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An approximated quadratic programming optimization is proposed to determine a model predictive controller to guarantee end-to-end delay in the DiffServ architecture. The proposed algorithm, called the suboptimal model predictive control scheduler (SMPCS), regulates the service rates of aggregated traffic classes dynamically, such that some constraints on proportional or absolute delay can be guaranteed. This paper investigates SMPCS complexity and its implementation problems in high-speed routers. The main problem of model predictive control (and one which has limited its use to slow processes) is its complexity. Optimization is the most computationally complex part in a model predictive controller. To enable efficient implementation of such a computationally expensive algorithm, this paper proposes to reduce the precision of the optimizer while maintaining near-optimal values for the manipulated variables (service rates). Both control-theoretic analysis and simulations demonstrate that SMPCS performs stable and acceptable quality-of-service differentiations at core routers while maintaining end-to-end delay constraints.