A computationally efficient technique for transient analysis of repairable Markovian systems

Performance Evaluation

Volumn 24, Issue 4, 1996, Pages 311-331

  Malhotra, Manish ^a,b  

^a LUCENT TECHNOLOGIES   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

Availability; Dependability; Markov chains; Ordinary differential equations; Performability; Reliability; Repairable systems; Stability; Stiffness; Transient analysis

Indexed keywords

AVAILABILITY; DIFFERENTIAL EQUATIONS; INTERCONNECTION NETWORKS; MATHEMATICAL MODELS; MULTIPROCESSING SYSTEMS; NUMERICAL ANALYSIS; PERFORMANCE; PROBLEM SOLVING; RELIABILITY; SYSTEMS ANALYSIS;

DEPENDABILITY; ORDINARY DIFFERENTIAL EQUATIONS; REPAIRABLE MARKOVIAN SYSTEMS; TRANSIENT ANALYSIS;

MARKOV PROCESSES;

EID: 0030084157     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/0166-5316(94)00033-6     Document Type: Article

References (34)

1. O. Axelsson. A class of A-stable methods. BIT, 9 (1969) 185-199.
2. R.E. Bank, W.M. Coughran, W. Fichtner, E.H. Grosse, D.J. Rose, and R.K. Smith. Transient simulation of Silicon devices and circuits. IEEE Transactions on Computer-Aided Design, 4 (1985) 436-451.
3. J.T. Blake and K.S. Trivedi. Reliability analysis of interconnection networks using hierarchical composition. IEEE Transactions on Reliability, 38 (1) (1989) 111-120.
4. A. Bobbio and K.S. Trivedi. An aggregation technique for the transient analysis of stiff Markov chains. IEEE Transactions on Computers, 35 (9) (1986) 803-814.
5. G. Ciardo, J.K. Muppala, and K.S. Trivedi. SPNP: Stochastic Petri Net Package. Proc. Int. Workshop on Petri Nets and Performance Models. Kyoto, Japan, December 1989, pp. 803-814.
6. C.A. Clarotti. The Markov approach to calculating system reliability: Computational problems. in: A. Serra and R.E. Barlow, editors, Proc. Int. School of Physics, Course XCIV, North-Holland, Amsterdam (1986) 55-66.
7. E. de Souza e Silva and H.R. Gail. Performability analysis of computer systems: from model specification to solution. Performance Evaluation, 14 (1992) 157-196.
8. I.S. Duff, A.M. Erisman, and J.K. Reid. Direct Methods for Sparse Matrices. Oxford University Press, Oxford (1986).
9. D. Dyer. Unification of reliability/availability/repairability models for Markov systems. IEEE Transactions on Reliability, 38 (2) (1989) 246-252.
10. E. Fehlberg. Klassische Runge-Kutta formeln vierter und niedrigerer Ordnung mit Schrittweiten-kontrolle und ihre Anwendung auf Warmeleitungsprobleme. Computing, 6 (1970) 61-71.
11. C.W. Gear. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Clifss, N.J. (1971).
12. R. Geist and K.S. Trivedi. Ultra-high reliability prediction for fault-tolerant computer systems. IEEE Transactions on Computers, 32 (12) (1983) 1118-1127.
13. G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, Md., 2nd ed. (1989).
14. A. Goyal, S. Lavenberg, and K.S. Trivedi. Probabilistic modeling of computer system availability. Annals of Operations Research, 8 (1987) 285-306.
15. W.K. Grassmann. Transient solution in Markovian queuing systems. Computers and Operations Research, 4 (1977) 47-56.
16. W. K. Grassmann. Finding transient solutions in markovian event systems through randomization. in: W.J. Stewart, editor, Numerical Solution of Markov Chains. Marcel Dekker, New York (1991) 357-371.
17. D. Gross and D. Miller. The randomization technique as a modeling tool and solution procedure for transient Markov processes. Operations Research, 32 (2) (1984) 334-361.
18. E. Hairer, S.P. Norsett, and G. Wanner. Solving Ordinary Differential Equations I - Nonstiff Problems. Springer, Berlin (1987).
19. E. Hairer and G. Wanner. Solving Ordinary Differential Equations II - Stiff and Differential Algebraic Problems. Springer, Berlin (1991).
20. A. Jensen. Markoff chains as an aid in the study of Markoff processes. Skand. Aktuarietidskrift., 36 (1953) 87-91.
21. A.M. Johnson and M. Malek. Survey of software tools for evaluating reliability, availability and serviceability. ACM Computing Surveys, 20 (4) (1988) 227-269.
22. J. Keilson. Markov Chain Models: Rarity and Exponentiality. Springer, Berlin (1979).
23. J.D. Lambert. Stiffness. in: I. Gladwell and D.K. Sayers, editors, Computational Techniques for Ordinary Differential Equations. Academic Press, New York (1980) 19-46.
24. J.D. Lambert. Numerical Methods for Ordinary Differential Systems. Wiley, New York (1991).
25. M. Malhotra and K.S. Trivedi. Higher-order methods for transient analysis of stiff Markov chains. Proc. 3rd Int. Conf. on Performance of Distributed Systems and Integrated Communication Networks, 1991.
26. R. Marie. Transient numerical solutions of stiff Markov chains. Proc. 20th ISATA Symp., 1989, pp. 255-270.
27. R.A. Marie, A.L. Reibman, and K.S. Trivedi. Transient solution of acyclic Markov chains. Performance Evaluation, 7 (3) (1987) 175-194.
28. B. Melamed and M. Yadin. Randomization procedures in the computation of cumulative-time distributions over discrete state Markov processes. Operations Research, 32 (4) (1984) 926-944.
29. D.R. Miller. Reliability calculation using randomization for Markovian fault-tolerant computing systems. 13th Annual Int. Symp. on Fault-Tolerant Computing, Milano, Italy, 1983, pp. 284-289.
30. W.L. Miranker. Numerical Methods for Stiff Equations and Singular Perturbation Problems. D. Reidel, Dordrecht (1981).
31. L. Petzold. Automatic selection of methods for solving stiff and nonstiff systems of differential equations. SIAM J. Sci. Stat. Comput., 4 (1) (1983) 136-148.
32. A. Reibman and K.S. Trivedi. Numerical transient analysis of Markov models. Computers and Operations Research, 15 (1) (1988) 19-36.
33. A. Reibman, K.S. Trivedi, and R. Smith. Markov and Markov reward model transient analysis: An overview of numerical approaches. European Journal of Operations Research, 40 (2) (1989) 257-267.
34. D.P. Siewiorek. Multiprocessors: Reliability modeling and graceful degradation. Infotech State of the Art Conf. on System Reliability, Infotech International, London, 1977, pp. 48-73.