Expansions for steady-state characteristics of (max, +)-linear systems

An expansion formula is given for the expected value of a general class of functions of steady state variables in open, stochastic (max, +)-linear systems with Poisson input. Expansions for Laplace transforms, moments, distribution functions and tail probabilities of these steady state variables are considered as specific instances of our general expansion formula. Such (max, +)-linear systems are known to allow one to represent a class of discrete event networks called stochastic event graphs. Examples of such event graphs pertaining to queueing theory and Petri net theory are given in the paper in order to illustrate the proposed expansion method. We also include some comments on numerical analysis