Ergodicity of one-dimensional resource sharing systems

We study one-dimensional resource sharing systems which can be seen as interacting particle systems taking values in ({0,1,…,C}M)Z. We first get, by coupling techniques, an estimate of their invariant measures. Then, for processes having a reversible measure, we show the uniqueness of the invariant measure and conclude that they are ergodic. As a consequence, we prove that every loss network on Z with calls of bounded length is ergodic.