IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v26y2024i2d10.1007_s11009-024-10090-1.html
   My bibliography  Save this article

Performance and Optimization Analysis of a Queue with Delayed Uninterrupted Multiple Vacation and N-Policy

Author

Listed:
  • Yaxing He

    (School of Mathematical Sciences, Sichuan Normal University)

  • Yinghui Tang

    (School of Mathematical Sciences, Sichuan Normal University)

  • Miaomiao Yu

    (School of Mathematical Sciences, Sichuan Normal University)

  • Wenqing Wu

    (School of Science, Southwest University of Science and Technology)

Abstract

This paper considers an M/G/1 queue with delayed uninterrupted multiple vacation and N-policy, in which (i) the server remains dormant from vacation to a non-empty system with no more than N customers, and (ii) when the system becomes exhausted, the server waits for a random time instead of immediately going on vacation (applicable to many scenarios and common to human behavior). We first study the transient queue length distribution from an arbitrary initial state and obtain its Laplace transform expressions. Then, the recursive formulas of the stationary queue length distribution are developed. Meanwhile, some crucial performance measures are presented. Finally, the cost optimization problems are discussed with and without the average waiting time constraint. Four numerical examples are illustrated to determine the optimal control policy for minimizing cost under the conditions that the random variables obey different phase-type (PH) distributions.

Suggested Citation

  • Yaxing He & Yinghui Tang & Miaomiao Yu & Wenqing Wu, 2024. "Performance and Optimization Analysis of a Queue with Delayed Uninterrupted Multiple Vacation and N-Policy," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-28, June.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10090-1
    DOI: 10.1007/s11009-024-10090-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10090-1
    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/s11009-024-10090-1?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. K. R. Balachandran, 1973. "Control Policies for a Single Server System," Management Science, INFORMS, vol. 19(9), pages 1013-1018, May.
    2. Daniel P. Heyman, 1977. "The T-Policy for the M/G/1 Queue," Management Science, INFORMS, vol. 23(7), pages 775-778, March.
    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. Zhang, Xuelu & Wang, Jinting & Do, Tien Van, 2015. "Threshold properties of the M/M/1 queue under T-policy with applications," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 284-301.
    2. P. Vijaya Laxmi & E. Girija Bhavani & K. Jyothsna, 2023. "Analysis of Markovian queueing system with second optional service operating under the triadic policy," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 256-275, March.
    3. Miaomiao Yu & Attahiru Sule Alfa, 2016. "Some analysis results associated with the optimization problem for a discrete-time finite-buffer NT-policy queue," Operational Research, Springer, vol. 16(2), pages 161-179, July.
    4. uit het Broek, Michiel A.J. & Van der Heide, Gerlach & Van Foreest, Nicky D., 2020. "Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs," European Journal of Operational Research, Elsevier, vol. 287(3), pages 916-928.
    5. Dong-Yuh Yang & Po-Kai Chang, 2015. "A parametric programming solution to the -policy queue with fuzzy parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 590-598, March.
    6. Zhang, Zhe George & Tadj, Lotfi & Bounkhel, Messaoud, 2011. "Cost evaluation in M/G/1 queue with T-policy revisited, technical note," European Journal of Operational Research, Elsevier, vol. 214(3), pages 814-817, November.
    7. Eugene Feinberg, 2005. "On essential information in sequential decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 399-410, December.
    8. Renbin Liu & Attahiru Sule Alfa & Miaomiao Yu, 2019. "Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks," Operational Research, Springer, vol. 19(2), pages 449-477, June.
    9. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
    10. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(C).
    11. R. E. Lillo, 2000. "Optimal Operating Policy for an M/G/1 Exhaustive Server-Vacation Model," Methodology and Computing in Applied Probability, Springer, vol. 2(2), pages 153-167, August.
    12. Zhen Wang & Liwei Liu & Yiqiang Q. Zhao, 2022. "Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 870-908, May.
    13. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2013. "A MAP-modulated fluid flow model with multiple vacations," Annals of Operations Research, Springer, vol. 202(1), pages 19-34, January.
    14. Wang, Jinting & Zhang, Xuelu & Huang, Ping, 2017. "Strategic behavior and social optimization in a constant retrial queue with the N-policy," European Journal of Operational Research, Elsevier, vol. 256(3), pages 841-849.
    15. Ying Xu & Alan Scheller-Wolf & Katia Sycara, 2015. "The Benefit of Introducing Variability in Single-Server Queues with Application to Quality-Based Service Domains," Operations Research, INFORMS, vol. 63(1), pages 233-246, February.
    16. Wei Yingyuan & Tang Yinghui & Yu Miaomiao, 2020. "Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy," Journal of Systems Science and Information, De Gruyter, vol. 8(4), pages 367-386, August.

    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:26:y:2024:i:2:d:10.1007_s11009-024-10090-1. 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.