We study one-dimensional continuous loss networks with length distribution
G and cable capacity C. We prove that the unique stationary distribution et
a(L) of the network for which the restriction on the number of calls to be
less than C is imposed only in the segment [-L, L] is the same as the distr
ibution of a stationary M/G/infinity queue conditioned to be less than C in
the time interval [-L, L]. For distributions G which are of phase type (=
absorbing times of finite state Markov processes) we show that the limit as
L --> infinity of eta(L) exists and is unique. The limiting distribution t
urns out to be invariant for the infinite loss network. This was conjecture
d by Kelly (1991).