Products of random Max-plus matrices

Max-plus stochastic linear systems describe a wide variety of non-linear queueing processes. The dynamics of these systems are dominated by a Max-plus analogue of the Lyupanov exponent the value of which depends on the structure of the underlying support graphs as well as the properties of the waiting-time distributions. For matrices whose associated weighted graphs have identically distributed edge weights (componentwise homogeneity) we are able to decouple these two effects and provide a sandwich of bounds for the Max-plus Lyupanov exponent relating it to some classical properties of the support graph and some extreme value expectations of the waiting-time distributions. This sandwich inequality is then applied to products of componentwise exponential, Gaussian and uniform matrices.