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This is the appendix to the paper Temporal Analysis of Static Priority Preemptive Scheduled Cyclic Streaming Applications using CSDF Models [1]. The temporal analysis approach presented in [1] makes use of an iterative algorithm that computes so-called maximum busy periods over multiple task phases. The algorithm contains a stop criterion indicating after which iteration of the algorithm subsequent iterations do not need to be considered. The intuition behind that stop criterion is given in the paper and supplemented by a formal proof in this appendix.

Connection-oriented guaranteed-throughput mesh-based networks on chip have been proposed as a replacement for buses in real-time embedded multiprocessor systems such as software defined radios. Even with attractive features like throughput and latency guarantees they are not always used because their hardware cost tends to be higher than buses. In this paper we present a communication ring that provides throughput and latency guarantees. This ring is an attractive communication network as replacement for buses for small to medium scale embedded multiprocessor systems for real-time stream processing because of its relatively low hardware cost. We show that the data serialization of our ring makes it contention free and enables sharing of buffers which reduces the hardware cost. A further cost reduction is achieved by implementing end-to-end flow-control in software and by supporting only writes over the network. Data-flow analysis techniques are used to prove that throughput and latency guarantees can be given despite that the proposed communication ring is connectionless. We evaluated the performance and hardware cost of our communication ring using a 16 core multiprocessor system and a real-time PAL video decoder application. This design was implemented on a Virtex 6 FPGA and the ring was found to use roughly 2% of the logic cells used for the complete MPSoC design. Such a low hardware cost can justify the use of the ring in systems with low bandwidth utilization, as is the case for our PAL video decoder application which uses only 3% of the available bandwidth.