Analytic expressions in stochastic max-plus-linear algebra

In stochastic max-plus-linear systems one often needs to compute the expectation of a max-plus-scaling function. The algorithms available in literature are either too computationally expensive or only give an approximation. In this paper we derive an analytic expression for this expectation in the case of a uniform distribution, resulting in a piecewise polynomial function in the components of the free control variable. This function can be evaluated in a quick and efficient way.