The timed dataflow model of computation is a useful performance analysis tool for electronic system level design automation and embedded software synthesis. Its determinism gives it strong analyzability properties. Its monotonic temporal behavior provides hard real-time guarantees on throughput and latency. It is expressive enough to cover a large class of applications and platforms. The trend however, in both embedded applications and their platforms is to become more dynamic, reaching the limits of what the model can express and analyze with tight performance guarantees. Scenario-aware dataflow (SADF) allows more dynamism to be expressed, introducing a controlled amount of non-determinism into the model to represent different scenarios of behavior. We investigate so-called weakly consistent graphs in which the scenario changes are not tightly coupled with periods of repetitive behavior of the static dataflow behavior in scenarios as in previous methods. We define the semantics of such graphs in terms of (max,+)-algebra and we introduce a method to analyze throughput using a generalization of (max,+)-automata. We show that weakly-consistent SADF generalizes many of the existing analyzable dynamic dataflow models, such as CSDF, PDF and CFDF and we present an algorithm to convert CSDF graphs to SADF.