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Volumn 207, Issue 3, 2010, Pages 1380-1397

The cross-entropy method with patching for rare-event simulation of large Markov chains

Author keywords

Cross entropy; Importance sampling; Large scale Markov chains; Rare events

Indexed keywords

CROSS ENTROPY; CROSS-ENTROPY METHOD; IMPORTANCE SAMPLING; IMPORTANCE SAMPLING METHOD; JACKSON NETWORKS; MARKOV CHAIN; MARKOVIAN; QUEUEING MODEL; RARE EVENT; RARE EVENT PROBABILITIES; RARE EVENT SIMULATION; RELATIVE ERRORS; RELIABILITY MODEL; RUNNING TIME; STATE SPACE; STATE-DEPENDENT;

EID: 77957692431     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.07.002     Document Type: Article
Times cited : (14)

References (43)
  • 1
    • 33744819512 scopus 로고    scopus 로고
    • Adaptive importance sampling for Markov chains using stochastic approximation
    • I. Ahamed, V.S. Borkar, and S. Juneja Adaptive importance sampling for Markov chains using stochastic approximation Operations Research 54 2006 489 504
    • (2006) Operations Research , vol.54 , pp. 489-504
    • Ahamed, I.1    Borkar, V.S.2    Juneja, S.3
  • 2
    • 0035466285 scopus 로고    scopus 로고
    • Estimating reliability measures for highly-dependable Markov systems using balanced likelihood ratios
    • C. Alexopoulos, and B.C. Shultes Estimating reliability measures for highly-dependable Markov systems using balanced likelihood ratios IEEE Transactions on Reliability 50 2001 265 280
    • (2001) IEEE Transactions on Reliability , vol.50 , pp. 265-280
    • Alexopoulos, C.1    Shultes, B.C.2
  • 3
    • 0000025104 scopus 로고
    • On the choice of alternative measures in importance sampling with Markov chains
    • S. Andradóttir, D.P. Heyman, and T.J. Ott On the choice of alternative measures in importance sampling with Markov chains Operations Research 43 1995 509 519
    • (1995) Operations Research , vol.43 , pp. 509-519
    • Andradóttir, S.1    Heyman, D.P.2    Ott, T.J.3
  • 4
    • 85168066417 scopus 로고
    • Steady-state rare-events simulation in queueing models and its complexity properties
    • S. Asmussen, and R.Y. Rubinstein Steady-state rare-events simulation in queueing models and its complexity properties J. Dshalalow, Advances in Queueing: Models, Methods and Problems 1995 CRC Press Boca Raton 429 466
    • (1995) Advances in Queueing: Models, Methods and Problems , pp. 429-466
    • Asmussen, S.1    Rubinstein, R.Y.2
  • 5
    • 0012352350 scopus 로고    scopus 로고
    • Adaptive state-dependent importance sampling simulation of Markovian queueing networks
    • P.T. Boer, and V.F. Nicola Adaptive state-dependent importance sampling simulation of Markovian queueing networks European Transactions on Telecommunications 13 2002 303 315
    • (2002) European Transactions on Telecommunications , vol.13 , pp. 303-315
    • Boer, P.T.1    Nicola, V.F.2
  • 7
    • 0001892448 scopus 로고
    • Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains
    • J.A. Bucklew, P. Ney, and J.S. Sadowsky Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains Journal of Applied Probability 27 1990 44 59
    • (1990) Journal of Applied Probability , vol.27 , pp. 44-59
    • Bucklew, J.A.1    Ney, P.2    Sadowsky, J.S.3
  • 9
    • 0033709988 scopus 로고    scopus 로고
    • Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains
    • T. Dayar, and W.J. Stewart Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains SIAM Journal on Scientific Computing 21 2000 1691 1705
    • (2000) SIAM Journal on Scientific Computing , vol.21 , pp. 1691-1705
    • Dayar, T.1    Stewart, W.J.2
  • 10
    • 33748288282 scopus 로고    scopus 로고
    • Analysis of state-independent importance sampling measures for the two-node tandem queue
    • P.T. de Boer Analysis of state-independent importance sampling measures for the two-node tandem queue ACM Transactions on Modeling and Computer Simulation 16 2006 225 250
    • (2006) ACM Transactions on Modeling and Computer Simulation , vol.16 , pp. 225-250
    • De Boer, P.T.1
  • 12
    • 0035696492 scopus 로고    scopus 로고
    • A Markov chain perspective on adaptive Monte Carlo algorithms
    • P. Desai, and P.W. Glynn A Markov chain perspective on adaptive Monte Carlo algorithms B. Peters, J. Smith, D. Medeiros, M. Rohrer, Proceedings of 2001 Winter Simulation Conference 2001 IEEE Press 379 384
    • (2001) Proceedings of 2001 Winter Simulation Conference , pp. 379-384
    • Desai, P.1    Glynn, P.W.2
  • 13
    • 0027677866 scopus 로고
    • An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation
    • M. Devetsikiotis, and J.K. Towsend An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation IEEE Transactions on Communications 41 1993 1464 1473
    • (1993) IEEE Transactions on Communications , vol.41 , pp. 1464-1473
    • Devetsikiotis, M.1    Towsend, J.K.2
  • 14
    • 14544270331 scopus 로고    scopus 로고
    • Dynamic importance sampling for uniformly recurrent Markov chains
    • P. Dupuis, and H. Wang Dynamic importance sampling for uniformly recurrent Markov chains Annals of Applied Probability 15 2005 1 38
    • (2005) Annals of Applied Probability , vol.15 , pp. 1-38
    • Dupuis, P.1    Wang, H.2
  • 15
    • 36749081203 scopus 로고    scopus 로고
    • Dynamic importance sampling for queueing networks
    • P. Dupuis, D. Sezer, and H. Wang Dynamic importance sampling for queueing networks Annals of Applied Probability 17 2007 1306 1346
    • (2007) Annals of Applied Probability , vol.17 , pp. 1306-1346
    • Dupuis, P.1    Sezer, D.2    Wang, H.3
  • 16
    • 0026406217 scopus 로고
    • Optimally efficient estimation of the statistics of rare events in queueing networks
    • M. Frater, T. Lennon, and B. Anderson Optimally efficient estimation of the statistics of rare events in queueing networks IEEE Transactions on Automatic Control 36 1991 1395 1405
    • (1991) IEEE Transactions on Automatic Control , vol.36 , pp. 1395-1405
    • Frater, M.1    Lennon, T.2    Anderson, B.3
  • 17
    • 0007195244 scopus 로고    scopus 로고
    • Ph.D. Thesis, Faculty of Mathematical Science, University of Twente, The Netherlands
    • Garvels, M.J.J., 2000. The splitting method in rare event simulation. Ph.D. Thesis, Faculty of Mathematical Science, University of Twente, The Netherlands.
    • (2000) The Splitting Method in Rare Event Simulation
    • Garvels, M.J.J.1
  • 20
    • 0001240715 scopus 로고
    • Importance sampling for stochastic simulations
    • P.W. Glynn, and D.L. Iglehart Importance sampling for stochastic simulations Management Science 35 1989 1337 1392
    • (1989) Management Science , vol.35 , pp. 1337-1392
    • Glynn, P.W.1    Iglehart, D.L.2
  • 23
    • 23244451581 scopus 로고    scopus 로고
    • Large deviations for processes with discontinuous statistics
    • I. Ignatiouk-Robert Large deviations for processes with discontinuous statistics Annals of Probability 33 2005 1292 1329
    • (2005) Annals of Probability , vol.33 , pp. 1292-1329
    • Ignatiouk-Robert, I.1
  • 24
    • 33744829164 scopus 로고    scopus 로고
    • Efficient simulation of buffer overflow probabilities in Jackson networks with feedback
    • S. Juneja, and V.F. Nicola Efficient simulation of buffer overflow probabilities in Jackson networks with feedback ACM Transactions on Modeling and Computer Simulation 15 2005 281 315
    • (2005) ACM Transactions on Modeling and Computer Simulation , vol.15 , pp. 281-315
    • Juneja, S.1    Nicola, V.F.2
  • 25
    • 0035322354 scopus 로고    scopus 로고
    • Fast simulation of Markov chains with small transition probabilities
    • S. Juneja, and P. Shahabuddin Fast simulation of Markov chains with small transition probabilities Management Science 47 2001 547 562
    • (2001) Management Science , vol.47 , pp. 547-562
    • Juneja, S.1    Shahabuddin, P.2
  • 26
    • 0035466297 scopus 로고    scopus 로고
    • Splitting based importance sampling algorithm for fast simulation of Markov reliability models with general repair policies
    • S. Juneja, and P. Shahabuddin Splitting based importance sampling algorithm for fast simulation of Markov reliability models with general repair policies IEEE Transactions on Reliability 50 2001 235 245
    • (2001) IEEE Transactions on Reliability , vol.50 , pp. 235-245
    • Juneja, S.1    Shahabuddin, P.2
  • 27
    • 77950483923 scopus 로고    scopus 로고
    • Rare-event simulation techniques: An introduction and recent advances
    • Simulation
    • S. Juneja, and P. Shahabuddin Rare-event simulation techniques: An introduction and recent advances S. Henderson, B. Nelson, Handbooks in Operations Research and Management Science Simulation vol. 13 2006 Elsevier Amsterdam 291 350
    • (2006) Handbooks in Operations Research and Management Science , vol.13 , pp. 291-350
    • Juneja, S.1    Shahabuddin, P.2
  • 30
    • 84898475656 scopus 로고    scopus 로고
    • Effective approximation of zero-variance simulation in a reliability setting
    • Sklenar, J., Bertelle, C., Fortino, G. (Eds.)
    • L'Ecuyer, P., Tuffin, B., 2007. Effective approximation of zero-variance simulation in a reliability setting. In: Sklenar, J., Bertelle, C., Fortino, G. (Eds.), Proceedings of the 2007 European Simulation and Modeling Conference, pp. 48-54.
    • (2007) Proceedings of the 2007 European Simulation and Modeling Conference , pp. 48-54
    • L'Ecuyer, P.1    Tuffin, B.2
  • 32
    • 34247277188 scopus 로고    scopus 로고
    • Efficient importance sampling heuristics for the simulation of population overflow in Jackson networks
    • V.F. Nicola, and T.S. Zaburnenko Efficient importance sampling heuristics for the simulation of population overflow in Jackson networks ACM Transactions on Modeling and Computer Simulation 17 2 2006
    • (2006) ACM Transactions on Modeling and Computer Simulation , vol.17 , Issue.2
    • Nicola, V.F.1    Zaburnenko, T.S.2
  • 33
    • 0024479530 scopus 로고
    • A quick simulation method for excessive backlogs in networks of queues
    • S. Parekh, and J. Walrand A quick simulation method for excessive backlogs in networks of queues IEEE Transactions on Automatic Control 34 1989 54 66
    • (1989) IEEE Transactions on Automatic Control , vol.34 , pp. 54-66
    • Parekh, S.1    Walrand, J.2
  • 34
    • 3042683131 scopus 로고    scopus 로고
    • Combining importance sampling and temporal difference control variates to simulate Markov chains
    • R. Randhawa, and S. Juneja Combining importance sampling and temporal difference control variates to simulate Markov chains ACM Transactions on Modelling and Computer Simulation 14 2004 1 30
    • (2004) ACM Transactions on Modelling and Computer Simulation , vol.14 , pp. 1-30
    • Randhawa, R.1    Juneja, S.2
  • 38
    • 0000895730 scopus 로고
    • Importance sampling for simulation of highly reliable Markovian systems
    • P. Shahabuddin Importance sampling for simulation of highly reliable Markovian systems Management Science 40 1994 333 352
    • (1994) Management Science , vol.40 , pp. 333-352
    • Shahabuddin, P.1
  • 39
    • 0028423227 scopus 로고
    • Fast transient simulation of Markovian models of highly dependable systems
    • P. Shahabuddin Fast transient simulation of Markovian models of highly dependable systems Performance Evaluation 20 1994 267 286
    • (1994) Performance Evaluation , vol.20 , pp. 267-286
    • Shahabuddin, P.1
  • 41
    • 0035162385 scopus 로고    scopus 로고
    • Underestimation of Rare Event Probabilities in Importance Sampling Simulations
    • P.J. Smith Underestimation of Rare Event Probabilities in Importance Sampling Simulations Simulation 75 2001 140 150
    • (2001) Simulation , vol.75 , pp. 140-150
    • Smith, P.J.1
  • 42
    • 0346922977 scopus 로고    scopus 로고
    • Numerical methods for computing stationary distributions of finite irreducible Markov chains
    • W.J. Stewart Numerical methods for computing stationary distributions of finite irreducible Markov chains W. Grassmann, Advances in Computational Probability 1999 Kluwer (Chapter 3)
    • (1999) Advances in Computational Probability
    • Stewart, W.J.1
  • 43
    • 34548073680 scopus 로고    scopus 로고
    • Performance modeling and Markov chains
    • Formal Methods for Performance Evaluation. SFM 2007
    • W.J. Stewart Performance modeling and Markov chains M. Bernardo, J. Hillston, Formal Methods for Performance Evaluation. SFM 2007 LNCS vol. 4486 2007 Springer 1 33
    • (2007) LNCS , vol.4486 , pp. 1-33
    • Stewart, W.J.1


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