  Most of the published articles on random motions have been devoted to the
study of the telegraph process or its generalizations that describe the random
motion in $R^n$ of a single particle in a Markov or semi-Markov medium.
However, up to our best knowledge there are no published papers dealing with
the interaction of two or more particles which move according to the telegraph
processes. In this paper, we construct the system of telegraph processes with
interactions, which can be interpreted as a model of ideal gas. In this model,
we investigate the free path times of a family of particles before they are
collided with any other particle. We also study the distribution of particles,
which described by telegraph processes with hard collisions and reflecting
boundaries, and investigate its limiting properties.
