Optimal Schedules for Cycle-Stealing in a Network of Workstations with a Bag-of-Tasks Workload

  • Authors:
  • Arnold L. Rosenberg

  • Affiliations:
  • Univ. of Massachusetts, Amherst

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 2002

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Abstract

We refine the model underlying our prior work on scheduling bag-of-tasks (驴embarrassingly parallel驴) workloads via cycle-stealing in networks of workstations obtaining a model wherein the scheduling guidelines ofproduce optimal schedules for every such cycle-stealing opportunity. We thereby render prescriptive the descriptive model of those sources. Although computing optimal schedules usually requires the use of general 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 often 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驴nor even a natural notion of approximately optimal schedule驴within the model.Within our refined model, though, we derive computationally simple schedules for heavy-tailed opportunities, which can be 驴tuned驴 to accomplish an expected amount of work that is arbitrarily close to optimal.