Efficient routing schemes for multiple broadcasts in hypercubes

During the execution of parallel algorithms in a network of processors, it is often necessary that one of the processors broadcast a piece of information to all others; subsequent broadcasts (possibly by different processors) may also take place, until the algorithm terminates. A problem is formulated where packets to be broadcast are generated by the nodes of the d-dimensional hypercube at random instants, according to Poisson processes with rate λ. All packets are taken to have unit length; also, it is assumed that no other packet transmissions are taking place in the network. First, the limitations applying to all legitimate routing schemes (concerning their stability and delay properties) are derived. Given these limitations, the authors establish a set of performance criteria, and then devise and analyze several routing schemes that meet them