In earlier work, we have described the Real-Time Execution Performance Agent (RT EPA) which accommodates mixed hard and soft real-time processing with measurable reliability by providing a confidence-based scheduling and execution fault handling framework. Based on experience with the RT EPA with a space telescope application, a theory was formed for determining scheduling feasibility for a set of services partitioned into multiple scheduling epochs, which are simultaneously active, yet mutually exclusive. This paper explains the multi-epoch theory whose utility has been demonstrated, but for which a formal implementation within the RT EPA framework remains to be completed.