Asymptotic throughput of stochastic max-plus linear systems.

In a Max-plus linear system every coordinate is known to have an asymptotic cycle time. For their stochastic counterpart, this is only true for the backward systems. We investigate the conditions under which this fact implies the existence of asymptotic cycle time for the original system and show that there are two types of obstructions. This gives a necessary and sufficient condition for i.i.d. systems and a bunch of sufficient conditions under weaker assumptions.