Optimal single hop multiple bus networks

The authors propose a class of single hop multiple bus networks based on balanced incomplete block design (BIBD). After introducing the basic concepts of multiple bus networks, a theorem is presented, which justifies the restriction of critically single hop bus (CSHB) networks. A model for performance analysis of CSHB networks is introduced, and it is proved that a CSHB network is optimal if both bus load and processor fanout are constant. Since topologies of such a balanced CSHB based on BIBD do not exist for all n, the number of processors, two theorems are included for the construction of CSHB networks for all n, with bounded skew in the bus loading and processor fanout