Efficient Routing Schemes for Multiple Broadcasts in Hypercubes

We analyze the following problem: Each node of the d-dimensional hypercube independently generates packets according to a Poisson process with rate A; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, we show that the system can be stable in steady-state only if the load factor pdef 2A"' satisfies p < 1; moreover, we establish some lower bounds for the steady-state average delay D per packet. We devise and analyze several distributed routing schemes that prove to be efficient, in the following sense: Stability is maintained for all p < p*, where p* does not depend on the dimensionality d of the network, while the delay D is O(d) + O(d)p for small values of p. Performance evaluation of the various schemes is exact to a considerable extent; in some cases, exact analysis is intractable and we resort to approximations and/or simulations. t Research supported by the NSF under Grant ECS-8552419, with matching funds from Bellcore Inc. and Du Pont, by the ARO under Grant DAAL03-86-K-0171, and by a Fellowship from the Vinton Hayes Fund. i Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Mass. 02139, USA.