This paper gives finite and infinite expansion formulas for the expected value of functions of the steady state variables in open, stochastic $(\max,+)$--linear systems with Poisson input. Expansions for Laplace transforms, moments and tail functions of these steady state variables are considered as specific instances of our main formulas. Such $(\max,+)$--linear systems are known to allow to represent a class of discrete event networks called stochastic event graphs. A few examples of such event graphs pertaining to queueing theory are given in the paper in order to illustrate the proposed expansion method.