On the sensitivity of transient solutions of Markov models

TitleOn the sensitivity of transient solutions of Markov models
Publication TypeJournal Article
Year of Publication1993
AuthorsAV Ramesh, and K Trivedi
JournalProceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993
Start Page122
Pagination122 - 134
Date Published06/1993
Abstract

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.

DOI10.1145/166955.166998
Short TitleProceedings of the 1993 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1993