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Section: New Results

Stochastic Networks: Jackson Networks

Participant : Danielle Tibi.

Lyapunov functions and essential spectral radius of Jackson networks, joint work with I. Ignatiouk-Robert (University of Cergy-Pontoise). A family of explicit multiplicative Lyapunov functions is constructed for any stable Jackson network. Optimizing the multiplicative factor over this family provides an upper bound for the essential spectral radius of the associated Markov process. For Jackson networks corresponding to some particular class of routing matrices, this bound actually coincides with the exact value of the essential spectral radius, as can be derived from large deviations arguments.


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