Optimal schedules for cycle-stealing in a network of workstations with a bag-of-tasks workload

We refine the model underlying our prior work on scheduling bag-of-tasks ("embarrassingly parallel") workloads via cycle-stealing in networks of workstations (S.N. Bhatt et al., 1997; A.L. Rosenberg, 1999), obtaining a model wherein the scheduling guidelines of Rosenberg produce 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, nor even a natural notion of approximately optimal schedule, within the model of Bhatt and Rosenberg. 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.