A Fast Monte Carlo Method for Evaluating Reliability Indexes

IEEE Transactions on Reliability

Volumn 48, Issue 3, 1999, Pages 256-261

  Lieber, Dmitrii ^a   Nemirovskii, Arkadii ^a   Rubinstein, Reüven Y ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Importance sampling; Rare event; Score function; Sensitivity analysis; Simulation

Indexed keywords

EID: 0000504339     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/24.799896     Document Type: Article

References (35)

1. S. Asmussen, "Conjugate processes and the simulation of ruin problems", Stochastic Process Applications, vol 20, 1985, pp 213 - 229.
2. S. Asmussen, Applied Probability and Queues, 1987; John Wiley & Sons.
3. S. Asmussen, "Risk theory in a Markovian environment", Sound. Actuarial J, 1989, pp 69 - 100.
4. S. Asmussen, "Siegmund duality, Markov dependence and applications", Manuscript, 1994; Aalborg University, Aalborg.
5. S. Asmussen, R.Y. Rubinstein, "Regenerative rare-events simulation via likelihood ratios", J. Applied Probability, vol 31, iiuin 3, 1994, pp 797 - 815.
6. S. Asmussen, R.Y. Rubinstein, "Complexity properties of steady-state rare-events simulation in queuing models", Advances in Queuing: Theory, Methods and Open Problems (J. Dshalalow, Ed), 1995, pp 429 - 462, CRC Press.
7. O.S. Chaiig, P. Heidelberger, S. Juneja, P. Shahabuddin, "Effective bandwidth and fast simulation of ATM in tree networks", Performance Evaluation, vol 20, 1994, pp 45 65.
8. O.S. Chang, P. Heidelberger, P. Shahabuddin, "Fast simulation of packet loss rates in a shared buffer communications switch", ACM Trans. Modeling and Computer Simulation, vol 5, num 4, 1995, pp 306 - 325.
9. M. Cottrel, J.C. Fort, G. Malgoures, "Deviations and rare events in the study of stochastic algorithms", IEEE Trans. Automatic Control, vol AC-28, 1983, pp 907 - 918.
10. A. Dembo, O. Zeitouni, Deviation Techniques, 1993; Jones & Bartlett.
11. P. Glasserman, T.W. Liu, "Rare-event simulation for multistage production-inventory systems", Management Science, vol 42, 1995, pp 1292 - 1307.
12. P. Glasserman, Sh.-G. Kou, "Analysis of importance sampling estimator for tandem queues", ACM Trans. Modeling and Computer Simulation, vol 5, 1995 Jan, pp 22 42.
13. A. Goyal, P. Shahabuddin, P. Heidelberger, et al, "A unified framework for simulating Markovian models of highly dependable systems", IEEE Trans. Computers, vol 41, 1992, pp 36 - 51.
14. S.H.P. Gunha, M.V.F. Pereira, L.M.V.G. Pinto, C.C. Oliveira, "Composite generation and transmission reliability evaluation in large hydroelectric systems", IEEE Trans. Power Apparatus and Systems, vol PAS-104, 1985 Oct, pp 2657 - 2663.
15. P. Heidelberger, "Fast simulation of rare events in queuing and reliability models", A CM Trans. Modeling and Computer Simulation, vol 5, num 1, 1993, pp 43 - 85.
16. P. Heidelberger, P. Shahabuddin, V.F. Nicola, "Bounded relative error in estimating transient measures of highly dependable non-Markovian systems", A CM Trans, Modeling and Computer Simulation, vol 2, 1994 Apr, pp 137 - 164.
17. I. Kovalenko, "Approximations of queues via small parameter method", Advances in Queuing: Theory, Methods and Open Problems (3. Dshalalow, Ed), 1995, pp 481 509; CRC Press.
18. V. Kriman, R.Y. Rubinstein, "Polynomial and exponential time algorithms for estimation of rare events in queuing models", Frontiers in Queuing: Models and Applications in Science and Engineering (3. Dshalalow, Ed), 1994; CRC Press.
19. D. Lieber, R.Y. Rubinstein, D. Elmakis, "Quick estimation of rare events in stochastic networks", IEEE Trans. Reliahilitij, vol 46, num 2, 1997 Jun, pp 254 - 265.
20. M. Mandjes, "Rare event analysis of communication networks", PhD Thesis, 1996; Vrije Universiteit, Amsterdam.
21. M. Mandjes, "Fast simulation of blocking probabilities in loss networks", Eurnpe.an .1. Operations Research, vol 101, num 2, 1997, pp 393 - 405.
22. V.F. Nicola, P. Shahabuddin, P. Heidelberger, P..W. Glynn, "Fast simulation of steady-state availability in nonMarkovian highly dependable systems", Proc. Twentieth Int'l Symp. Fault-Tolerant Computing, 1993, pp 491 - 498; IEEE Computer Society Press.
23. S. Parekh, J. Walrand, "A quick simulation method for excessive backlogs in networks of queues", IEEE Trans. Automatic Control, vol 34, 1989, pp 54 - 66.
24. Reliability Test System Task Force of the Application of Probability Methods Subcommittee (Chair'n, P.P. Albrecht), "IEEE Reliability Test System", IEEE Trans. Power Apparatus and Systems, vol PAS-98, num 6, 1979 Nov/Dec, pp 2047 - 2054.
25. R.Y. Rubinstein, B. Melamed, Efficient Simulation and Modeling, 1998; John Wiley fc Sons.
26. R.Y. Rubinstein, A. Shapiro, Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization via the Score Function Method, 1993; John Wiley & Sons.
27. J.S. Sadowsky, "Deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue", IEEE Trans. Automatic Control, vol 36, 1991, pp 1383 - 1394.
28. J.S. Sadowsky, "On the optimality and stability of exponential twisting in Monte Carlo simulation". IEEE Trans. Information Theory, vol 39, 1993, pp 119 - 128.
29. J.S. Sadowsky, J.S. Bucklew, "On deviations theory and asymptotically efficient Monte Carlo estimation", IEEE Trans. Information Theory, vol 36, 1990, pp 579 - 588.
30. P. Shahabuddin, "Fast simulation of packet loss rates in communications networks with priorities," Proc. 1994 Winter Simulation Conf, 1994, pp 274 - 281; IEEE Press.
31. P. Shahabuddin, "Importance sampling for the simulation of highly reliable Markovian systems", Management Science, vol 40, num 3, 1994, pp 333 - 352.
32. P. Shahabuddin, "Rare event simulation of stochastic systems", Proc. 1995 Winter Simulation Conf, 1995, pp 178 - 185; IEEE Press.
33. A. Shwartz, A. Weiss, Deviation for Performance Analysis: Queues, Communication and Computers, 1995; Chapman-Hall.
34. P. Tsoucas, "Rare events in series of queues", J. Applied Probability, vol 29, 1992, pp 168 - 175.
35. "Workshop proceedings - Power system planning research needs and priorities", it EPRI Report EL-3152, 1983 Jul.