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A novel algorithm for buffer management and packet scheduling is presented for providing loss and delay differentiation for traffic classes at a network router. The algorithm, called JoBS (Joint Buffer Management and Scheduling), provides delay and loss differentiation independently at each node, without assuming admission control or policing. The novel capabilities of the proposed algorithm are that (1) scheduling and buffer management decisions are performed in a single step, and (2) both relative and (whenever possible) absolute QoS requirements of classes are supported. Numerical simulation examples, including results for a heuristic approximation, are presented to illustrate the effectiveness of the approach and to compare the new algorithm to existing methods for loss and delay differentiation.