Construction of Lyapunov functions via relative entropy with application to caching

Nicolas Gast (1)

1 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems

We consider a system of interacting objects that is a generalization of the model of the cache-replacement policy RAND(m) policy introduced in [6]. We provide a mean-field approximation of this system. We show how to use relative entropy to construct a Lyapunov function for this model. This guarantees that the mean-field model converges to its unique fixed point.

Domaines: Réseaux et télécommunications [cs.NI]; Performance et fiabilité [cs.PF]; Mathématiques [math]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Nicolas Gast. Construction of Lyapunov functions via relative entropy with application to caching. The 18th Workshop on MAthematical performance Modeling and Analysis, Jun 2016, Nice, France. ⟨hal-01321017v1⟩