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This paper presents a new bandwidth preemption algorithm supporting differentiated services aware traffic engineering (DS-TE) in the multi-protocol label switching (MPLS). The paper presents the following contributions. Firstly, we look at the problem of organizing the mapping of label switching paths (LSPs) in an optimal way such that we can compromise between several traffic engineering (TE) objectives: load-balancing, avoiding network bottlenecks, reducing routing cost, and minimizing path hop count. Secondly, we introduce DS-TE bandwidth management and admission control mechanisms by proposing a new bandwidth preemption algorithm for the maximum allocation model (MAM). Finally, in our proposed scheme, we conduct preemption in tow dimensions: class type (CT) and preemption level so that an LSP of CT ct and priority p can not be preempted as long as any LSP of weaker precedence remains. A case study is also provided to show how our algorithm performs in MPLS networks where DS-TE is applied.