Engineering a large IP backbone network without an accurate, network-wide view of the traffic demands is challenging. Shifts in user behavior, changes in routing policies, and failures of network elements can result in significant (and sudden) fluctuations in load. In this paper, we present a model of traffic demands to support traffic engineering and performance debugging of large Internet Service Provider networks. By defining a traffic demand as a volume of load originating from an ingress link and destined to a set of egress links, we can capture and predict how routing affects the traffic traveling between domains. To infer the traffic demands, we propose a measurement methodology that combines flow-level measurements collected at all ingress links with reachability information about all egress links. We discuss how to cope with situations where practical considerations limit the amount and quality of the necessary data. Specifically, we show how to infer interdomain traffic demands using measurements collected at a smaller number of edge links --- the peering links connecting to neighboring providers. We report on our experiences in deriving the traffic demands in the AT&T IP Backbone, by collecting, validating, and joining very large and diverse sets of usage, configuration, and routing data over extended periods of time. The paper concludes with a preliminary analysis of the observed dynamics of the traffic demands and a discussion of the practical implications for traffic engineering.