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This paper presents a bandwidth management framework for the support of differentiated-service-aware traffic engineering (DS-TE) in multiprotocol label switching (MPLS) networks. Our bandwidth management framework contains both bandwidth allocation and preemption mechanisms in which the link bandwidth is managed in two dimensions: class type (CT) and preemption priority. We put forward a Max-Min bandwidth constraint model in which we propose a novel "use it or lend it" strategy. The new model is able to guarantee a minimum bandwidth for each CT without causing resource fragmentation. Furthermore, we design three new bandwidth preemption algorithms for three bandwidth constraint models, respectively. An extensive simulation study is carried out to evaluate the effectiveness of the bandwidth constraint models and preemption algorithms. When compared with the existing constraint models and preemption rules, the proposed Max-Min constraint model and preemption algorithms improve not only bandwidth efficiency, but also robustness and fairness. They achieve significant performance improvement for the well-behaving traffic classes in terms of bandwidth utilization and bandwidth blocking and preemption probability. We also provide guidelines for selecting different DS-TE bandwidth management mechanisms.