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We present a new graph-based real-time task model that can specify complex job arrival patterns and global statebased mode switching. The mode switching is of a mixedcriticality style, enabling immediate changes to the parameters of active jobs upon mode switches. The resulting task model therefore generalizes previously proposed task graph models as well as mixed-criticality (sporadic) task models, and further allows for the modeling of timing properties not found in any of these models. We outline an EDF uniprocessor schedulability analysis procedure by combining ideas from prior analysis methods for graph-based and mixed-criticality task scheduling.