Efficient computation of buffer capacities for multi-rate real-time systems with back-pressure

A key step in the design of multi-rate real-time systems is the determination of buffer capacities. In our multi-processor system, we apply back-pressure as caused by bounded buffers in order to control jitter. This requires the derivation of buffer capacities that both satisfy the temporal constraints as well as constraints on the buffer capacity. Existing exact solutions suffer from the computational complexity associated with the required conversion from a multi-rate dataflow graph to a single-rate dataflow graph. In this paper we present an algorithm, with linear computational complexity, that does not require this conversion and that determines close to minimal buffer capacities. The algorithm is applied to an MP3 play-back application that is mapped on our network based multi-processor system.