The delay that you see is a function of a number of BGP nodes all taking their sweet time about dealing with the changes. Its what BGP does. Think of BGP as an old man, its very stately and dignified.
There is a function on the PE which will allow it to withdraw routes immediately based on loss of a connected interface, rather than waiting for a peer timout. This helps when the tail circuit goes down, which is after all the most likely scenario. The only thing you can do to increase the reconvergence rate here really is to reduce the peer advertisement interval, but this requires changes to your ISP's networks. Alternatively move to Cable and Wireless's IPVPN as we have already "tweaked" our network and can reconverge in about 10 seconds ;-)
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...