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This paper investigates an optimal task-assignment policy for a random-graph model of a distributed program. The model of the distributed computer system assumes that communications overhead adds to total run time and that total run time decreases as the number of processors running the program are increased. When the processors are homogeneous, the optimal task-assignments are extremal in the sense that tasks are totally distributed among all processors as evenly as possible or not distributed at all. The point at which the policy shows a sharp change of behavior depends upon the ratio of runtimes to communication times. We derive two important properties of the optimal task-assignments for heterogeneous processors. The first property is that an optimal policy distributes the cost of processing among the processors as evenly as possible so that a processor with higher speed gets more tasks and vice versa. The second property determines the number of processors among which to distribute the tasks evenly. In the special case when there is a uniform degradation of processing speed it is shown that the optimal policy again exhibits an extremal characteristic.
Program processors, Computational modeling, Bandwidth, Computers, Runtime, Delay, Educational institutions, task assignments, Computer networks, distributed computers, local area networks, multiprocessors, optimal partitioning, random-graph models

"Optimal partitioning of randomly generated distributed programs," in IEEE Transactions on Software Engineering, vol. 12, no. , pp. 483-495, 1986.
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