Performance analysis of the hypercube line switch

Our first effort went into designing and analyzing the hypercube network as a message passing switch. We aimed at making a VLSI chips, one for each node, which should store and forward the messages. Message passing have some negative effects: Message delays are both unpredictable and significant, nodes have to be able to store messages, thereby increasing chip size, and finally it was discovered during simulation tests that deadlocks occurred rather frequently. Later a remedy for deadlock was found, but the other negative indicators are still valid. The result: we abandoned the message passing method and turned to line switching. Still there should be one chip in each node. The hypercube line switching node has one communication path to each neighbor (D lines in a D dimensional cube) and two paths to the node computer. The chip should be able to participate in decentralized routing through the cube, and when a connection is established: hold a path through the node. An outline of the node functions will be given. A line switching hypercube network will have enormous data transmission capacity. In a D dimensional cube with N=2D nodes, at most N channels can be active at the same time. (Remember that each node computer has both an input port and an output port). 10 MB/sec data transfer rate on each channel is well within reach. The critical operation is to establish a path through the hypercube. Set up time varies with network size and load, clock frequency and actual path through the network. With the same clock frequency as already mentioned, the normal set up time under light load conditions is from 1 to 3 microseconds. An analysis of the path setup process has been carried out. The focus has been on the probability of being able to establish a path under a given load condition. The load is defined as the number of established (active) channels over N. Two approximate analytical models are developed and compared with results from a simulation model. All models give the same picture, and it is safe to say that for loads less or equal to 50% the probability of getting through is very high, almost 1.0 for larger cubes, i.e. D > 8. For loads larger than 80% almost all requests are denied.