Efficient routing schemes for multiple broadcasts in hypercubes

The authors analyze the problem in which each node of the binary hypercube independently generates packets according to a Poisson process with rate lambda ; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, it is observed that the system can be stable in steady-state only if the load factor rho identical to lambda (2/sup d/-1)/d satisfies rho <1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authors establish some lower bounds for the steady-state average delay D per packet and devise and analyze two distributed routing schemes that are efficient in the sense that stability is maintained for all rho < rho * where rho * does not depend on the dimensionality d of the network, while the average delay D per packet satisfies D>