IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v164y2008i1p193-21010.1007-s10479-008-0429-8.html
   My bibliography  Save this article

Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes

Author

Listed:
  • Tuǧrul Dayar
  • Akın Meriç

Abstract

Two approximative fixed-point iterative methods based on decomposition for closed queueing networks with Coxian service distributions and arbitrary buffer sizes are extended to include phase-type service distributions. The irreducible Markov chain associated with each subnetwork in the respective decompositions is represented hierarchically using Kronecker products. The two methods are implemented in a software tool capable of computing the steady-state probability vector of each subnetwork by a multilevel method at each fixed-point iteration and are compared with other methods for accuracy and efficiency. Numerical results indicate that there is a niche filled by the two approximative methods. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Tuǧrul Dayar & Akın Meriç, 2008. "Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes," Annals of Operations Research, Springer, vol. 164(1), pages 193-210, November.
    • Handle: RePEc:spr:annopr:v:164:y:2008:i:1:p:193-210:10.1007/s10479-008-0429-8
    DOI: 10.1007/s10479-008-0429-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0429-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0429-8?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. Yao, David D. & Buzacott, J. A., 1986. "The exponentialization approach to flexible manufacturing system models with general processing times," European Journal of Operational Research, Elsevier, vol. 24(3), pages 410-416, March.
    2. Uysal, Ertugrul & Dayar, Tugrul, 1998. "Iterative methods based on splittings for stochastic automata networks," European Journal of Operational Research, Elsevier, vol. 110(1), pages 166-186, October.
    3. William J. Gordon & Gordon F. Newell, 1967. "Closed Queuing Systems with Exponential Servers," Operations Research, INFORMS, vol. 15(2), pages 254-265, April.
    4. Tayfur Altiok, 1989. "Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking," Operations Research, INFORMS, vol. 37(4), pages 601-610, August.
    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. Å nipas, Mindaugas & Radziukynas, Virginijus & ValakeviÄ ius, Eimutis, 2018. "Numerical solution of reliability models described by stochastic automata networks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 570-578.

    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. Santiago R. Balseiro & David B. Brown & Chen Chen, 2021. "Dynamic Pricing of Relocating Resources in Large Networks," Management Science, INFORMS, vol. 67(7), pages 4075-4094, July.
    2. Korporaal, R. & Ridder, A.A.N. & Kloprogge, P. & Dekker, R., 1999. "Capacity planning of prisons in the Netherlands," Econometric Institute Research Papers EI 9909-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Berkley, Blair J., 1996. "Analyzing service blueprints using phase distributions," European Journal of Operational Research, Elsevier, vol. 88(1), pages 152-164, January.
    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. Tan, Baris & Yeralan, Sencer, 1996. "A fuzzy decomposition method for multistation production systems subject to blocking," International Journal of Production Economics, Elsevier, vol. 42(3), pages 245-262, April.
    6. Peter Buchholz & Gianfranco Ciardo & Susanna Donatelli & Peter Kemper, 2000. "Complexity of Memory-Efficient Kronecker Operations with Applications to the Solution of Markov Models," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 203-222, August.
    7. 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.
    8. Remco Bierbooms & Ivo Adan & Marcel Vuuren, 2013. "Approximate analysis of single-server tandem queues with finite buffers," Annals of Operations Research, Springer, vol. 209(1), pages 67-84, October.
    9. Oliveira, Fernando S., 2010. "Limitations of learning in automata-based systems," European Journal of Operational Research, Elsevier, vol. 203(3), pages 684-691, June.
    10. Zhang, Xiaoju & Zeng, Qingcheng & Sheu, Jiuh-Biing, 2019. "Modeling the productivity and stability of a terminal operation system with quay crane double cycling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 181-197.
    11. 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.
    12. Xiaoju Zhang & Huijuan Li & Meng Wu, 2022. "Optimization of Resource Allocation in Automated Container Terminals," Sustainability, MDPI, vol. 14(24), pages 1-16, December.
    13. Osorio, Carolina & Bierlaire, Michel, 2012. "A tractable analytical model for large-scale congested protein synthesis networks," European Journal of Operational Research, Elsevier, vol. 219(3), pages 588-597.
    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. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    16. Kozlowski, Dawid & Worthington, Dave, 2015. "Use of queue modelling in the analysis of elective patient treatment governed by a maximum waiting time policy," European Journal of Operational Research, Elsevier, vol. 244(1), pages 331-338.
    17. Abderezak Touzene, 2008. "A Tensor Sum Preconditioner for Stochastic Automata Networks," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 234-242, May.
    18. Sahba, Pedram & BalcIog[small tilde]lu, BarIs, 2011. "The impact of transportation delays on repairshop capacity pooling and spare part inventories," European Journal of Operational Research, Elsevier, vol. 214(3), pages 674-682, November.
    19. Gusak, Oleg & Dayar, Tugrul & Fourneau, Jean-Michel, 2003. "Lumpable continuous-time stochastic automata networks," European Journal of Operational Research, Elsevier, vol. 148(2), pages 436-451, July.
    20. Asaduzzaman, Md & Chaussalet, Thierry J., 2014. "Capacity planning of a perinatal network with generalised loss network model with overflow," European Journal of Operational Research, Elsevier, vol. 232(1), pages 178-185.

    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:164:y:2008:i:1:p:193-210:10.1007/s10479-008-0429-8. 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.