IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v35y1988i1p23-34.html
   My bibliography  Save this article

Priorities in M/G/1 queue with server vacations

Author

Listed:
  • Offer Kella
  • Uri Yechiali

Abstract

The M/G/1 queue with single and multiple server vacations is studied under both the preemptive and non‐preemptive priority regimes. A unified methodology is developed to derive the Laplace‐Stieltjes transform and first two moments of the waiting time Wk of a class‐k customer for each of the four models analyzed. The results are given a probabilistic representation involving mean residual lifetimes.

Suggested Citation

  • Offer Kella & Uri Yechiali, 1988. "Priorities in M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 23-34, February.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:1:p:23-34
    DOI: 10.1002/1520-6750(198802)35:13.0.CO;2-B
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198802)35:13.0.CO;2-B
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198802)35:13.0.CO;2-B?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
    ---><---

    References listed on IDEAS

    as
    1. Michel Scholl & Leonard Kleinrock, 1983. "On the M / G /1 Queue with Rest Periods and Certain Service-Independent Queueing Disciplines," Operations Research, INFORMS, vol. 31(4), pages 705-719, August.
    2. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    3. Hanoch Levy & Leonard Kleinrock, 1986. "A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition," Operations Research, INFORMS, vol. 34(3), pages 426-436, June.
    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. Steve Derkic & James E. Stafford, 2002. "Symbolic Computation of Moments in Priority Queues," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 261-277, August.
    2. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    3. Jinting Wang & Zhongbin Wang & Yunan Liu, 2020. "Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates," Operations Research, INFORMS, vol. 68(6), pages 1648-1667, November.
    4. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

    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. B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    2. P. H. Brill & C. M. Harris, 1992. "Waiting times for M/G/1 queues with service‐time or delay‐dependent server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 775-787, October.
    3. Wu-Lin Chen, 2019. "Computing the Moments of Polling Models with Batch Poisson Arrivals by Transform Inversion," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 515-526, July.
    4. Jacob K. Daniel & R. Ramanarayanan, 1988. "An (s,S) inventory system with rest periods to the server," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 119-123, February.
    5. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case," Economics Working Papers 314, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 1998.
    6. Dimitris Bertsimas & José Niño-Mora, 1999. "Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part I, The Single-Station Case," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 306-330, May.
    7. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    8. 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.
    9. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    10. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    11. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    12. Awi Federgruen & Ziv Katalan, 1998. "Determining Production Schedules Under Base-Stock Policies in Single Facility Multi-Item Production Systems," Operations Research, INFORMS, vol. 46(6), pages 883-898, December.
    13. Jau-Chuan Ke, 2006. "An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 357-369, May.
    14. Hideaki Takagi & Tetsuya Takine & Onno J. Boxma, 1992. "Distribution of the workload in multiclass queueing systems with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 41-52, February.
    15. Zhang, Zhe G. & Tian, Naishuo, 2004. "An analysis of queueing systems with multi-task servers," European Journal of Operational Research, Elsevier, vol. 156(2), pages 375-389, July.
    16. I. Atencia & P. Moreno, 2006. "A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures," Annals of Operations Research, Springer, vol. 141(1), pages 85-107, January.
    17. Deena Merit C.K. & Haridass M. & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Energy Efficiency in a Base Station of 5G Cellular Networks using M/G/1 Queue with Multiple Sleeps and N-Policy," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-28, June.
    18. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case," Economics Working Papers 302, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998.
    19. 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).
    20. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:35:y:1988:i:1:p:23-34. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.