Simulating GI/GI/1 queues and insurance risk processes with subexponential distributions

Winter Simulation Conference Proceedings

Volumn 1, Issue , 2000, Pages 656-665

  Boots, Nam Kyoo ^a   Shahabuddin, Perwez ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; PACKET NETWORKS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; RISK ASSESSMENT;

INSURANCE RISK PROCESSES;

QUEUEING NETWORKS;

EID: 0034431316     PISSN: 02750708     EISSN: None     Source Type: Journal    
DOI: 10.1109/WSC.2000.899777     Document Type: Article

References (29)

1. S. Asmussen Conjugate processes and the simulation of ruin problems Stochastic Processes and their Applications 20 213 229 1985
2. S. Asmussen K. Binswanger Simulation of ruin probabilities for subexponential claims ASTIN Bulletin 27 2 297 318 1997
3. S. Asmussen K. Binswanger B. Hojgaard Rare event simulation for heavy-tailed distributions 1998 Sweden, Lund Dept. of Mathematical Statistics, Lund University
4. S. Asmussen K. Binswanger B. Hojgaard Rare event simulation for heavy-tailed distributions Bernoulli 6 2 303 322 2000
5. S. Asmussen C. Kiüppelberg Large deviations results for subexponential tails, with applications to insurance risk Stochastic Processes and their Applications 64 103 125 1996
6. Ν. Κ. Boots P. Shahabuddin Simulating tail probabilities in GI/GI/1 queues and insurance risk processes with subexponential distributions 2000 NY Dept. of Industrial Engineering and Operations Research, Columbia University
7. J. A. Bucklew Large Deviations techniques in decision, simulation, and estimation 1990 John Wiley & Sons, Inc.
8. C. S. Chang S. Juneja P. Heidelberger P. Shahabuddin Effective bandwidth and fast simulation of ATM intree networks Performance Evaluation 20 45 65 1994
9. M. Cottrell J. C. Fort G. Malgouyres Large deviations and rare events in the study of stochastic algorithms IEEE Transactions on Automatic Control AC28 907 920 1983
10. V. P. Chistyakov A theorem on sums of independent positive random variables and its applications to branching processes Theory of Probability and its Applications 9 640 648 1964
11. P. Embrechts C. Klüppelberg T. Mikosch Modelling extremal events. Berlin Heidelberg 1997 Springer-Verlag
12. P. Embrechts C. Klüppelberg Some aspects of insurance mathematics Theory of Probability and its Applications 38 2 262 295 1993
13. M. Falkner M. Devetsikiotis I. Lambadaris Fast simulation of networks of queues using effective and decoupling bandwidths ACM Transactions on Modeling and Computer Simulation 9 45 58 1999
14. M. R. Frater T. M. Lenon B. D. O Anderson Optimally efficient estimation of the statistics of rare events in networks IEEE Transactions on Automatic Control 36 1395 1405 1991
15. Α. Feldmann W. Whitt Fitting mixtures of exponentials to long-tail distributions to analyze network performance models Performance Evaluation 31 245 279 1998
16. W. Feller An introduction to probability theory and its applications II 1966 John Wiley & Sons, Inc.
17. P. Glasserman P. Heidelberger P. Shahabuddin T. Zajic Multilevel splitting for estimating rare event probabilities Operations Research 47 585 600 1999
18. P.W. Glynn D.L. Iglehart Importance sampling for stochastic simulations Management Science 35 11 1367 1393 1989
19. P.W. Glynn W. Whitt The asymptotic efficiency of simulation estimators Operations Research 40 505 520 1992
20. C.M. Goldie S. Resnick Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution Advances in Applied Probability 20 706 718 1988
21. S. Juneja P. Shahabuddin Simulating heavy-tailed processes using delayed hazard rate twisting 1999 NY Research Report Dept. of Industrial Engineering and Operations Research, Columbia University
22. P. Heidelberger Fast simulation of rare events in queueing and reliability models ACM Transactions on Modeling and Computer Simulation 6 43 85 1995
23. T. Lehtohnen H. Nyrhinen Simulating level-crossing probabilities by importance sampling Advances in Applied Probability 24 858 874 1992
24. W. Leland M. Taqqu W. Willinger D. Wilson On the self-similar nature of Ethernet trafic IEEE/ACM Transactions on Networking 2 1 15 1994
25. A.G. Pakes On the tails of waiting time distributions Journal of Applied Probability 12 555 564 1975
26. S. Parekh J. Walrand A quick simulation method for excessive backlogs in network of queues IEEE Transactions on Automatic Control 54 56 1989
27. J.S. Sadowsky Large deviations and efficient estimation of excessive backlogs in GI/G/m queue IEEE Transactions on Automatic Control 36 1991 1383 1394 1991
28. P. Shahabuddin Importance sampling for the simulation of highly reliable Markovian systems Management Science 40 333 352 1994
29. D. Siegmund Importance sampling in the Monte Carlo study of sequential tests The Annals of Statistics 4 673 684 1976