The analysis of fixed priority preemptive scheduling has been extended in various ways to improve its usefulness for the design of real-time systems. In this paper, we define the layered preemptive priority scheduling policy which generalizes fixed preemptive priorities by combination with other policies in a layered structure. In particular, the combination with the Round Robin scheduling policy is studied. Its compliance with Posix 1003.1b requirements is shown and its timing analysis is provided. For this purpose and as a basis for the analysis of other policies, the concept of majorizing work arrival function, is introduced to synthesize essential ideas used in existing analysis of the fixed preemptive priority policy. If critical resources are protected by semaphores, the Priority Ceiling Protocol (PCP) can be used under fixed preemptive priorities to control resulting priority inversions. An extension of the PCP is proposed for Round Robin, to allow a global control of priority inversions under the layered priority policy and to prevent deadlocks. The initial timing analysis is extended to account for the effects of the protocol. The results are illustrated by a small test case.