A workflow represents a complex activity that is often modeled by a directed acyclic graph (DAG) in which each vertex is a task and each directed edge represents both precedence and communication. Recently, Hybrid DAG has emerged as a new model. In this model, unlike the traditional DAG model, tasks can also interact during their executions. Hybrid workflows that are composed of tasks and super-tasks can be modeled using hybrid DAGs. With respect to scheduling workflows to run on the Grid, Lookahead is an important list-based algorithm. To assign a processor to a task, it predicts the status of the system after the children of this task are scheduled and then makes the final decision on this task. One source of sometimes low performance of Lookahead is that unscheduled parents of these children are not given higher priority over the corresponding children’s tasks. In this paper, we have proposed the Extended Lookahead algorithm in which this deficiency of Lookahead is removed. In next step, the Extended Lookahead, HEFT, and Lookahead approaches are modified such that they are able to schedule hybrid workflows that will be executed in the utility Grid. The experimental comparison results show that the performance of the new approach is improved compared to both HEFT and Lookahead.

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