A large deviations perspective on the efficiency of multilevel splitting

IEEE Transactions on Automatic Control

Volumn 43, Issue 12, 1998, Pages 1666-1679

  Glasserman, Paul ^b   Heidelberger, Philip ^a,c   Shahabuddin, Perwez ^a,d   Zajic, Tim ^e  

^a IEEE

^b Och Spine at New York Presbyterian Hospitals   (United States)

^c IBM T J WATSON RESEARCH CENTER   (United States)

^d University of Minnesota ^*  (United States)

^e UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Large deviations; Monte Carlo; Rare event; Simulation; Variance reduction

Indexed keywords

ASYNCHRONOUS TRANSFER MODE; FAULT TOLERANT COMPUTER SYSTEMS; MONTE CARLO METHODS; OPTIMIZATION; PROBABILITY;

LARGE DEVIATION; MULTILEVEL SPLITTING; RARE EVENT; VARIANCE REDUCTION;

COMPUTER SIMULATION;

EID: 0032302337     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.736061     Document Type: Review

References (37)

1. S. Andradóttir, D. P. Heyman, and T. J. Ott, "On the choice of alternative measures in importance sampling with Markov chains," Oper. Res., vol. 43, no. 3, pp. 509-519, 1995.
2. V. Anantharam, "The optimal buffer allocation problem," IEEE Trans. Inform. Theory, vol. 35, pp. 721-725, 1939.
3. J. A. Bucklew, Large Deviation Techniques in Decision, Simulation and Estimation. New York: Wiley, 1990.
4. C. S. Chang, "Stability, queue length and delay of deterministic and stochastic queueing networks," IEEE Trans. Automat. Contr., vol. 39, pp. 913-931, 1994.
5. C. S. Chang, P. Heidelberger, S. Juneja, and P. Shahabuddin, "Effective bandwidth and fast simulation of ATM in tree networks," Perf. Eval., vol. 20, pp. 45-65, 1994.
6. C. S. Chang, P. Heidelberger, and P. Shahabuddin, "Fast simulation of packet loss rates in a shared buffer communications switch," ACM Trans. Modeling and Computer Simulation, vol. 5, no. 4, pp. 306-325, 1995.
7. J. Collamore, "Hitting probabilities and large deviations," Ann. Probability, vol. 24, no. 4, pp. 2065-2078, 1996.
8. M. Cottrell, J.-C. Fort, and G. Malgouyres, "Large deviations and rare events in the study of stochastic algorithms," IEEE Trans. Automat. Contr., vol. 28, pp. 907-920, 1983.
9. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. London, U.K.: Jones and Bartelett, 1993.
10. M. Devetsikiotis and J. K. Townsend, "An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation," IEEE Trans. Commun., vol. 41, no. 10, pp. 1464-1473, 1990.
11. A. Dubi, "General statistical model for geometrical splitting in Monte Carlo - Part I," Transport Theory and Statistical Phys., vol. 14, pp. 167-193, 1985.
12. M. R. Frater, T. M. Lenon, and B. D. O. Anderson, "Optimally efficient estimation of the statistics of rare events in queueing networks," IEEE Trans. Automat. Contr., vol. 36, pp. 1395-1405, 1991.
13. P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic, "Multileva splitting for estimating rare event probabilities," Yorktown Heights, NY, IBM T. J. Watson Res. Center Rep. RC 20478, 1996 and Ops Res., to be published.
14. _, "Splitting for rare event simulation: Analysis of simple cases," in Proc. Winter Simulation Conf. San Diego, CA: IEEE Computer Soc. Press, 1996, pp. 302-308.
15. _, "A look at multilevel splitting," in Monte Carlo and Quasi-Monte Carlo Methods, H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof, Eds. New York: Springer-Verlag, 1997, pp. 98-108.
16. P. Glasserman and S. G. Kou, "Analysis of an importance sampling estimator for tandem queues," ACM Trans. Modeling and Computer Smulation, vol. 5, no. 1, pp. 22-42, 1995.
17. P. Glasserman and Y. Wang, "Counterexamples in importance sampling for large deviations probabilities," Ann. Appl. Probability, vol. 7, pp. 731-746, 1997.
18. P. W. Glynn and W. Whitt, "The asymptotic efficiency of simulation estimators," Oper. Res., vol. 40, pp. 505-520, 1992.
19. A. Goyal, P. Shahabuddin, P. Heidelberger, V. F. Nicola, and P. W. Glynn, "A unified framework for simulating Markovian models of highly reliable systems," IEEE Trans. Comput., vol. 41, pp. 36-51, 1992.
20. J. Hammersley and D. Handscomb, Monte Carlo Methods. London, U.K.: Methuen, 1965.
21. P. Heidelberger, "Fast simulation of rare events in queueing and reliability models," ACM Trans. Modeling and Computer Simulation, vol. 5, no. 1, pp. 43-85, 1995.
22. H. Kahn and T. E. Harris, "Estimation of particle transmission by random sampling," Nat. Bur. Standards Appl. Math. Series, vol. 12, pp. 27-30, 1951.
23. G. Kesidis and J. Walrand, "Quick simulation of ATM buffers with on-off multiclass Markov fluid sources," ACM Trans. Modeling and Computer Simulation, vol. 3, no. 3, pp. 269-276, 1993.
24. S. Parekh and J. Walrand, "A quick simulation method for excessive backlogs in networks of queues," IEEE Trans. Automat. Contr., vol. 34, pp. 54-56, 1989.
25. J. S. Sadowsky, "Large deviations and efficient simulation of excessive backlogs in a GI/G/m queue," IEEE Trans. Automat. Contr., vol. 36, pp. 1383-1394, 1991.
26. _, "On the optimally and stability of exponential twisting in Monte Carlo estimation," IEEE Trans. Inform. Theory, vol. 39, pp. 119-128, 1993.
27. J. S. Sadowsky and J. A. Bucklew, "On large deviations theory and asymptotically efficient Monte Carlo estimation," IEEE Trans. Inform. Theory, vol. 36, pp. 579-588, 1990.
28. F. Schreiber and C. Görg, "Rare event simulation: A modified RESTART-method using LRE-algorithm," in Proc. Int. Telecommunications Conf., J. Labetoulle and J. W. Roberts, Eds. Amsterdam, The Netherlands: Elsevier Sci., 1994, pp. 787-796.
29. P. Shahabuddin, "Importance sampling for the simulation of highly reliable Markovian systems," Management Sci., vol. 40, no. 3, pp. 333-352, Mar. 1994.
30. A. Shwartz and A. Weiss, Large Deviations for Performance Analysis: London, U.K.: Chapman & Hall, 1995.
31. D. Siegmund, "Importance sampling in the Monte Carlo study of hypothesis tests," Ann. Satist., vol. 4, pp. 673-684, 1976.
32. A. V. Starkov, "Monte Carlo splitting importance sampling," Monte Carlo Methods and Appl., vol. 1, pp. 241-250, 1995.
33. G. de Veciana, C. Courcoubetis, and J. Walrand, "Decoupling bandwidths for networks: A decomposition approach to resource management," in IEEE INFOCOM Proc. New York: IEEE Computer Soc. Press, 1994, pp. 466-473.
34. M. Villén-Altamirano, A. Martínez-Marrón, J. Gamo, and F. Fernández-Cuesta, "Enhancements of the accelerated simulation method RESTART by considering multiple thresholds," in Proc. Int. Telecommunications Conf. 14, J. Labetoulle and J. W. Roberts, Eds. Amsterdam, The Netherlands: Elsevier Sci., 1994, pp. 797-810.
35. M. Villén-Altamirano and J. Villén-Altamirano, "RESTART: A method for accelerating rare event simulations," Queueing, Performance and Control in ATM, J. W. Cohen and C. D. Pack, Eds. Amsterdam, The Netherlands: Elsevier Sci., 1991, pp. 71-76.
36. _, "RESTART: A straightforward method for fast simulation of rare events," in Proc. Wnter Simulation Conf. San Diego, CA: Society for Computer Simulation, 1994, pp. 282-289.
37. T. Zajic, "On the typical path to hitting a rare set," in Proc. 34th Annual Allerton Conf. Communication, Control and Computing. Urbana-Champaign, IL: Univ. Illinois, 1996, pp. 751-759.