Multistage interconnection networks (MINs) have a number of applications in many areas, for example in communication networks or parallel computer systems. While several performance analyses have been done, as far as we know a formal description of the behaviour of such networks is lacking. In the paper we define Markov chains describing the behaviour of the buffered M1N with a butterfly interconnection structure and 2×2 switching elements. We study several models of packet flow, which appear in the literature and develop technical mathematical tools which allow us to compare them. We prove some equivalence results regarding the models.