Throughput analysis of pipelined multiprocessor modules

Abstract

A feasible form of parallel architecture would be one which consists of several pipeline stages each of which is a multiprocessor module of a large number of processing elements (PE's). In many applications like real-time image processing, dynamic control, etc., the optimized computing structure would be in this form. In this study, the performance of a parallel processing model of such an organization has been analyzed. In particular, the eflect of interstage communication on throughput of the model has been investigated to suggest an eficient way of transferring data between stages. Parallel Processing ModelA generic representation of a task may be given as follows:where/ is a processing function to be applied to an input ata I and 0 an output result.A task may be partitioned in both spatial and temporal dimensions. That is, a processing function can be decomposed into several subfunctions which are sequentially applied to data, i.e., pipelining, and the input data to each stage may be partitioned for multiprocessing when data parallelism is exploitable in the sta e. Therefore, assuming I< pipeline stages and Mi P E s in the i-th stage [l], 5 where C represents composition, and f ! and I,, are the processing function and the input data of the j-th partition of multiprocessing in the i-th stage of the pipeline, respective1 . Based on Eq. (2!, a parallel processin model of i elined multiprocessor modules may be formulated bf For this model, let t,,, denote computation time of the j-th partition in the i-th stage, and t,, communication time between stage i and stage i + 1 In an earlier work 11, throughput of the parallel case when there is only one P E in each stage. Some of the important observations are: i) The throughput decreases almost linearly as the variation of computation time increases, ii) The closer any two stages with processing model has f, een analyzed in detail for the a larger (than the other stages) variation of computation time, the greater the decrease in the throughput, and iii) the throughput can be significantly improved by increasing the number of buffers in front of and behind the stage with a largest variation of computation time. Multiple-PE-Stage PipelineIn this paper, we consider the case where each sta e of the parallel processing model consists of multije PE's. Inter-stage communication is a data transfer from multiple PE's to multiple PE's.One major factor affecting system throu hput considerably is the number of physical channefs between successive stages, denoted by n,. A larger number of channels would generally achieve a higher throughput since less channel contention is expected. But, a more meaningful approach would be to find the optimum number of channels from the viewpoint of costeffectiveness. Another factor which is to be considered in this analysis is the number of buffers between successive stages, more specifically, the number of buffers per channel, b,.System performance also depends on the characteristics of a task to be executed. Therefore, we cannot carry out perfo...