Poisson Hypothesis for Open Networks at Low Load

TL;DR

This paper analyzes large mean-field communication networks with low input flow rates, demonstrating their ergodicity and independence from initial conditions, contrasting with high load regimes.

Contribution

It introduces a coupling technique for Non-Linear Markov Processes to prove ergodicity in low load mean-field networks.

Findings

Network is ergodic at low load

Stationary state is independent of initial conditions

Technique based on coupling of Markov processes

Abstract

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.