On the sensitivity of transient solutions of Markov models
Publication
, Journal Article
Ramesh, AV; Trivedi, K
Published in: Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993
June 1, 1993
We consider the sensitivity of transient solutions of Markov models to perturbations in their generator matrices. The perturbations can either be of a certain structure or can be very general. We consider two different measures of sensitivity and derive upper bounds on them. The derived bounds are sharper than previously reported bounds in the literature. Since the sensitivity analysis of transient solutions is intimately related to the condition of the exponential of the CTMC matrix, we derive an expression for the condition number of the CTMC matrix exponential which leads to some interesting implications. We compare the derived sensitivity bounds both numerically and analytically with those reported in the literature.
Duke Scholars
Published In
Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993
DOI
Publication Date
June 1, 1993
Start / End Page
122 / 134
Related Subject Headings
- Networking & Telecommunications
Citation
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Ramesh, A. V., & Trivedi, K. (1993). On the sensitivity of transient solutions of Markov models. Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993, 122–134. https://doi.org/10.1145/166955.166998
Ramesh, A. V., and K. Trivedi. “On the sensitivity of transient solutions of Markov models.” Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993, June 1, 1993, 122–34. https://doi.org/10.1145/166955.166998.
Ramesh AV, Trivedi K. On the sensitivity of transient solutions of Markov models. Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993. 1993 Jun 1;122–34.
Ramesh, A. V., and K. Trivedi. “On the sensitivity of transient solutions of Markov models.” Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993, June 1993, pp. 122–34. Scopus, doi:10.1145/166955.166998.
Ramesh AV, Trivedi K. On the sensitivity of transient solutions of Markov models. Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993. 1993 Jun 1;122–134.
Published In
Proceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993
DOI
Publication Date
June 1, 1993
Start / End Page
122 / 134
Related Subject Headings
- Networking & Telecommunications