Evaluating mean time to security failure based on continuous-time Markov chains

Abstract

In the article, we consider a Markov model of computer attacks, in the framework of which attacks and the system responses are modelled by homogeneous Poisson point processes. We describe a method of solving the corresponding Kolmogorov system of equations by calculating eigenvalues and eigenvectors of some matrix. An important random variable associated with the corresponding Markov chain and called the time to security failure is explored in detail. The comparison of the results obtained and the results of simulation modelling are presented.