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We refine the model underlying our prior work on scheduling cycle-stealing opportunities in NOWs [5, 16], obtaining a model wherein the scheduling guidelines of [16] produce optimal schedules for every such opportunity. Although computing optimal schedules usually requires the use of general (often inefficient) function-optimizing methods, we show how to compute optimal schedules efficiently for the broad class of opportunities whose durations come from a concave probability distribution. Even when no such efficient computation of an optimal schedule is available, our refined model always suggests a natural notion of approximately optimal schedule, which may be efficiently computable. We illustrate such efficient approximability via the important class of cycle-stealing opportunities whose durations come from a heavy-tailed distribution. Such opportunities do not admit any optimal schedule—nor even a natural notion of approximately optimal schedule—within the model of [5, 16]. Within our refined model, though, we derive computationally simple schedules for heavy-tailed opportunities, which can be “tuned” to have expected work-output that is arbitrarily close to optimal.

Optimal schedules for data-parallel cycle-stealing in networks of workstations (extended abstract)