Asymptotic growth rate of stochastic max-plus systems that with a positive probability have a sunflower-like support

In this paper the asymptotic growth rate of stochastic max-plus linear systems is studied. Special attention is paid to systems whose system matrix with a positive probability is supported by a basic sunflower graph, i.e., a graph that contains precisely one circuit, which has length one (a self-loop), and in which each node has precisely one predecessor. It is shown that for such systems all state components have the same asymptotic growth rate. The result is illustrated by means of an example. Also two generalizations will be briefly presented