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In this study, we propose the use of specialized influence models to capture the dynamic behavior of a Network-on-Chip (NoC). Our goal is to construct a versatile modeling framework that will help in the development and analysis of distributed and adaptive features for NoCs. As an application testbench, we use this framework to construct a design methodology for dynamic voltage and frequency scaling (DVFS). We also point out similarities of the proposed model with backpressure mechanisms that could be potentially exploited toward enhanced models for estimation and optimization of NoCs.