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Abstract:

Abstract—We show that deadlocks due to dependencies on consumption channels are a fundamental problem in wormhole multicast routing. This type of resource deadlocks has not been addressed in many previously proposed wormhole multicast algorithms. We also show that deadlocks on consumption channels can be avoided by using multiple classes of consumption channels and restricting the use of consumption channels by multicast messages. We provide upper bounds for the number of consumption channels required to avoid deadlocks. In addition, we present a new multicast routing algorithm, column-path, which is based on the well-known dimension-order routing used in many multicomputers and multiprocessors. Therefore, this algorithm could be implemented in existing multicomputers with simple changes to the hardware. Using simulations, we compare the performance of the proposed column-path algorithm with the previously proposed Hamiltonian-path-based multipath and an e-cube-based multicast routing algorithms. Our results show that for multicast traffic, the column-path routing offers higher throughputs, while the multipath algorithm offers lower message latencies. Another result of our study is that the commonly implemented simplistic scheme of sending one copy of a multicast message to each of its destinations exhibits good performance provided the number of destinations is small. Index Terms—Consumption channels, deadlocks, multicasts, multicomputers, routing algorithms, wormhole routing.

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