On Blocking Probabilities for Switching Networks

A network N consists of a set of switches, a set of links, and two sets of terminals denoted by / and ft, and called, respectively, the set of input terminals and output terminals. The union of all paths that can be used to connect one call between an input terminal u and an output terminal v is called the linear graph determined by u and v, and is denoted by G{u,v). (A linear graph is also called a channel graph.10) LetP* be the union of all paths connecting input terminals to output terminals. A state of N is a subset S of P* such that no two paths in S have a common link. For a given state S, a link is busy if it is on a path in S. Otherwise it is idle. Many existing switching networks consist of several stages. We say that AT is an n-stage network if the set of switches of N can be partitioned into n sets, called stages, and links exist only between a switch in stage i and a switch in stage i + 1, for 1