Real-time systems are growing in complexity and real-time and soft real-time applications are becoming common in general-purpose computing environments. Thus, there is a growing need for scheduling solutions that simultaneously support processes with a variety of different timeliness constraints. Toward this goal we have developed the Resource Allocation/Dispatching (RAD) integrated scheduling model and the Rate-Based Earliest Deadline (RBED) integrated multi-class real-time scheduler based on this model. We present RAD and the RBED scheduler and formally prove the correctness of the operations that RBED employs. We then describe our implementation of RBED and present results demonstrating how RBED simultaneously and seamlessly supports hard real-time, soft real-time, and best-effort processes.