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In this paper, we analyze the performance of the bandwidth enforcement strategy applied for the bursty traffic. As a bandwidth enforcement strategy, we consider the leaky-bucket (LB) strategy which has been regarded as the most promising and easily implementable strategy. In this analysis, we use an Markov-modulated Poisson process (MMPP) as a model for the burst input traffic. With a token and a token pool as models for the transmission right and the allowed burstiness of the input traffic, respectively, we analyze and obtain the performance of the traffic under the LB bandwidth enforcement strategy. We also present some numerical results to show the effects of the system parameters on the performance of the traffic measured by the cell delay and the cell blocking probability.