IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i2d10.1007_s10957-007-9253-6.html
   My bibliography  Save this article

Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time

Author

Listed:
  • K.-H. Wang

    (National Chung-Hsing University)

  • C.-C. Kuo

    (National Chiao Tung University)

  • W. L. Pearn

    (National Chiao Tung University)

Abstract

We investigate the optimal management problem of an M/G/1/K queueing system with combined F policy and an exponential startup time. The F policy queueing problem investigates the most common issue of controlling the arrival to a queueing system. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to obtain the steady state probability distribution of the number of customers in the system. The method is illustrated analytically for exponential service time distribution. A cost model is established to determine the optimal management F policy at minimum cost. We use an efficient Maple computer program to calculate the optimal value of F and some system performance measures. Sensitivity analysis is also investigated.

Suggested Citation

  • K.-H. Wang & C.-C. Kuo & W. L. Pearn, 2007. "Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 285-299, November.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9253-6
    DOI: 10.1007/s10957-007-9253-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9253-6
    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/s10957-007-9253-6?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. Kimura, Toshikazu, 1981. "Optimal control of an M/G/1 queuing system with removable server via diffusion approximation," European Journal of Operational Research, Elsevier, vol. 8(4), pages 390-398, December.
    2. Gupta, U. C. & Srinivasa Rao, T. S. S., 1996. "On the M/G/1 machine interference model with spares," European Journal of Operational Research, Elsevier, vol. 89(1), pages 164-171, February.
    3. Jau-Chuan Ke, 2003. "The operating characteristic analysis on a general input queue with N policy and a startup time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 235-254, May.
    4. Ke, Jau-Chuan & Wang, Kuo-Hsiung, 2002. "A recursive method for the N policy G/M/1 queueing system with finite capacity," European Journal of Operational Research, Elsevier, vol. 142(3), pages 577-594, November.
    5. Teghem, J., 1987. "Optimal control of a removable server in an M/G/1 queue with finite capacity," European Journal of Operational Research, Elsevier, vol. 31(3), pages 358-367, September.
    6. Colin E. Bell, 1971. "Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server," Operations Research, INFORMS, vol. 19(1), pages 208-218, February.
    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. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. 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.

    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. Ke, Jau-Chuan & Wang, Kuo-Hsiung, 2002. "A recursive method for the N policy G/M/1 queueing system with finite capacity," European Journal of Operational Research, Elsevier, vol. 142(3), pages 577-594, November.
    2. 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.
    3. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    4. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    5. Niño-Mora, José, 2012. "Towards minimum loss job routing to parallel heterogeneous multiserver queues via index policies," European Journal of Operational Research, Elsevier, vol. 220(3), pages 705-715.
    6. Wei Li & Attahiru Sule Alfa, 2000. "Optimal policies for M/M/m queue with two different kinds of (N, T)‐policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 240-258, April.
    7. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    8. R. Sudhesh & A. Mohammed Shapique, 2022. "Transient analysis of power management in wireless sensor network with start-up times and threshold policy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 80(1), pages 1-16, May.
    9. Kennedy, W. J. & Wayne Patterson, J. & Fredendall, Lawrence D., 2002. "An overview of recent literature on spare parts inventories," International Journal of Production Economics, Elsevier, vol. 76(2), pages 201-215, March.
    10. R.E. Lillo, 2001. "Optimal control of an M/G/1 queue with impatient priority customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 201-209, April.
    11. Shengli Lv, 2021. "Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    12. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
    13. Tayfur Altiok & Goang An Shiue, 1995. "Single‐stage, multi‐product production/inventory systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 889-913, September.
    14. Benjamin Legros, 2021. "Age-based Markovian approximation of the G/M/1 queue," Post-Print hal-03605431, HAL.
    15. Wojciech M. Kempa & Dariusz Kurzyk, 2022. "Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups," Energies, MDPI, vol. 15(22), pages 1-15, November.
    16. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    17. 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.
    18. Vasiliki Kostami, 2020. "Price and Lead time Disclosure Strategies in Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2760-2788, December.
    19. 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.
    20. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.

    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:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9253-6. 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.