Analyzing a security and reliability model using Krylov methods and matrix functions

It has been recently shown how the computation of performability measures for Markov models can be recasted as the evaluation of a bilinear forminduced by appropriate matrix functions. In view of these results, we show how to analyze a security model, inspired by a real world scenario. The model describes a mobile cyber-physical system of communicating nodes which are subject to security attacks. We take advantage of the properties of matrix functions of block matrices, and provide efficient evaluation methods.Moreover, we show how this new formulation can be used to retrieve interesting theoretical results, which can also rephrased in probabilistic terms.