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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) classes at each state. The quality of service (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. Extending the effective bandwidth concept to such a buffer system is a challenging topic. We find the minimal effective bandwidth in the asymptotic regime of large buffers and small loss probabilities by optimally setting the partition thresholds. The minimal effective bandwidth achieves efficient resource utilization and can be used to do admission control for heterogeneous multiclass Markovian sources in an additive way. The buffer partition thresholds are dynamically adjusted according to the input traffic load to guarantee QoS. Numerical analysis and simulation results verify the QoS satisfaction and the obvious improvement of resource utilization compared with previously published results, when the minimal effective bandwidth is used for resource allocation with the proposed dynamic buffer partitioning techniques.