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In real-time systems, the application's behavior has to be predictable at compile-time to guarantee timing constraints. However, modern streaming applications which exhibit adaptive behavior due to mode switching at run-time, may degrade system predictability due to unknown behavior of the application during mode transitions. Therefore, proper temporal analysis during mode transitions is imperative to preserve system predictability. To this end, in this paper, we initially introduce Mode Aware Data Flow (MADF) which is our new predictable Model of Computation (MoC) to efficiently capture the behavior of adaptive streaming applications. Then, as an important part of the operational semantics of MADF, we propose the Maximum-Overlap Offset (MOO) which is our novel protocol for mode transitions. The main advantage of this transition protocol is that, in contrast to self-timed transition protocols, it avoids timing interference between modes upon mode transitions. As a result, any mode transition can be analyzed independently from the mode transitions that occurred in the past. Based on this transition protocol, we propose a hard real-time analysis as well to guarantee timing constraints by avoiding processor overloading during mode transitions. Therefore, using this protocol, we can derive a lower bound and an upper bound on the earliest starting time of the tasks in the new mode during mode transitions in such a way that hard real-time constraints are respected., Comment: Accepted for presentation at EMSOFT 2018 and for publication in IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) as part of the ESWEEK-TCAD special issue