Bounds for independent regulated inputs multiplexed in a service curve network element

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 (Kesidis et al., (2000), and Chang et al., (2001)) 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 Kesidis and Chang to such cases. As a by-product, we also provide a slight improvement to the bound in Chang. Our bounds are valid for both discrete and continuous time models.