Dynamic Broadcasting in Parallel Computing

We consider the problem where broadcast requests are dynamically 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, distributed routing scheme to execute the broadcasts in this dynamic environment. Our scheme consists of repeated execution of a partial multinode broadcast task, which is a static communication task where any M < N arbitrary nodes of an N-processor network broadcast a packet to all the other nodes. The dynamic broadcasting scheme that we propose can be used in any topology, regular or not, for which partial multinode broadcast algorithms with certain properties can be found. We derive such an algorithm and we analyze the corresponding dynamic broadcasting scheme for the hypercube network. We show that its stability region 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. Our analysis does not use any approximating assumptions.