Multi-core platforms are becoming the dominant computing architecture for next generation embedded systems. Nevertheless, designing, programming, and analyzing such systems is not easy and a solid methodology is still missing. In this paper, we propose two powerful abstractions to model the computing power of a parallel machine, which provide a general interface for developing and analyzing real-time applications in isolation, independently of the physical platform. The proposed abstractions can be applied on top of different types of service mechanisms, such as periodic servers, static partitions, and P-fair time partitions. In addition, we developed the schedulability analysis of a set of real-time tasks on top of a parallel machine that ...