Memory Loss Property for Products of Random Matrices in the Max-Plus Algebra

Products of random matrices in the max-plus algebra are used as models of a wide range of discrete event systems, including train or queueing networks, job shops, timed digital circuits, or parallel processing systems. Several mathematical models such as timed event graph or task-resources models also lead to max-plus products of matrices.

Some stability and computability results, such as convergence of waiting times to a unique stationary regime or limit theorems for the throughput, have been proved under the so-called memory loss property (MLP).

When the random matrices are i.i.d., we prove that this property is generic in the following sense: if it is not fulfilled, the support of the common law of the random matrices is included in a union of finitely many affine hyperplanes.