Dynamic Broadcasting in Parallel Computing

We consider the problem where broadcast requests are generated at random time instants at each node of a multiprocessor network. In particular, in our model packets arrive at each node of a network according to a Poisson process, and each packet has to be broadcast to all the other nodes. We propose an on-line decentralized routing scheme to execute the broadcasts in this dynamic environment. A related, although static, communication task is the partial multinode broadcast task, where M < N arbitrary nodes of an N-processor network broadcast a packet to all the other nodes. The results that we obtain for the dynamic broadcasting scheme apply to any topology, regular or not, for which partial multinode broadcast algorithms with certain properties can be found. For the dynamic scheme we find an upper bound on the average delay required to serve a broadcast request, and we evaluate its stability region. As an application we give a near-optimal partial multinode broadcast algorithm for the hypercube network. The stability region of the corresponding hypercube dynamic scheme tends to the maximum possible as the number of nodes of the hypercube tends to infinity. Furthermore, for any fixed load in the stability region, the average delay is of the order of the diameter of the hypercube. 1 Research supported by NSF under Grant NSF-DDM-8903385 and by the ARO under Grant DAAL03-86K-0171. 2 Laboratory for Information and Decision Systems, M.I.T, Cambridge, Mass. 02139. 1