Numerically Stable Methods for the Computation of Exit Rates in Markov Chains

We consider the exit rate from a finite class of transient states of a continuous-time Markov chain and develop numerically stable methods for the computation with bounded from above approximation error of the steady-state exit rate and the time-dependent exit rate. Finally, we develop an also numerically stable method for the computation with bounded from above approximation error of reachable bounds for the time-dependent exit rate which are independent of the initial probability distribution. Applications for the latter include the cyclic analysis of fault-tolerant systems and the analysis of fault-tolerant systems with unobservable up state. The methods compare well from a computational cost point of view with existing alternatives, some with inferior quality regarding error control.