Streaming systems are naturally modeled with synchronous dataflow graphs (SDFGs). The max-plus semantics of an SDFG is a compact matrix representation of its timing behavior. The max-plus semantics enables us to analyze and control timing properties of the systems, such as the obtainable minimum guaranteed throughput and maximum latency. Deriving the max-plus semantics, and consequently, performance analysis may be computationally expensive since the state-of-the-art method simulates one iteration of an SDFG. This holds, in particular, for systems whose components operate at different levels of granularity, as this results in many executions of some components in one iteration. This article aims at efficiently calculating the max-plus semantics of SDFGs. This article proposes an optimization framework exploring decompositions of a given SDFG and finding a composition sequence whose computational effort for compositionally obtaining the max-plus semantics is minimal. Not only does our proposed technique accelerate the performance analysis of multiscale streaming systems, but it also allows us to compute the max-plus semantics of some systems for which the state-of-the-art method does not succeed because of memory limitations.