ASBR MoFRR in the inter-AS environment allows the leaf PE to signal a primary path to the remote root through the first ASBR and a backup path through the second ASBR, so that there is an active LSP signaled from the leaf node to the first local root (ASBR-1 in Figure: BGP neighboring for MoFRR) and a backup LSP signaled from the leaf node to the second local root (ASBR-2 in Figure: BGP neighboring for MoFRR) through the best IGP path in the AS.
Using Figure: BGP neighboring for MoFRR as an example, ASBR-1 and ASBR-2 are local roots for the leaf node, and ASBR-3 and ASBR-4 are local roots for ASBR-1 or ASBR-2. The actual root node (ROOT-1) is also a local root for ASBR-3 and ASBR-4.
In Figure: BGP neighboring for MoFRR, ASBR-2 is a disjointed ASBR; with the AS spanning from the leaf to the local root, which is the ASBR selected in the AS, the traditional IGP MoFRR is used. ASBR MoFRR is used from the leaf node to the local root, and IGP MoFRR is used for any P router that connects the leaf node to the local root.