The Performance Limits of a Two-dimensional Network of Load-sharing Processors

A process of computation in a two-dimensional mesh of processors is analysed in this work. A computational task is assumed to be arbitrarily divisible between processors. The load of the job is transferred from the originating processor to other processors by a point to point communication network. Communication delays are taken into consideration. The time costs of computation and communication are assumed to be linear function of the data size. Simple formulae are found to determine the distribution of the task's load and the equivalent speed of the whole network of processors. The performance of the two-dimensional mesh architecture is analysed. It turns out that in realistic situations the performance of this kind of the network is limited.