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With the advent of large scale heterogeneous environments, there is a need for matching and scheduling algorithms which can allow multiple DAG-structured applications to share the computational resources of the network. The paper presents a matching and scheduling framework where multiple applications compete for the computational resources on the network. In this environment, each application makes its own scheduling decisions. Thus, no centralized scheduling resource is required. Applications do not need direct knowledge of the other applications. The only knowledge of other applications arrives indirectly through load estimates (like queue lengths). The paper also presents algorithms for each portion of this scheduling framework. One of these algorithms is modification of a static scheduling algorithm, the DLS algorithm, first presented by Sih and Lee (1993). Other algorithms attempt to predict the …