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The desire or ability of an ISP to provide differentiated service is a current hotly debated topic. In this paper, we quantify the value of having differentiated service (i.e., class-of-service (CoS)) support in an IP backbone. We compare the capacity requirements of a Diffserv environment providing service for applications that require delay or loss assurances in comparison to a network that provides classless (i.e., best-effort) service and still has to meet the same performance assurances. Our modeling framework first develops a link model that quantifies the required extra capacity (REC) in order for a classless link to provide the same level of performance as experienced by premium class traffic passing through a fixed capacity CoS link. We develop the REC calculations for the cases when average delay or the average loss probability is the target performance goal with Poisson or Markov modulated Poisson process (MMPP) input traffic. Our primary contribution is in quantifying the value of the CoS support in a network setting.