Data-flow models are convenient to represent signal processing systems. They precisely reflect the data-dependencies and numerous algorithms exist to compute a static schedule that optimizes a given criterion especially for parallel implementations. Once deployed the data-flow models must be refined with constraints imposed by the environment and the execution platform. In this paper, we show how we can model data dependencies supported by multi-dimensional synchronous data flow with logical time and extend these data dependencies with additional logical constraints imposed by the environment. Making explicit these external constraints allows the exploration of further solutions during the scheduling computation.