The sediment transport dynamics and the population level of a buffer in automated production line systems can be described by the same class of stochastic differential equations. The ubiquitous noise is generated by continuous time Markov chains. The probability densities which describe the dynamics are governed by high order hyperbolic systems of partial differential equations. While this hyperbolic nature clearly exhibits a non-diffusive character of the processes: (diffusion would imply a parabolic evolution of the probability densities), one nevertheless can use a central limit theorem which holds for the large times regimes. This enables analytical estimations of the time evolution of the moments of these processes. A particular emphasis is devoted to non-Markovian, dichotomous alternating renewal processes which enter directly into the description of the applications presented