Fast simulation of Markov fluid models

Journal of Applied Probability

Volumn 33, Issue 3, 1996, Pages 786-803

  Ridder, A D ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Continuous flow systems; Importance sampling; Large deviations; Overflow probability

Indexed keywords

EID: 0030494096     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002190020010021X     Document Type: Article

References (23)

1. ANANTHARAM, V. (1988) How large delays build up in a GI/G/1 queue. Queueing Systems 5, 345-368.
2. ANICK, D., MITRA, D. AND SONDHI, M. M. (1982) Stochastic theory of a data-handling system with multiple sources. Bell Syst. Tech. J. 61, 1871-1894.
3. BLICKLEW, J. A., NEY, P. AND SADOWSKY, J. S. (1990) Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains. J. Appl. Prob. 21, 44-59.
4. CHANG, C.-S., HEIDELBERGER, P., JUNEJA, S. AND SHAHABUDDIN, P. (1992) Effective bandwidth and fast simulation of ATM intree networks. IBM Research Paper.
5. COTTRELL, M., FORT, J.-C. AND MALGOUYRES, G. (1983) Large deviations and rare events in the study of stochastic algorithms. IEEE Trans. Automatic Control 9, 907-920.
6. DE VECIANA, G., OLIVIER, C. AND WALRAND, J. (1993) Large deviations of birth-death Markov fluids. Prob. Eng. Inf. Sci. 7, 237-255.
7. ELLIS, R. S. (1985) Entropy, Large Deviations and Statistical Mechanics. Springer, New York.
8. ELWALID, A. I. AND MITRA, D. (1991) Analysis and design of rate-based congestion control of high speed networks, I: Stochastic fluid models, access regulation. Queueing Systems 9, 29-64.
9. ELWALID, A. I. AND MITRA, D. (1993) Effective bandwidth of general Markovian traffic sources and admission control of high speed networks. IEEE/ACM Trans. Network. 1, 329-343.
10. FREIDLIN, M.I. AND WENTZELL, A. D. (1984) Random Perturbations of Dynamical Systems. Springer, New York.
11. GIBBENS, R. J. AND HUNT, P. J. (1991) Effective bandwidths for the multi-type UAS channel. Queueing Systems 9, 17-28.
12. GLYNN, P. W. AND IGLEHART, D. L. (1989) Importance sampling for stochastic simulations. Management Sci. 35, 1367-1392.
13. KELLY, F. P. (1991) Effective bandwidths at multi-class queues. Queueing Systems 9, 5-16.
14. KESIDIS, G. AND WALRAND, J. (1993) Quick simulation of ATM buffers with on-off multiclass Markov fluid sources. ACM Trans. Model. Comput. Simul. 3, 269-276.
15. KESIDIS, G. AND WALRAND, J. (1993) Relative entropy between Markov transition rate matrices. IEEE Trans. Inf. Theory 39, 1056-1057.
16. KESIDIS, G., WALRAND, J. AND CHANG, C. S. (1993) Effective bandwidths for multiclass Markov fluids and other ATM sources. IEEE/ACM Trans. Network. 1, 424-428.
17. KIFER, Y. (1988) Random Perturbations of Dynamical Systems. Birkhäuser, Boston.
18. KOSTEN, L. (1984) Stochastic theory of data-handling systems with groups of multiple sources. In Performance of Computer-Communication Systems, ed. H. Rudin and W. Bux. Elsevier, Amsterdam, pp. 321-331.
19. PAREKH, S. AND WALRAND, J. (1989) A quick simulation method for excessive backlog in network of queues. IEEE Trans. Automatic Control 34, 54-66.
20. RIDDER, A. AND WALRAND, J. (1992) Some large deviations results in Markov fluid models. Prob. Eng. Inf. Sci. 6, 543-560.
21. SADOWSKY, J. S. (1993) On the optimality and stability of exponential twisting in Monte Carlo estimation. IEEE Trans. Inf. Theory 39, 119-128.
22. SIEGMUND, D. (1976) Importance sampling in the Monte Carlo study of sequential tests. Ann. Statist. 4, 673-684.
23. WENTZELL, A. D. (1976) Rough limit theorems on large deviations for Markov stochastic processes, part II. Theory Prob. Appl. 21, 499-512.