Analysis of stochastic min-max-plus systems: Results and conjectures

Systems in which the operations min, max and addition appear simultaneously are called min-max-plus systems. Such systems, which are extensions of timed discrete event systems (which on their turn are based on the max-plus algebra, i.e., on the operations max and addition only), have been studied for some years now [1–3]. In these references only deterministic systems were studied. In the current paper, some stochastic extensions will be considered. It will be shown that extensions of eigenvalues, Lyapunov coefficients, exist for these stochastic systems. Some conjectures will be given which are supported by characteristic examples.