of the first DAG in the set of multiple DAGs to finish time of the last task of the last DAG in the set of mul-The problem of scheduling a single DAG onto hetero-tiple DAGs), another objective could be to achieve a geneous systems has been studied extensively. In this certain level of Quality of Service for the given DAGs. paper, we focus on the problem of scheduling more than Such a level of Quality of Service could be based on one DAG at the same time onto a set of heterogeneous priorities (for instance, one requirement could be to resources. The aim is not only to optimize the overall complete the execution of one DAG as soon as possimakespan, but also to achieve fairness, defined on the ble) or other constraints. In this paper, we focus on basis of the slowdown that each DAG would experience fairness, which is defined on the basis of the slowdown as a result of competing for resources with other DA Gs.that each DAG would experience (as a result of sharing Two policies particularly focussing to deliver fairness the resources with other DAGs as opposed to having are presented and evaluated along with another four the resources on its own); to achieve fairness, the aim policies that can be used to schedule multiple DAGs.is to make this slowdown equal for all DAGs, yet without affecting the overall makespan of the multiple DAG schedule. The paper describes two policies to schedule