Fast simulation of overflow probabilities in a queue with Gaussian Input

ACM Transactions on Modeling and Computer Simulation

Volumn 16, Issue 2, 2006, Pages 119-151

  Dieker, A B ^a,b   Mandjes, M ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Asymptotic efficiency; Gaussian processes; Importance sampling; Large deviations; Overflow probability; Queueing theory

Indexed keywords

ASYMPTOTIC EFFICIENCY; GAUSSIAN PROCESSES; IMPORTANCE SAMPLING; LARGE DEVIATIONS; OVERFLOW PROBABILITY;

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; NUMERICAL METHODS; QUEUEING THEORY;

PROBABILITY;

EID: 33745202557     PISSN: 10493301     EISSN: 10493301     Source Type: Journal    
DOI: 10.1145/1138464.1138466     Document Type: Article

References (40)

1. ADDIE, R., MANNERSALO, P., AND NORROS, I. 2002. Most probable paths and performance formulae for buffers with Gaussian input traffic. European Trans. Telecommun. 13, 183-196.
2. ASMUSSEN, S. 1989. Risk theory in a Markovian environment. Scared. Actuar, J., 69-100.
3. ASMUSSEN, S. 2000. Ruin Probabilities. World Scientific Publishing Co. Inc.
4. ASMUSSEN, S. AND BINSWANOER, K. 1997. Simulation of ruin probabilities for subexponential claims. ASTIN Bull. 27, 297-318.
5. ASMUSSEN, S. AND RUBINSTEIN, R. Y. 1995. Steady state rare events simulation in queueing models and its complexity properties. In Advances in Queueing, J. Dshalalow, ed. CRC, Boca Raton, Fla. 429-461.
6. BAHADUR, R. R. AND ZABELL, S. L. 1979. Large deviations of the sample mean in general vector spaces. Ann. Probab. 7, 587-621.
7. BALDI, P. AND PACCHIAROTTI, B. 2004. Importance sampling for the ruin problem for general Gaussian processes. Preprint.
8. BINGHAM, N. H., GOLDIE, C. M., AND TEUGELS, J. L. 1989. Regular Variation. Cambridge University Press, Cambridge, Mass.
9. BOOTS, N. K. AND MANDJES, M. 2002. Fast simulation of a queue fed by a superposition of many (heavy-tailed) sources. Probab. Engrg. Inform. Sci. 16, 205-232.
10. BUCKLEW, J. A., NEY, P., AND SADOWSKY, J. S. 1990. Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains. J. Appl. Probab. 27, 44-59.
11. COLLAMORE, J. F. 2002. Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors. Ann. Appl. Probab. 12, 382-421.
12. DAVIES, R. B. AND HARTE, D. S. 1987. Tests for Hurst effect. Biometrika 74, 95-102.
13. DȨBICKI, K. AND MANDJES, M. 2003. Exact overflow asymptotics for queues with many Gaussian inputs. J. Appl. Probab. 40, 704-720.
14. DȨBICKI, K. AND PALMOWSKI, Z. 1999. On-off fluid models in heavy traffic environment. Queueing Syst. 33, 327-338.
15. DEMBO, A. AND ZEITOUNI, O. 1998. Large Deviations Techniques and Applications, 2nd ed. Springer Verlag, New York.
16. DEUSCHEL, J.-D. AND STROOCK, D. W. 1989. Large Deviations. Academic Press, Boston, Mass.
17. DIEKER, A. B. 2005. Conditional limit theorems for queues with Gaussian input, a weak convergence approach. Stochastic Process. Appl. 115, 849-873.
18. DIEKER, A. B. AND MANDJES, M. 2003. On spectral simulation of fractional Brownian motion. Probab. Engrg. Inform. Sci. 17, 417-434.
19. DIEKER, A. B. AND MANDJES, M. 2005. On asymptotically efficient simulation of large deviation probabilities. Adv. in Appl. Probab. 37, 539-552.
20. DIETRICH, C. R. AND NEWSAM, G. N. 1997. Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. SIAMJ. Sci. Comput. 18, 4, 1088-1107.
21. DUPUIS, P. AND WANG, H. 2004. Importance sampling, large deviations, and differential games. Stock. Stock. Rep. 76, 481-508.
22. GANESH, A., O'CONNELL, N., AND WISCHIK, D. 2004. Big Queues. Springer Verlag, Berlin.
23. GLASSERMAN, P. AND WANG, Y. 1997. Counterexamples in importance sampling for large deviations probabilities. Ann. Appl. Probab. 7, 731-746.
24. HEIDELBERGER, P. 1995. Fast simulation of rare events in queueing and reliability models. ACM Trans. Model. Comput. Simul. 5, 43-85.
25. HUANG, C., DEVETSIKIOTIS, M., LAMBADARIS, I., AND KAYE, A. R. 1999. Fast simulation of queues with long-range dependent traffic. Comm. Statist. Stochastic Models 15, 3, 429-460.
26. KELLY, F. 1996. Notes on effective bandwidths. In Stochastic Networks: Theory and Applications, F. Kelly et al. eds. Oxford University Press, 141-168.
27. LEHTONEN, T. AND NYRHINEN, H. 1992a. On asymptotically efficient simulation of ruin probabilities in a Markovian environment. Scand. Actuar. J., 60-75.
28. LEHTONEN, T. AND NYRHINEN, H. 1992b. Simulating level-crossing probabilities by importance sampling. Adv. in Appl. Probab. 24, 858-874.
29. LELAND, W. E., TAQQU, M. S., WILLINGER, W., AND WILSON, D. V. 1994. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. on Networ. 2, 1, 1-15.
30. LIKHANOV, N. AND MAZUMDAR, R. 1999. Cell loss asymptotics for buffers fed with a large number of independent stationary sources. J. Appl. Probab. 36, 86-96.
31. MICHNA, Z. 1999. On tail probabilities and first passage times for fractional Brownian motion. Math. Meth. Oper. Res. 49, 335-354.
32. MITRINOVIĆ, D. S. 1970. Analytic Inequalities. Springer Verlag, New York.
33. NORROS, I. 1994. A storage model with self-similar input. Queueing Syst. 16, 387-396.
34. ROCKAFELLAR, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, N.J.
35. SADOWSKY, J. 1991. Large deviations and efficient simulation of excessive backlogs in a GI/G/m queue. IEEE Trans. Autom. Control 36, 579-588.
36. SADOWSKY, J. S. AND BUCKLEW, J. A. 1990. On large deviations theory and asymptotically efficient Monte Carlo estimation. IEEE Trans. Inform. Theory 36, 579-588.
37. SIEGMUND, D. 1976. Importance sampling in the Monte Carlo study of sequential tests. Ann, Statist. 4, 673-684.
38. WISCHIK, D. 2001a. Moderate deviations in queueing theory. Preprint.
39. WISCHIK, D. 2001b. Sample path large deviations for queues with many inputs. Ann. Appl. Probab. 11, 379-404.
40. d. J. Comput. Graphical Statistics 3, 4, 409-432.