The migration of a company's information systems to a cloud platform is a crucial part of the transformation of IT infrastructure. However, due to the mixture of business goals and limitations in existing IT systems, the selection and realization of these goals is not a simple one. In this paper, we present a model describing the possibility of migrating business information systems into a cloud environment by following the stochastic model approach. By properly identifying and defining various process aspects, it is relatively simple to adapt analysis and limit the transition probability matrix to well-known stochastic models. Careful manipulation of such a matrix allows using standard formulas for scaling discrete event systems to solve cloud migration problems. A detailed case study with simulation results, pointing to some of the practical limitations of the model, is presented at the end of this paper.