The rearrangement process in a two-stage broadcast switching network

The rearrangement process in the two-stage broadcast switching network presented by F.K. Hwang and G.W. Richards (ibid., vol.COM-33, no.10, p.1025-1035, Oct. 1985) is considered. By defining a certain function it is possible to calculate an upper bound on the number of connections to be moved during a rearrangement. When each inlet channel appears twice, the maximum number of connections to be moved is found. For a special class of inlet assignment patterns in the case of which each inlet channel appears three times, the maximum number of connections to be moved is also found. In the general case, an upper bound is given when the number of outlets at each second-stage switch is kept below a certain bound