TCP is max-plus linear and what it tells us on its throughput
Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication
Some Ergodic Results on Stochastic Iterative Discrete Events Systems
Discrete Event Dynamic Systems
Towards a (Max,+) Control Theory for Public TransportationNetworks
Discrete Event Dynamic Systems
A characterisation of (max,+)-linear queueing systems
Queueing Systems: Theory and Applications
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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.