We present a new task model called BGW for preemptable, periodic task sets, scheduled on a uniprocessor embedded platform. The tasks may be subject to faults and the processor may be overloaded. According to BGW, any Black job has to execute a primary algorithm before deadline, any Grey job may execute either the primary or the backup algorithm and any White job may be discarded. We describe several Earliest Deadline First (EDF) based scheduling frameworks suitable for this model. We also present and discuss the results of experiments that compare the EDF scheduler applied to conventional Liu and Layland task sets to various schedulers applied to BGW task sets. The Quality of Service is observed through metrics including ratio of deadline success, preemption rate, etc.