Evaluating the Divisible Load Assumption in the Context of Economic Grid Scheduling with Deadline-Based QoS guarantees

The ef¿cient scheduling of jobs is an essential part of any grid resource management system. At its core, it involves ¿nding a solution to a problem which is NP-complete by reduction to the knapsack problem. Consequently, this problem is often tackled by using heuristics to derive a more pragmatic solution. Other than the use of heuristics, simpli¿cations and abstractions of the workload model may also be employed to increase the tractability of the scheduling problem. A possible abstraction in this context is the use of Divisible Load Theory (DLT), in which it is assumed that an application consists of an arbitrarily divisible load (ADL). Many applications however, are composed of a number of atomic tasks and are only modularly divisible. In this paper we evaluate the consequences of the ADL assumption on the performance of economic scheduling approaches for grids, in the context of CPU-bound modularly divisible applications with hard deadlines. Our goal is to evaluate to what extent DLT can still serve as a useful workload abstraction for obtaining tractable scheduling algorithms in this setting. The focus of our evaluation is on the recently proposed tsfGrid heuristic for economic scheduling of grid workloads which operates under the assumptions of ADL. We demonstrate the effect of the ADL assumption on the actual instantiation of schedules and on the user value realized by the RMS. In addition we describe how the usage of a DLT heuristic in a high-level admission controller for a mechanism which does take into account the atomicity of individual tasks, can signi¿cantly reduce communication and computational overhead.