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To enable the end-to-end quality of service (QoS) guarantees in the Internet, based on the border gateway protocol (BGP), inter-domain QoS advertising and routing are important. However, little research has been done in this area so far. Two major challenges, scalability and heterogeneity, make the QoS extension to BGP difficult. Two existing approaches, link capacity routing (LCR) and available bandwidth routing (ABR), address QoS advertising and routing in BGP with respect to the bandwidth metric, but neither of them can solve the two challenges well. We extend BGP to advertise bandwidth information, but, instead of using link capacities or instantaneous available bandwidth values, a novel QoS metric, available bandwidth index (ABI), is defined and used to perform bandwidth advertising and routing. The two major contributions of ABI are: (1) ABI dynamically abstracts available bandwidth into a probability interval, therefore, it is very flexible to represent heterogenous and dynamic bandwidth values; (2) by capturing the statistical property of the detailed available bandwidth distribution, ABI is so efficient that it can highly decrease the message overhead in routing, thereby making the QoS advertising and routing very scalable. Our extensive simulations confirm both contributions of the ABI extension to BGP very well.