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Job-Dispatching Problem in Multiprocessor System for Image Processing

When a picture is to be generated in a multiprocessor system for image processing, the picture generation time can be reduced by dividing the picture into several subpictures, which are then assigned to the processors for parallel processing. In such a scheme, there exists a trade-off relation between the parallelism of the subpicture processing and the overhead for assignment. When the number of subpictures is increased, the parallelism is enhanced, while the time of the subpicture assignment is increased. By contrast, when the number of subpictures is small, the time for the subpicture assignment is reduced, while the parallelism is decreased. This paper discusses this tradeoff relation. In other words, discussions are made of the effect of the number of processors composing the multiprocessor system for image processing and the number of subpictures to be processed by the system, on the time for picture generation and the system efficiency. First, a discrete approximate solution for the picture generation time is derived using the Markov process. Then an approximate solution by the queuing network theory is presented. Those methods are applied to actual examples to derive numerical solutions, indicating that there exists the optimum number of subpictures minimizing the picture generation time. A simulation was performed, and the result indicated that the two methods of analysis agree well, further indicating the validity of the approximations introduced in the course of the analysis.