Bounding the Mean Cumulated Reward up to Absorption

Markov models are the most used tools when analyzing complex systems from the performance, dependability or performability points of view. They can capture most of the important aspects of the systems, at the price however of a possible combinatorial explosion in the number of states of the models. In such a case, the many available numerical methods are often of no use, and one of the possible answers to the problem is to design methods that are able to provide bounds of the needed metrics, at moderate costs. This paper proposes such a method when the model is an absorbing Markov process. The method is designed to be accurate in the case of models of highly reliable systems, and can handle the case of models with rewards. The paper illustrates its properties with different numerical examples.