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Network dimensioning is typically based on a traffic matrix that contains the bandwidth demand for each source-destination pair. We consider a different approach, which assumes that only the maximum amount of premium traffic that can be carried across each access link is known. Based on this information, we present three algorithms for determining the bandwidth required for premium traffic in the core network. The first algorithm intermediately estimates the traffic matrix based on the "gravity model". The other two algorithms compute the worst-case requirements for premium traffic when there are no link failures and fixed routing is used (second algorithm), and when there are link failures and alternative routing paths are available (third algorithm). An important feature of the two worst-case algorithms is that they allow admission control decisions to be based solely on the availability of bandwidth for premium traffic at the access links. We apply and compare the three algorithms for the Greek Research and Technology Network (GRNET), which currently uses the third algorithm for its premium IP service.