In this paper we consider the problem of determining traffic matrices for end-to-end demands in an IP/MPLS network that supports multiple quality of service (QoS) classes. More precisely, we want to determine the set of traffic matrices Ti for each QoS class i separately. Ti contains average bandwidth levels for QoS class i for every pair of routers within the network. We propose a new method for obtaining QoS class specific traffic matrices that combines estimation and measurement methods: We take advantage of the fact that the total traffic matrix can be measured precisely in MPLS networks using either the LDP or RSVP-TE protocol. These measurements can then be used in a mathematical model to improve estimation methods – known as network tomography – that estimate QoS class specific traffic matrices from QoS class specific link utilizations. In addition to the mathematical model, we present results of the proposed method from its application in Deutsche Telekom’s global IP/MPL...