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When EIGRP loses Successor route and transfers to Feasible Successor route does it calculate another Feasible Successor right away? So the first Feasible Successor becomes the Successor and new FS is calculated. Or does it wait for both Successor and FS to die and only then it looks for new best routes?

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If the Reported Distance for a route is less than or equal to the Feasible Distance, then the route is a Feasible Successor. You can have multiple Feasible Successors, or none at all. The Feasible Distance is the historic, since the route went Active, best metric for a destination. It is possible for there to be multiple routes to the destination, but none are Feasible Successors because the Reported Distances are all larger than the Feasible Distance.

If the Successor route goes away, then the Feasible Successor with the best metric takes over, end of story. If there are no Feasible Successors (because none of the other routes' Reported Distances meet the Feasible Distance), then a query goes out to see if there are any neighbors that know how to reach the destination. If so, then the new Successor, and possibly Feasible Successors, are chosen.

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