IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v214y2011i3p814-817.html
   My bibliography  Save this article

Cost evaluation in M/G/1 queue with T-policy revisited, technical note

Author

Listed:
  • Zhang, Zhe George
  • Tadj, Lotfi
  • Bounkhel, Messaoud

Abstract

This note clarifies the concept of regeneration cycle used in evaluating the average operating cost of the M/G/1 queue with T-policy studied in 70s. Two ways of defining the regeneration cycle are compared and advantages and disadvantages of each way are pointed out. In addition, we establish the convexity of the cost function based on the service cycle.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:814-817
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711004917
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Daniel P. Heyman, 1977. "The T-Policy for the M/G/1 Queue," Management Science, INFORMS, vol. 23(7), pages 775-778, March.
    2. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    3. Daniel P. Heyman, 1968. "Optimal Operating Policies for M / G /1 Queuing Systems," Operations Research, INFORMS, vol. 16(2), pages 362-382, April.
    4. Alfa, Attahiru Sule & Frigui, Imed, 1996. "Discrete NT-policy single server queue with Markovian arrival process and phase type service," European Journal of Operational Research, Elsevier, vol. 88(3), pages 599-613, February.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    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. 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. Tirdad, Ali & Grassmann, Winfried K. & Tavakoli, Javad, 2016. "Optimal policies of M(t)/M/c/c queues with two different levels of servers," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1124-1130.
    3. 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.
    4. 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.
    5. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    5. 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.
    6. Srinivas R. Chakravarthy & Serife Ozkar, 2016. "Crowdsourcing and Stochastic Modeling," Business and Management Research, Business and Management Research, Sciedu Press, vol. 5(2), pages 19-30, June.
    7. 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.
    8. Shunfu Jin & Xiuchen Qie & Wenjuan Zhao & Wuyi Yue & Yutaka Takahashi, 2020. "A clustered virtual machine allocation strategy based on a sleep-mode with wake-up threshold in a cloud environment," Annals of Operations Research, Springer, vol. 293(1), pages 193-212, October.
    9. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    10. F. P. Barbhuiya & U. C. Gupta, 2020. "A Discrete-Time GIX/Geo/1 Queue with Multiple Working Vacations Under Late and Early Arrival System," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 599-624, June.
    11. Alexander Dudin & Sergei Dudin & Valentina Klimenok & Yuliya Gaidamaka, 2021. "Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    12. 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).
    13. Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.
    14. Igor Kleiner & Esther Frostig & David Perry, 2023. "Busy Periods for Queues Alternating Between Two Modes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    15. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    16. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    17. Meena, Rakesh Kumar & Jain, Madhu & Sanga, Sudeep Singh & Assad, Assif, 2019. "Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 858-873.
    18. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    19. Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    20. Zhongbin Wang & Yunan Liu & Lei Fang, 2022. "Pay to activate service in vacation queues," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2609-2627, June.

    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:eee:ejores:v:214:y:2011:i:3:p:814-817. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.