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Given the increasing demand for services that can guarantee a maximum end-to-end delay in the Internet, it is important to understand the behaviour of different existing networks. We consider networks that implement scheduling per aggregate flow. We give a worst case bound that is valid for any network topology given the maximum hop count for every flow and the utilization at every link. Unfortunately, this bound is finite only for small utilization. Using the context of arrival and service curves we can improve the result for the case of a ring.