We consider the problem of bounding the probability of buffer overflow in a network node receiving independent inputs that are each constrained by arrival curves, but that are served as an aggregate. Existing results (for example \cite{kesidis-00-b} and \cite{chang-01-a}) assume that the node is a constant rate server. However, in practice, one finds various types of schedulers that do not provide a constant service rate, and thus to which the existing bounds do not apply. Now many schedulers can be adequately abstracted by a service curve property. We extend the results in \cite{kesidis-00-b} and \cite{chang-01-a} to such cases. As a by-product, we also provide a slight improvement to the bound in \cite{chang-01-a}. Our bounds are valid for both discrete and continuous time models.