & Bruneel, Herwig, 2006. "System delay versus system content for discrete-time queueing systems subject to server interruptions," European Journal of Operational Research, Elsevier, vol. 175(1), pages 362-375, November.
    8. Glock, Christoph H. & Grosse, Eric H., 2021. "The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature," European Journal of Operational Research, Elsevier, vol. 288(3), pages 703-720.
    9. Herbon, Avi & David, Israel, 2023. "Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain," Operations Research Perspectives, Elsevier, vol. 10(C).
    10. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    11. Peymankar, Mahboobe & Dehghanian, Farzad & Ghiami, Yousef & Abolbashari, Mohammad Hassan, 2018. "The effects of contractual agreements on the economic production quantity model with machine breakdown," International Journal of Production Economics, Elsevier, vol. 201(C), pages 203-215.
    12. Mitali Sarkar & Li Pan & Bikash Koli Dey & Biswajit Sarkar, 2020. "Does the Autonomation Policy Really Help in a Smart Production System for Controlling Defective Production?," Mathematics, MDPI, vol. 8(7), pages 1-21, July.
    13. Wakhid Ahmad Jauhari & I Nyoman Pujawan & Mokh Suef, 2023. "Sustainable inventory management with hybrid production system and investment to reduce defects," Annals of Operations Research, Springer, vol. 324(1), pages 543-572, May.
    14. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    15. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    16. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    17. Sinisterra, Wilfrido Quiñones & Lima, Victor Hugo Resende & Cavalcante, Cristiano Alexandre Virginio & Aribisala, Adetoye Ayokunle, 2023. "A delay-time model to integrate the sequence of resumable jobs, inspection policy, and quality for a single-component system," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    18. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    19. Paola Cappanera & Filippo Visintin & Carlo Banditori & Daniele Feo, 2019. "Evaluating the long-term effects of appointment scheduling policies in a magnetic resonance imaging setting," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 212-254, March.
    20. Zamani, Shokufeh & Arkat, Jamal & Niaki, Seyed Taghi Akhavan, 2022. "Service interruption and customer withdrawal in the congested facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).

    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:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-2060-9. 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.