Poisson Hypothesis for Open Networks at Low Load

Alexandre Rybko (1) , Senya Shlosman (2, 1, 3) , Alexandre Vladimirov (1)

1 IITP - Institute for Information Transmission Problems
2 CPT - E5 Physique statistique et systèmes complexes
3 CPT - Centre de Physique Théorique - UMR 7332

We study large communication networks of the mean-field type. The input flows to the nodes of the network are supposed to be stationary and with low rate. We show that such a network is ergodic, i.e. it goes to the stationary state, which does not depend on the initial state of the network. This is in contrast with the high load regime, when the large time behavior of the network might depend on its initial state. Our technique is based on the coupling construction, which couples two Non-Linear Markov Processes.

Domaines: Probabilités [math.PR]

Alexandre Rybko, Senya Shlosman, Alexandre Vladimirov. Poisson Hypothesis for Open Networks at Low Load. Moscow Mathematical Journal, 2017, 17 (1), pp.145-160. ⟨hal-01265620⟩