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Average transmission rate and rate oscillation are two important performance metrics for most wireless services. Both are often needed to be optimized in multi-user scheduling and resource management. In this paper we introduce a utility function that increases with average rate but decreases with rate variance. It is capable of facilitating resource allocation with flexible combinations of the two performance metrics. A generalized gradient scheduling algorithm (GGSA) is then developed to maximize the proposed utility. It is shown that the best scheduler should maximize the sum of concave functions of instantaneous transmission rates in order to maximize the utility of average rate and rate oscillation. The scheduler reduces to the traditional gradient scheduling algorithm when the rate variance term in the new utility function is omitted. We analyze the dynamics of average transmission rates and rate variances using ordinary differential equation and show that GGSA is asymptotically optimal under the condition that the transmission rate vector, after an appropriate scaling, converges to a fixed vector as time goes into infinity.