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This paper considers traffic engineering (TE) for the provision of end-to-end quality of service (QoS) guarantees across multiple autonomous systems (ASes) in the Internet. We review an inter-AS QoS management model, and consider algorithms for offline inter-AS and intra-AS TE. We consider two approaches, decoupled and integrated, to allow these systems to work together to achieve optimal TE performance. We quantify through simulation the lower TE costs incurred by the integrated approach.