Limit behaviour of loss networks

Resource sharing systems are used to model situations where several servers must complete jobs using some resources which must be shared with other servers. This kind of situations appear, for example, in computer and communications networks. In this paper we consider a Markovian class of processes of this type, loss networks, where the servers are communication stations arranged along a line which can be identified with Z. For these processes, the uniqueness of equilibrium measure is obtained and, as a consequence, the ergodicity of loss networks with calls of finite length is proved