Model stiffness is a major problem that affects the computational efficiency of numerical solution methods for Markov models of highly dependable systems. Stiffness is related to the simultaneous presence of time constants of different orders of magnitude in the model. This is often the case in Markov models of highly dependable systems where typically failure events are rare. When faiures occur, repair events, targetted at correcting the failure, are fast. Furthermore, several interesting dependability measures like the instantaneous availability, interval availability, steady-state availability, and mean time to failure are computed using the Markov models.

In this talk, we will first formulate the computation of dependability measures in terms of solution of Markov models. We then highlight the problems due to stiffness encountered in the solution of these models. We then reflect on our past experience in dealing with the stiffness problem by showcasing several numerical techniques especially formulated for dealing with model stiffness but aimed at solving the problem for specific measures of interest. We highlight the common theme in all these different methods, and speculate on a generic approach for dealing with model stiffness.