IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v50y2004i7p883-895.html
   My bibliography  Save this article

A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks

Author

Listed:
  • P. T. de Boer

    (Department of Electrical Engineering, Mathematics, and Computer Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

  • D. P. Kroese

    (Department of Mathematics, University of Queensland, Brisbane 4072, Australia)

  • R. Y. Rubinstein

    (Faculty of Industrial Engineering and Management, Technion, Haifa, Israel)

Abstract

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

Suggested Citation

  • P. T. de Boer & D. P. Kroese & R. Y. Rubinstein, 2004. "A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 883-895, July.
  • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:7:p:883-895
    DOI: 10.1287/mnsc.1030.0139
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1030.0139
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.1030.0139?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
    ---><---

    References listed on IDEAS

    as
    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    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. Jianhui Yang & Yaoben Lin, 2019. "Study on Evolution of Food Safety Status and Supervision Policy—A System Based on Quantity, Quality, and Development Safety," Sustainability, MDPI, vol. 11(23), pages 1-13, November.
    2. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    3. Fatma Başoğlu Kabran & Ali Devin Sezer, 2022. "Approximation of the exit probability of a stable Markov modulated constrained random walk," Annals of Operations Research, Springer, vol. 310(2), pages 431-475, March.
    4. Pieter-Tjerk de Boer, 2005. "Rare-Event Simulation of Non-Markovian Queueing Networks Using a State-Dependent Change of Measure Determined Using Cross-Entropy," Annals of Operations Research, Springer, vol. 134(1), pages 69-100, February.
    5. Bahar Kaynar & Ad Ridder, 2009. "The Cross-Entropy Method with Patching for Rare-Event Simulation of Large Markov Chains," Tinbergen Institute Discussion Papers 09-084/4, Tinbergen Institute.
    6. Ad Ridder, 2005. "Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy," Annals of Operations Research, Springer, vol. 134(1), pages 119-136, February.
    7. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    8. K.-P. Hui & N. Bean & M. Kraetzl & Dirk Kroese, 2005. "The Cross-Entropy Method for Network Reliability Estimation," Annals of Operations Research, Springer, vol. 134(1), pages 101-118, February.
    9. Cadini, F. & Santos, F. & Zio, E., 2014. "An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 109-117.
    10. Kaynar, Bahar & Ridder, Ad, 2010. "The cross-entropy method with patching for rare-event simulation of large Markov chains," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1380-1397, December.
    11. Loretta Mastroeni & Giuseppe D'Acquisto & Maurizio Naldi, 2014. "Evaluation of Credit Risk Under Correlated Defaults: The Cross-Entropy Simulation Approach," Departmental Working Papers of Economics - University 'Roma Tre' 0193, Department of Economics - University Roma Tre.
    12. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    13. Joakim Kalvenes & Neil Keon, 2007. "Traffic Estimation and Capacity Assignment in Multimedia Distribution Networks with Guaranteed Quality of Service," Operations Research, INFORMS, vol. 55(3), pages 518-531, June.
    14. Ali Kadhem, Athraa & Abdul Wahab, Noor Izzri & Aris, Ishak & Jasni, Jasronita & Abdalla, Ahmed N., 2017. "Computational techniques for assessing the reliability and sustainability of electrical power systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 1175-1186.
    15. M. Garvels, 2011. "A combined splitting—cross entropy method for rare-event probability estimation of queueing networks," Annals of Operations Research, Springer, vol. 189(1), pages 167-185, September.

    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. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    2. Kin-Ping Hui, 2011. "Cooperative Cross-Entropy method for generating entangled networks," Annals of Operations Research, Springer, vol. 189(1), pages 205-214, September.
    3. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
    4. K.-P. Hui & N. Bean & M. Kraetzl & Dirk Kroese, 2005. "The Cross-Entropy Method for Network Reliability Estimation," Annals of Operations Research, Springer, vol. 134(1), pages 101-118, February.
    5. Mohammad Hassan Salmani & Kourosh Eshghi, 2017. "A Metaheuristic Algorithm Based on Chemotherapy Science: CSA," Journal of Optimization, Hindawi, vol. 2017, pages 1-13, February.
    6. Patelli, Edoardo & Feng, Geng & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2017. "Simulation methods for system reliability using the survival signature," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 327-337.
    7. Saranya, K. & Prasanna, P. Krishna, 2018. "Estimating stochastic volatility with jumps and asymmetry in Asian markets," Finance Research Letters, Elsevier, vol. 25(C), pages 145-153.
    8. Fahimnia, Behnam & Sarkis, Joseph & Eshragh, Ali, 2015. "A tradeoff model for green supply chain planning:A leanness-versus-greenness analysis," Omega, Elsevier, vol. 54(C), pages 173-190.
    9. Ludvík Friebel & Jana Friebelová, 2012. "Stochastic analysis of maintenance process costs in the IT industry: a case study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 393-408, September.
    10. Singh, Vijay P. & Oh, Juik, 2015. "A Tsallis entropy-based redundancy measure for water distribution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 360-376.
    11. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2022. "An automated prior robustness analysis in Bayesian model comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 583-602, April.
    12. Duc Manh Nguyen & Hoai An Le Thi & Tao Pham Dinh, 2014. "Solving the Multidimensional Assignment Problem by a Cross-Entropy method," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 808-823, May.
    13. Jasmit Shah & Somnath Datta & Susmita Datta, 2014. "A multi-loss super regression learner (MSRL) with application to survival prediction using proteomics," Computational Statistics, Springer, vol. 29(6), pages 1749-1767, December.
    14. Caballero, Rafael & Hernández-Díaz, Alfredo G. & Laguna, Manuel & Molina, Julián, 2015. "Cross entropy for multiobjective combinatorial optimization problems with linear relaxations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 362-368.
    15. Ad Ridder, 2004. "Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy," Tinbergen Institute Discussion Papers 04-018/4, Tinbergen Institute.
    16. Angelia L. Grant & Joshua C.C. Chan, 2017. "A Bayesian Model Comparison for Trend‐Cycle Decompositions of Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 525-552, March.
    17. Arisara Romyen & Chukiat Chaiboonsri & Satawat Wannapan & Songsak Sriboonchitta, 2019. "Multi-Process-Based Maximum Entropy Bootstrapping Estimator: Application for Net Foreign Direct Investment in ASEAN," Economies, MDPI, vol. 7(3), pages 1-13, July.
    18. Kaveh, Mehrdad & Mesgari, Mohammad Saadi & Saeidian, Bahram, 2023. "Orchard Algorithm (OA): A new meta-heuristic algorithm for solving discrete and continuous optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 95-135.
    19. N-H Shih, 2005. "Estimating completion-time distribution in stochastic activity networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 744-749, June.
    20. Wang, Guibin & Zha, Yongxing & Wu, Ting & Qiu, Jing & Peng, Jian-chun & Xu, Gang, 2020. "Cross entropy optimization based on decomposition for multi-objective economic emission dispatch considering renewable energy generation uncertainties," Energy, Elsevier, vol. 193(C).

    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:inm:ormnsc:v:50:y:2004:i:7:p:883-895. 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 Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.