Perturbation of CTMC Trapping Probabilities with Application to Model Repair
Alexander Gouberman, Markus Siegle, Bharath Siva Kumar Tati · 2017
This paper studies properties of continuous-time Markov chains with one class of transient states and at least two absorbing states. We look at a perturbation of the chain that arises by uniformly decreasing all rates to absorption. For this situation, the monotonicity of the trapping probabilities is analysed, and their asymptotic limit is computed. The theoretical findings are then applied to a type of model repair problem, where a lower time-bounded and lower probability-bounded CSL until requirement needs to be satisfied. The paper presents an algorithm for this type of problem and proves its correctness.