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In this paper, the hierarchical parallel scheduling algorithm (HPS) is proposed, analyzed, and evaluated. This algorithm has a high level of simplicity which makes it more practical for implementation in packet switched networks. The simplicity of the HPS comes from the formulation of scheduling tasks as a linear programming problem that is solved using a simple greedy algorithm. The proposed scheduling algorithm is capable of independently controlling the bandwidth, delay, and delay jitter allocations for different service classes. Complete control of bandwidth-critical, delay-critical, and jitter-critical traffics is assured through the use of two optimization techniques based on the transportation problem and the 0-1 knapsack problem. An OPNET network model is built to verify the functionality and performance of the HPS.