Modelling and analysis of the variance in parallelism in parallel computations

In this paper, we introduce an analytical technique based on queueing networks and Petri nets for making a performance analysis of dataflow computations when executed on the Manchester machine. This technique is also applicable for the analysis of parallel computations on multiprocessors. We characterize the parallelism in dataflow computations through a four-parameter characterization, namely, the minimum parallelism, the maximum parallelism, the average parallelism and the variance in parallelism. We observe through detailed investigation of our analytical models that the average parallelism is a good characterization of the dataflow computations only as long as the variance in parallelism is small. However, significant difference in performance measures will result when the variance in parallelism is comparable to or higher than the average parallelism.