A New Approach Combining Simulation and Randomization for the Analysis of Large Continuous Time Markov Chains

ACM Transactions on Modeling and Computer Simulation

Volumn 8, Issue 2, 1998, Pages 194-222

  Buchholz, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Markov chains; Numerical techniques; Randomization; Simulation

Indexed keywords

COMPUTER SIMULATION; NUMERICAL ANALYSIS; PETRI NETS; PROBABILITY DISTRIBUTIONS; VECTORS; ALGORITHMS; RANDOM NUMBER GENERATION;

RANDOMIZATION; MARKOV CHAINS; NUMERICAL TECHNIQUES;

MARKOV PROCESSES;

EID: 0032036166     PISSN: 10493301     EISSN: None     Source Type: Journal    
DOI: 10.1145/280265.280274     Document Type: Article

References (32)

1. BALBO, G., BRUELL, S. C., AND GHANTA, S. 1988. Combining queueing networks and generalized stochastic Petri nets for the solution of complex models of system behavior. IEEE Trans. Computers 37, 10, 1251-1268.
2. BAUSE, F., BUCHHOLZ, P., AND KEMPER, P. 1995. QPN-tool for the specification and analysis of hierarchically combined queueing Petri nets. In Quantitative Evaluation of Computing and Communication Systems H. Beilner and F. Bause Eds., Springer Verlag, New York, 224-238.
3. BUCHHOLZ, P. 1992. A hierarchical view of GCSPNs and its impact on qualitative and quantitative analysis. J. Parallel Distrib. Comput. 15, 3, 207-224.
4. BUCHHOLZ, P. 1994, A class of hierarchical queueing networks and their analysis. Queueing Syst. 15, 1, 59-80.
5. BUCHHOLZ, P. 1997. A distributed numerical/simulative algorithm for the analysis of large continuous time Markov chains. In Proceedings of the 11th Workshop on Parallel and Distributed Simulation (PADS'97), IEEE CS-Press, 4-11.
6. CHIOLA, G. AND FERSCHA, A. 1993. Distributed simulation of Petri nets. IEEE Parallel Distrib. Technol. 1, 3, 33-50.
7. CHIOLA, G., FRANCESCHINIS, G., GAETA, R., AND RIBAUDO, M. 1996. GreatSPN1.7: graphical editor and analyzer for timed and stochastic Petri nets. Perform. Eval. 24, 1/2, 47-68.
8. CHIOLA, G., MARSAN, M. A., BALBO, G., AND CONTE, G. 1993. Generalized stochastic Petri nets: A definition at the net level and its implications. IEEE Trans. Softw. Eng. 19, 2, 89-107.
9. CIARDO, G., MUPPALA, J., AND TRIVEDI, K. S. 1991. On the solution of GSPN reward models. Perform. Eval. 12, 4, 237-253.
10. GERMAN, R., KELLING, C., ZIMMERMANN, A., AND HOMMEL, G. 1995. TimeNET - a toolkit for evaluating non-Markovian stochastic Petri nets. Perform. Eval. 24, 1/2, 69-87.
11. GRASSMANN, W. K. 1991. Finding transient solutions in Markovian event systems through randomization. In Numerical Solution of Markov Chain, W. J. Stewart Ed., Marcel Dekker, 375-395.
12. GROSS, D. AND MILLER, D. 1984. The randomization technique as a modeling tool and solution procedure for transient Markov processes. Oper. Res. 32, 2, 926-944.
13. HEIDELBERGER, P. 1995. Fast simulation of rare events in queueing and reliability models. ACM Trans. Modeling Comput. Simul. 5, 1, 43-85.
14. HEIDELBERGER, P. AND NICOL, D. M. 1993. Conservative parallel simulation of continuous time Markov chains using uniformization. IEEE Trans. Parallel Distrib. Syst. 4, 8, 906-921.
15. HORDIJK, A., IGLEHART, D. L., AND SCHASSBERGER, R. 1976, Discrete time methods for simulating continuous time Markov chains. Advances Appl. Probab. 8, 772-788.
16. HOWARD, R. A. 1971. Dynamic Probabilistic Systems, vol. II: Semi-Markov and Decision Processes. Wiley, New York.
17. JAIN, R. 1991. The Art of Computer Systems Performance Analysis. Wiley, New York.
18. JENSEN, A. 1953. Markoff chains as an aid in the study of Markoff processes. Skandinavisk Aktuarietidskrift 36, 87-91.
19. KLEVANS, R. L. AND STEWART, W. J. 1996. From queueing networks to Markov chains: The XMARCA interface. Perform. Eval. 24, 1/2, 23-46.
20. LAW, A. M. AND KELTON, W. D. 1991. Simulation Modeling and Analysis. Wiley, New York.
21. LI, Y. AND WOODSIDE, C. M. 1995. Complete decomposition of stochastic petri nets representing generalized service networks. IEEE Trans. Computers 44, 4, 577-592.
22. LITZBA, D., SCZITTNICK, M., AND STEWING, F. J. 1989. Yet another simulation output analysis algorithm: the autoregressive, online-update evaluation technique of the modelling tool, HIT. In Proceedings of the 3rd European Simulation Congress.
23. MUNTZ, R. R., DE SOUZA E SILVA, E., AND GOYAL, A. 1989, Bounding availability of repairable computer systems. Perform. Eval. Rev. 17, 1, 29-38.
24. NICOL, D. M. AND HEIDELBERGER, P. 1993. Optimistic parallel simulation of continuous time Markov chains using uniformization. J. Parallel Distrib. Comput. 18, 4, 395-410.
25. NICOL, D. M. AND HEIDELBERGER, P. 1995. A comparative study of parallel algorithms for simulating continuous time Markov chains. ACM Trans. Modeling Comput. Simul. 5, 4, 326-354.
26. SANDERS, W. H. AND MALHIS, L. M. 1992. Dependability evaluation using composed SAN-based reward models. J. Parallel Distrib. Comput. 15, 3, 238-254.
27. SCHWETMAN, H. D. 1978. Hybrid simulation models of computer systems. Commun. ACM 21, 9, 718-723.
28. SHANTIKUMAR, J. G. 1986. Uniformization and hybrid simulation/analytic models of renewal processes. Oper. Res. 34, 4, 573-580.
29. SHANTIKUMAR, J. G. AND SARGENT, R. G. 1983. A unifying view of hybrid simulation/analytic models and modeling. Oper. Res. 31, 6, 1030-1052.
30. STEWART, W. J. 1994. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton, NJ.
31. TRIVEDI, K. S., MUPPALA, J. K., WOOLET, S. P., AND HAVERKORT, B. R. 1992. Composite performance and dependability analysis. Perform. Eval. 14, 3/4, 197-215.
32. WAGNER, D. B. AND LAZOWSKA, E. D. 1989. Parallel simulation of queueing networks: limitations and potentials. Perform. Eval. Rev. 17, 1, 146-155.