Some properties of piecewise linear Markov processe

Piecewise linear homogeneous Markov processes are considered which may be used in the models of a wide class of large systems.
Conditions of regularity, recurrency and finiteness of moments of order $\gamma$ of the first entrance time for a fixed set in the phase space are under investigation.
Main results are obtained by using the method of testing functions.
Some examples from the queuing theory are considered.