Abstract
This paper reports simulation experiments, applying the cross entropy method such as the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failure biasing schemes that have been proved to give estimators with bounded relative errors. The results from the experiments indicate a considerable improvement of the performance of the importance sampling estimators, where performance is measured by the relative error of the estimate, by the relative error of the estimator, and by the gain of the importance sampling simulation to the normal simulation.
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References
Alon, G., D.P. Kroese, T. Raviv, and R.Y. Rubinstein. (2005). “Application of the Cross-Entropy Method for Optimal Buffer Allocation in a Simulation Based Environment.” Annals of Operations Research 134, 137–151.
Asmussen, S. and R.Y. Rubinstein. (1995). “Steady State Rare Event Simulation in Queueing Models and its Complexity Properties.” In J. Dshalalow (ed.), Advances in Queueing Theory, Theory, Methods and Open Problems, CRC Press, Boca Raton, USA, pp. 429–461.
de Boer, P.-T., V. Nicola, and R.Y. Rubinstein. (2000). “Adaptive Importance Sampling Simulation of Queueing Networks.” In K.K.J.A. Jones, R.R. Bartor, and P. Fishwick (eds.), Proceedings of the 2000 Winter Simulation Conference, Orlando, Florida, pp. 646–655.
de Boer, P.-T., D.P. Kroese, and R.Y. Rubinstein. (2004). “A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks.” Management Science 50(7), 883–895.
de Mello, T.H. and R.Y. Rubinstein. (2002). “Rare Event Estimation for Static Models via Cross-Entropy and Importance Sampling” (submitted).
Goyal, A. and S. Lavenberg. (1987). “Modeling and Analysis of Computer System Availability.” IBM Journal of Research and Development 31, 651–664.
Goyal, A., W. Carter, E. de Souza e Silva, S. Lavenberg, and K. Trivedi. (1986). “The System Availability Estimator.” In Proceedings of 16-th Annual International Symposium on Fault Tolerance Computing, Vienna, Austria, pp. 84–89.
Goyal, A., S. Lavenberg, and K. Trivedi. (1987). “Probabilistic Modeling of Computer System Availability.” Annals of Operations Research 8, 285–306.
Goyal, A., P. Shahabuddin, P. Heidelberger, V. Nicola, and P. Glynn. (1992). “A Unified Framework for Simulating Markovian Models of Highly Dependable Systems.” IEEE Transactions on Computers 41, 36–51.
Heidelberger, P. (1995). “Fast Simulation of Rare Events in Queueing and Reliability Models.” ACM Transactions on Modelling and Computer Simulation 5, 43–85.
Hui, K.-P., N. Bean, M. Kraetzl, and D.P. Kroese. (2005). “The Cross-Entropy Method for Network Reliability.” Annals of Operations Research 134, 101–118.
Juneja, S. and P. Shahabuddin. (2001a). “Fast Simulation of Markov Chains with Small Transition Probabilities.” Management Science 47, 547–562.
Juneja, S. and P. Shahabuddin. (2001b). “Splitting-Based Importance Sampling Algorithm for Fast Simulation of Markov Reliability Models with General Repair Policies.” IEEE Transactions on Reliability 50, 235–245.
Lieber, D., A. Nemirovskii, and R. Rubinstein. (1999). “A Fast Monte Carlo Method for Evaluation of Reliability Indices.” IEEE Transactions on Reliability 48, 256–261.
Rubinstein, R.Y. (1997). “Optimization of Computer Simulation Models with Rare Events.” European Journal of Operations Research 99, 89–112.
Rubinstein, R.Y. (1999). “The Cross-Entropy Method for Combinatorial and Continuous Optimization.” Methodology and Computing in Applied Probability 1, 127–190.
Shahabuddin, P. (1994a). “Fast transient Simulation of Markovian Models of Highly Dependable Systems.” Performance Evaluation 20, 267–286.
Shahabuddin, P. (1994b). “Importance Sampling for the Simulation of Highly Reliable Markovian Systems.” Management Science 40, 333–352.
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Ridder, A. Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy. Ann Oper Res 134, 119–136 (2005). https://doi.org/10.1007/s10479-005-5727-9
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DOI: https://doi.org/10.1007/s10479-005-5727-9