Arnaud de La Fortelle's home page |
The previous results open several direction of research. From a theoretical point of vue, it is now clear that there exists a link between large deviations and Martin boundary, i.e. harmonic functions. Therefore, one direction would be to study instable (transient) behavior. A second direction would be to generalize the method developped for polling systems in order to include many other network models: we think it is possible to reach a result for homogeneous random walk with boundaries in dimension N.
From a more practical point of vue, we are studying the application of large deviations to several models of networks (polling, Jackson...) or protocols ( bandwidth sharing). These applications are intersting since they would allow to measure the performance of complex systems for which very few information is available by now. For stable systems, we analyse the behavior of the tail of the stationnary distribution, which turns to a difficult optimisation problem in a space of trajectories where there are discontinuities. This problem has been solved only for small dimensions (less than 3).
In addition, we are also applying probabilistic tools, i.e.
thermodynamic
limits, mean field... to the analysis of bandwidth
sharing. We are also trying to combine both tools in order to
analyse
performance (using large deviations) for large systems (using
thermodynamic
limit).
Bolivia's altiplano
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