The major drawback of using static schedules to execute dataflow applications is their high inflexibility. In real-time systems, periodic schedules make it easier to assert safety guarantees and to decrease the schedule size, but their characteristics remain hard to compute. This article presents an approach to automatically generate fixed priority schedules from a dataflow specification. To do so, precedence dependencies between actors in the dataflow graphs are abstracted, as well as the task periods, by using affine relations . This abstraction allows us to synthesize schedules efficiently considering two main objectives: the maximization of throughput and the minimization of buffer sizes. Given a dataflow graph to execute in a real-time environment, we transform it into an Affine DataFlow Graph (ADFG) and compute the task priorities, their mapping, the number of delays in the buffers, and the buffer sizes. This article is the first to present an overview of both theoretical and practical aspects of ADFG. On the theoretical side, it presents corrections and improvements on the fixed priority case. On the practical side, benchmark evaluations demonstrate the robustness and maturity of the approach that our scheduling synthesizer implements. Synthesized schedules are evaluated by using scheduling simulation and real-time implementation. Last but not least, the synthesized periods reach the optimal throughput if enough processors are available, and most of the time the periods reach the maximal processor utilization factor in the uni-processor case. Moreover, execution time of the synthesis is about only one second for the main proposed algorithms.