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In this paper, we propose the use of network decomposition under an optimal resource allocation framework. We develop a methodology where recursive formulas can be utilized for calculating the desired end-to-end performance bounds (i.e., backlog bound violation probability) of flows traversing tandem, acyclic queueing networks. We use those performance metrics in an optimization framework that allocates resources to network services with specific quality-of-service requirements. Finally, we evaluate our framework and compare its performance against a system utilizing deterministic bounds obtained from network calculus.