Perfect simulation for a continuous one-dimensional loss network

Sufficient conditions for ergodicity of a one-dimensional loss networks on R with length distribution G and cable capacity C are found. These processes are spatial birth-and-death processes with an invariant measure which is absolutely continuous with respect to a Poisson process and we implement the perfect simulation scheme based on the clan of ancestors introduced by Fernández, Ferrari and Garcia (2002) to obtain perfect samples viewed in a nite window of the in nite-volume invariant measure. Moreover, by a better understanding of the simulation process it is possible to get a better condition for ergodicity.