  We discuss the efficient computation of performance, reliability, and
availability measures for Markov chains; these metrics, and the ones obtained
by combining them, are often called performability measures. We show that this
computational problem can be recasted as the evaluation of a bilinear forms
induced by appropriate matrix functions, and thus solved by leveraging the fast
methods available for this task. We provide a comprehensive analysis of the
theory required to translate the problem from the language of Markov chains to
the one of matrix functions. The advantages of this new formulation are
discussed, and it is shown that this setting allows to easily study the
sensitivities of the measures with respect to the model parameters. Numerical
experiments confirm the effectiveness of our approach; the tests we have run
show that we can outperform the solvers available in state of the art
commercial packages on a representative set of large scale examples.
