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Proposal and evaluation of task allocation method for limited connected multiprocessor system

In multiprocessor systems, it is important to allocate tasks to each processor in order to realize the shortest processing time. This is called the task scheduling problem. Interprocessor communication consumes time in the task scheduling of real-life multiprocessing systems. Thus, not only each task's processing time, but also communication time must be taken into account. In this paper, we propose a method that has high proximity to the optimum solution of this problem. The proposed method is a kind of list scheduling. It makes a task priority list from prepriorities determined only by processing time of each task, and from the decrease in communication time realized from each task/processor combination. The prepriority of a task is the longest path length of task dependency sequences that are dependent on the task. The decrease in communication time is the time that is needed if a task is executed on other processors, but not needed if it is executed on the processor whose priority is to be obtained. We show the superiority of the proposed method using two programs, one for the numerical solution of ordinary differential equations by the Runge-Kutta method, and the other for performing the FFT, in complete network systems. The proposed method can also perform good allocation for incomplete network systems. In addition, it has advantages for task sets generated by random numbers. We measure the time required for allocation and show that the proposed method can solve a problem in polynomial time.