We describe a novel technique for computing efficient schedules for multi-threaded real-time programs. The technique makes use of abstractions which are constructed by embedding the model of the program in a geometric space and then constructing a decomposition of this space. This embedding uses the model of PV diagrams. We introduce a timed version for PV programs and diagrams, which allows us to define the worst-case response time of the schedules, and then to use the geometric abstractions for computing efficient schedules.