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Previous works on real-time task graph models have ignored the crucial resource sharing problem. Due to the non-deterministic branching behavior, resource sharing in graph-based task models is significantly more difficult than in the simple periodic or sporadic task models. In this work we address this problem with several different scheduling strategies, and quantitatively evaluate their performance. We first show that a direct application of the well-known EDF+SRP strategy to graph-based task models leads to an unbounded speedup factor. By slightly modifying EDF+SRP, we obtain a new scheduling strategy, called EDF+saSRP, which has a speedup factor of 2. Then we propose a novel resource sharing protocol, called ACP, to better manage resource sharing in the presence of branching structures. The scheduling strategy EDF+ACP, which applies ACP to EDF, can achieve a speedup factor of 1.618, the golden ratio.