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We consider the problem of bounding the probability of buffer overflow in a network node fed with independent arrival processes that are each constrained by arrival curves, but that are served as an aggregate. Existing results assume that the node is a constant rate server. However, in practice, one finds complex network nodes that do not provide a constant service rate, and thus, to which the existing bounds do not apply. Now many nodes can be adequately abstracted by a service curve property. We extend previous results to such cases. As a by-product, we also provide a slight improvement to the bound in Chang et al. (see Proc. Sigmettics 2001, Cambridge, MA, May 2001, p.184-193). Our bounds are valid for both discrete and continuous time models.