IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v162y2008i1p35-5510.1007-s10479-008-0317-2.html
   My bibliography  Save this article

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

Author

Listed:
  • Shuji Kijima
  • Tomomi Matsui

Abstract

In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for a closed Jackson network. Our algorithm is based on the Markov chain Monte Carlo (MCMC) method. Thus our scheme returns an approximate solution, for which the size of the error satisfies a given bound. To our knowledge, this algorithm is the first polynomial time MCMC algorithm for closed Jackson networks with multiple servers. We propose two new ergodic Markov chains, both of which have a unique stationary distribution that is the product form solution for closed Jackson networks. One of them is for an approximate sampler, and we show that it mixes rapidly. The other is for a perfect sampler based on the monotone coupling from the past (CFTP) algorithm proposed by Propp and Wilson, and we show that it has a monotone update function. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Shuji Kijima & Tomomi Matsui, 2008. "Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers," Annals of Operations Research, Springer, vol. 162(1), pages 35-55, September.
    • Handle: RePEc:spr:annopr:v:162:y:2008:i:1:p:35-55:10.1007/s10479-008-0317-2
    DOI: 10.1007/s10479-008-0317-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0317-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0317-2?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. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    2. William J. Gordon & Gordon F. Newell, 1967. "Closed Queuing Systems with Exponential Servers," Operations Research, INFORMS, vol. 15(2), pages 254-265, April.
    3. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    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. Nico Dijk & Barteld Schilstra, 2022. "On two product form modifications for finite overflow systems," Annals of Operations Research, Springer, vol. 310(2), pages 519-549, March.
    2. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.
    3. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    4. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    5. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    6. Sumi Kim & Seongmoon Kim, 2015. "Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing," Annals of Operations Research, Springer, vol. 230(1), pages 35-55, July.
    7. Haskose, A. & Kingsman, B. G. & Worthington, D, 2004. "Performance analysis of make-to-order manufacturing systems under different workload control regimes," International Journal of Production Economics, Elsevier, vol. 90(2), pages 169-186, July.
    8. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    9. Bretthauer, Kurt M., 1996. "Capacity planning in manufacturing and computer networks," European Journal of Operational Research, Elsevier, vol. 91(2), pages 386-394, June.
    10. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    11. Veneklaas, W. & Leeftink, A.G. & van Boekel, P.H.C.M. & Hans, E.W., 2021. "On the design, implementation, and feasibility of hospital admission services: The admission lounge case," Omega, Elsevier, vol. 100(C).
    12. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2019. "On Two Interacting Markovian Queueing Systems," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    13. van Dijk, N.M. & van der Sluis, E. & Bulder, L.N. & Cui, Y., 2024. "Flexible serial capacity allocation with intensive care application," International Journal of Production Economics, Elsevier, vol. 272(C).
    14. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    15. Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.
    16. Bing Lin & Rohit Bhatnagar & Yuchen Lin, 2024. "Admission Control of Parallel Queues with Fork Types of Jobs," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.
    17. John S. Hollywood, 2005. "An approximate planning model for distributed computing networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 590-605, September.
    18. Kurt M. Bretthauer, 2000. "Optimal service and arrival rates in Jackson queueing networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 1-17, February.
    19. D Worthington, 2009. "Reflections on queue modelling from the last 50 years," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 83-92, May.
    20. Daisik Nam & Minyoung Park, 2020. "Improving the Operational Efficiency of Parcel Delivery Network with a Bi-Level Decision Making Model," Sustainability, MDPI, vol. 12(19), pages 1-19, September.

    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:annopr:v:162:y:2008:i:1:p:35-55:10.1007/s10479-008-0317-2. 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.