A Generalized Packing Server for Scheduling Task Graphs on Multiple Resources

This paper presents the generalized packing server. It reduces the problem of scheduling tasks with precedence constraints on multiple processing units to the problem of scheduling independent tasks. The work generalizes our previous contribution made in the specific context of scheduling Map/Reduce workflows. The results apply to the generalized parallel task model, introduced in recent literature to denote tasks described by workflow graphs, where some subtasks may be executed in parallel subject to precedence constraints. Recent literature developed schedulability bounds for the generalized parallel tasks on multiprocessors. The generalized packing server, described in this paper, is a runtime mechanism that packs tasks into server budgets (in a manner that respects precedence constraints) allowing the budgets to be viewed as independent tasks by the underlying scheduler. Consequently, any schedulability results derived for the independent task model on multiprocessors become applicable to generalized parallel tasks. The catch is that the sum of capacities of server budgets exceeds by a certain ratio the sum of execution times of the original generalized parallel tasks. Hence, a scaling factor is derived that converts bounds for independent tasks into corresponding bounds for generalized parallel tasks. The factor applies to any workconserving scheduling policy in both the global and partitioned multiprocessor scheduling models. We show that the new schedulability bounds obtained for the generalized parallel task model, using the aforementioned conversion, improve in several cases upon the best known bounds in current literature. Hence, the packing server is shown to improve the schedulability of generalized parallel tasks. Evaluation results confirm this observation.