Abstract We present a new graph-based real-time task model that can specify complex job arrival patterns and global state-based mode switching. The mode switching is of a mixed-criticality style, meaning that it allows immediate changes to the parameters of active jobs upon mode switches. The resulting task model generalizes previously proposed task graph models as well as mixed-criticality (sporadic) task models; the merging of these mutually incomparable modeling paradigms allows formulation of new types of tasks. A sufficient schedulability analysis for EDF on preemptive uniprocessors is developed for the proposed model. Keywords Real-time · Mixed-criticality · Task graphs · Schedulability analysis