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We introduce a new general scheme for shared memory nonpreemptive scheduling policies. Our scheme utilizes a system of inequalities and thresholds and accepts a packet if it does not violate any of the inequalities. We demonstrate that many of the existing policies can be described using our scheme, thus validating its generality. We propose a new scheduling policy, based on our general scheme, which we call the harmonic policy. Our simulations show that the harmonic policy both achieves high throughput and easily adapts to changing load conditions. We also perform a theoretical analysis of the harmonic policy and demonstrate that its throughput competitive ratio is almost optimal.