Likelihood ratio derivative estimation for finite-time performance measures in generalized semi-Markov processes

Management Science

Volumn 44, Issue 10, 1998, Pages 1426-1441

  Nakayama, Marvin K ^a   Shahabuddin, Perwez ^a  

^a NONE

Author keywords

Generalized Semi Markov Processes; Gradient Estimation; Simulation

Indexed keywords

ALGORITHMS; ESTIMATION; MARKOV PROCESSES; OPTIMIZATION; PERTURBATION TECHNIQUES; QUEUEING THEORY; RELIABILITY;

GENERALIZED SEMI MARKOV PROCESSES; LIKELIHOOD RATIO DERIVATIVE ESTIMATION;

COMPUTER SIMULATION;

EID: 0032180528     PISSN: 00251909     EISSN: None     Source Type: Journal    
DOI: 10.1287/mnsc.44.10.1426     Document Type: Article

References (42)

1. Athreya, K. B. and P. E. Ney, Branching Processes, Springer-Verlag, Berlin, 1972.
2. Aleksandrov, V. M., V. I. Sysoyev, and V. V. Shemeneva, "Stochastic Optimization," Engineering Cybernetics, 5 (1968), 11-16.
3. Arsham, H., A. Feuerberger, D. L. McLeish, J. Kreimer, and R. Y. Rubinstein, "Sensitivity Analysis and the "What If" Problem in Simulation Analysis," Math. Comput. Modelling, 12 (1989), 193-219.
4. Billingsley, P., Probability and Measure (Second Ed.), John Wiley and Sons, New York, 1986.
5. Blum, A., P. Heidelberger, S. S. Lavenberg, M. K. Nakayama, and P. Shahabuddin, System Availability Estimator (SAVE) Language Reference and User's Manual, Version 4.0, Research Report RA 219 S, IBM T. J. Watson Research Center, Yorktown Heights, New York, 1993.
6. Bratley, P., B. L. Fox, and S. E. Schrage, A Guide to Simulation (Second Ed.), Springer-Verlag, New York, 1987.
7. Damerdji, H., "Maximum Likelihood Ratio Estimation for Generalized Semi-Markov Processes," Discrete Event Dynamic Systems: Theory and Applications, 6 (1996), 73-104.
8. Glasserman, P., Gradient Estimation Via Perturbation Analysis, Kluwer Academic Press, Norwell, MA, 1991a.
9. _, "Structural Conditions for Perturbation Analysis Derivative Estimates: Finite Time Performance Indices," Operations Res., 39 (1991b), 724-738.
10. _, "Structural Conditions for Perturbation Analysis of Queuing Systems," J. ACM, 38 (1991c), 1005-1025.
11. _ and P. W. Glynn, "Gradient Estimation for Regenerative Processes," Proc. 1992 Winter Simulation Conf., J. J. Swain, D. Goldsman, R. C. Crain, and J. R. Wilson (Eds.), IEEE Press, Piscataway, NJ 1992, 280-288.
12. _ and D. D. Yao, "Monotonicity in Generalized Semi-Markov Processes," Math. Oper. Res., 17 (1992a), 1-21.
13. _ and _, "Generalized Semi-Markov Processes: Antimatroid Structure and Second-Order Properties," Math. Oper. Res., 17 (1992b), 444-469.
14. _ and _, "Some Guidelines and Guarantees for Common Random Numbers," Management Sci., 38 (1992c), 884-908.
15. Glynn, P. W., "Stochastic Approximation for Monte Carlo Optimization," Proc. 1986 Winter Simulation Conf., J. Wilson, J. Henriksen, and S. Roberts (Eds.), IEEE Press, 1986, 356-364.
16. _, "Likelihood Ratio Gradient Estimation: An Overview," Proc. 1987 Winter Simulation Conf., A. Thesen, H. Grant, and W. D. Kelton (Eds.), IEEE Press, Piscataway, NJ 1987, 366-375.
17. _, "Optimization of Stochastic Systems via Simulation," Proc. 1989 Winter Simulation Conf., E. A. MacNair, K. J. Musselman, and P. Heidelberger (Eds.), IEEE Press, Piscataway, NJ 1989a, 90-105.
18. _, "A GSMP Formalism for Discrete-Event Systems," Proc. IEEE, 77 (1989b), 14-23.
19. _, "Likelihood Ratio Derivative Estimators for Stochastic Systems," Comm. ACM, 33, 10 (1990), 75-84.
20. _ and D. L. Iglehart, "Simulation Methods for Queues: An Overview," Queueing Systems: Theory and Applications, 3 (1988), 221-256.
21. _ and _, "Importance Sampling for Stochastic Simulations," Management Sci., 35 (1989), 1367-1393.
22. Haas, P. J. and G. S. Shedler, "Regenerative Generalized Semi-Markov Processes," Stochastic Models, 3 (1987), 409-438.
23. Heidelberger, P., X. R. Cao, M. A. Zazanis, and R. Suri, "Convergence Properties of Infinitesimal Perturbation Analysis Estimates," Management Sci., 34 (1988), 1281-1302.
24. _, P. Shahabuddin, and V. F. Nicola, "Bounded Relative Error in Estimating Transient Measures of Highly Dependable Non-Markovian Systems," ACM Trans. on Modeling and Computer Simulation, 4 (1994), 137-164.
25. Ho, Y. C. and X. R. Cao, "Optimization and Perturbation Analysis of Queueing Networks," J. Optimization Theory and Applications, 40 (1983), 559-582.
26. L'Ecuyer, P., "A Unified View of the IPA, SF, and LR Gradient Estimation Techniques," Management Sci., 36 (1990), 1364-1383.
27. _, "An Overview of Derivative Estimation," Proc. 1991 Winter Simulation Conf., B. L. Nelson, W. D. Kelton, and G. M. Clark (Eds.), IEEE Press, Piscataway, NJ 1991, 207-217.
28. _, "Note: On the Interchange of Derivative and Expectation for Likelihood Ratio Derivative Estimators," Management Sci., 41 (1995), 738-748.
29. Nakayama, M. K., "Asymptotics of Likelihood Ratio Derivative Estimators in Simulations of Highly Reliable Markovian Systems," Management Sci., 41 (1995), 524-554.
30. _, A. Goyal, and P. W. Glynn, "Likelihood Ratio Sensitivity Analysis for Markovian Models of Highly Dependable Systems," Operations Res., 42 (1994), 137-157.
31. _, P. Shahabuddin, and K. Sigman, "A Note on Exponential Moments for Branching Processes and Busy Periods for Queues," Preprint, 1996.
32. Nicola, V. F., M. K. Nakayama, P. Heidelberger, and A. Goyal, "Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes," IEEE Trans. on Computers, 14 (1993), 1440-1452.
33. _, P. Shahabuddin, P. Heidelberger, and P. W. Glynn, "Fast Simulation of Steady State Availability in Non-Markovian Highly Dependable Systems," Proc. Twenty-Third Annual International Symposium on Fault Tolerant Computing, IEEE Computer Society Press, Piscataway, NJ 1993, 38-47.
34. Prabhu N. U., Stochastic Processes, Macmillan, New York, 1965.
35. Reiman, M. I. and A. Weiss, "Sensitivity Analysis via Likelihood Ratios," Proc. 1986 Winter Simulation Conf., J. R. Wilson, J. O. Henriksen, and S. D. Roberts (Eds.), IEEE Press, Piscataway, NJ 1986, 285-289.
36. _ and _, "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Res., 37 (1989), 830-844.
37. Ross, S., Stochastic Processes, Wiley, New York, 1983.
38. Rubinstein, R. Y., "The Score Function Approach for Sensitivity Analysis of Computer Simulation Models," Mathematics Computer Simulation, 28 (1986), 351-379.
39. _, "Sensitivity Analysis and Performance Extrapolation for Computer Simulation Models," Operations Res., 37 (1989), 72-81.
40. _ and A. Shapiro, Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method, Wiley, New York, 1993.
41. Shassberger, R., "On the Equilibrium Distribution of a Class of Finite-State Generalized Semi-Markov Processes," Math. Oper. Res., 1 (1976), 395-406.
42. Whitt, W., "Continuity of Generalized Semi-Markov Processes," Math. Oper. Res., 5 (1980), 494-501.