Reduction of the Markovian system by the influence graph method: error bound and reliability computation

In a previous article, a new method allowing the treatment of large Markovian problems was presented. Based on a graph describing the influences between the components of the system, it performs successive approximate aggregations on the exact Markovian system to reduce its size. The main drawback of this method, as of any approximate method, is to assess its validity. That is why we develop a new presentation of the method here and we define, from this presentation, error bounds for the approximate results. They are then tested for two applications, one being very large with more than 1030 states for the exact Markovian system. We also extend the method, initially defined for availability problems, to reliability problems.