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We investigate the statistical multiplexing and admission control for a partitioned buffer, where the traffic is generated by multiclass Markov-modulated fluid sources. Each of the sources has J (> 1) QoS classes at each state. The QoS is described by the packet loss probability for each class. The buffer is partitioned with J - 1 thresholds to provide the J loss priorities. In the asymptotic regime of large buffers and small loss probabilities, the effective bandwidth is defined and derived based on fluid model analysis and buffer partitioning optimization, which is the minimal channel capacity required to serve a multiclass Markovian source while guaranteeing the QoS requirements of all the classes. For heterogeneous multiclass Markovian sources, numerical studies demonstrate that the proposed effective bandwidth can be used for admission control in an additive way.