IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v46y2015i4p590-598.html
   My bibliography  Save this article

A parametric programming solution to the -policy queue with fuzzy parameters

Author

Listed:
  • Dong-Yuh Yang
  • Po-Kai Chang

Abstract

This paper investigates the F-policy queue using fuzzy parameters, in which the arrival rate, service rate, and start-up rate are all fuzzy numbers. The F-policy deals with the control of arrivals in a queueing system, in which the server requires a start-up time before allowing customers to enter. A crisp F-policy queueing system generalised to a fuzzy environment would be widely applicable; therefore, we apply the α-cuts approach and Zadeh's extension principle to transform fuzzy F-policy queues into a family of crisp F-policy queues. This study presents a mathematical programming approach applicable to the construction of membership functions for the expected number of customers in the system. Furthermore, we propose an efficient solution procedure to compute the membership function of the expected number of customers in the system under different levels of α. Finally, we give an example of the proposed system as applied to a case in the automotive industry to demonstrate its practicality.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:4:p:590-598
    DOI: 10.1080/00207721.2013.792975
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2013.792975
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2013.792975?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. Chen, Shih-Pin, 2004. "Parametric nonlinear programming for analyzing fuzzy queues with finite capacity," European Journal of Operational Research, Elsevier, vol. 157(2), pages 429-438, September.
    2. Chen, Shih-Pin, 2005. "Parametric nonlinear programming approach to fuzzy queues with bulk service," European Journal of Operational Research, Elsevier, vol. 163(2), pages 434-444, June.
    3. 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.
    4. 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.
    5. Chuen-Horng Lin & Jau-Chuan Ke & Hsin-I Huang, 2012. "Reliability-based measures for a system with an uncertain parameter environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(6), pages 1146-1156.
    6. K. R. Balachandran, 1973. "Control Policies for a Single Server System," Management Science, INFORMS, vol. 19(9), pages 1013-1018, May.
    7. Madhu Jain & G.C. Sharma & Richa Sharma, 2012. "Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(2), pages 152-174.
    8. Ke, Jau-Chuan & Huang, Hsin-I & Lin, Chuen-Horng, 2007. "On retrial queueing model with fuzzy parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 272-280.
    9. Daniel P. Heyman, 1968. "Optimal Operating Policies for M / G /1 Queuing Systems," Operations Research, INFORMS, vol. 16(2), pages 362-382, 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. 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.
    2. Huang, Beijia & Mauerhofer, Volker, 2016. "Low carbon technology assessment and planning—Case analysis of building sector in Chongming, Shanghai," Renewable Energy, Elsevier, vol. 86(C), pages 324-331.
    3. Sanga, Sudeep Singh & Charan, Gannamaneni Sai, 2023. "Fuzzy modeling and cost optimization for machine repair problem with retrial under admission control F-policy and feedback," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 214-240.
    4. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

    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. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    2. Blanc, J.P.C. & den Hertog, D., 2008. "On Markov Chains with Uncertain Data," Other publications TiSEM b44dfb0a-1676-4ce3-8d16-f, Tilburg University, School of Economics and Management.
    3. 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.
    4. 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.
    5. Ke, Jau-Chuan & Huang, Hsin-I & Lin, Chuen-Horng, 2007. "On retrial queueing model with fuzzy parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 272-280.
    6. 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.
    7. 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.
    8. 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.
    9. Wang, Naichao & Li, Mingyuan & Xiao, Boping & Ma, Lin, 2019. "Availability analysis of a general time distribution system with the consideration of maintenance and spares," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    10. 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.
    11. Garcia-Sanz, M.D. & Fernandez, F.R. & Fiestras-Janeiro, M.G. & Garcia-Jurado, I. & Puerto, J., 2008. "Cooperation in Markovian queueing models," European Journal of Operational Research, Elsevier, vol. 188(2), pages 485-495, July.
    12. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.
    13. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    14. 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.
    15. Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    16. Bu, Qihui & Sun, Yun & Chai, Xudong & Liu, Liwei, 2020. "Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    17. 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.
    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. Li Xia & Zhe George Zhang & Quan‐Lin Li, 2022. "A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1191-1215, March.
    20. Douglas G. Down, 2022. "Optimal control of energy-aware queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 417-419, April.

    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:taf:tsysxx:v:46:y:2015:i:4:p:590-598. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    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.