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<p><b>Abstract</b>—We refine the model underlying our prior work on scheduling bag-of-tasks (“embarrassingly parallel”) workloads via cycle-stealing in networks of workstations obtaining a model wherein the scheduling guidelines of produce optimal schedules for <it>every</it> such cycle-stealing opportunity. We thereby render <it>pre</it>scriptive the <it>de</it>scriptive model of those sources. Although computing optimal schedules usually requires the use of general function-optimizing methods, we show how to compute optimal schedules <it>efficiently</it> for the broad class of opportunities whose durations come from a <it>concave</it> probability distribution. Even when no such efficient computation of an optimal schedule is available, our refined model often suggests a natural notion of <it>approximately</it> 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 <it>heavy-tailed</it> distribution. Such opportunities do not admit any optimal schedule—nor even a natural notion of approximately optimal schedule—within the model. Within our refined model, though, we derive computationally simple schedules for heavy-tailed opportunities, which can be “tuned” to accomplish an expected amount of work that is arbitrarily close to optimal.</p>
Cycle-stealing, bag-of-tasks workloads, heavy-tailed distributions, networks of workstations (NOWs), optimal scheduling, scheduling parallel computations.

A. L. Rosenberg, "Optimal Schedules for Cycle-Stealing in a Network of Workstations with a Bag-of-Tasks Workload," in IEEE Transactions on Parallel & Distributed Systems, vol. 13, no. , pp. 179-191, 2002.
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