This command doesn't a cause a route to be installed in the routing table. Instead, 'traffic-share min across interfaces' - causes the IOS to divide traffic only among the routes with the best metric across multiple interfaces.
An example would make it to easier to explain.
RouterA has 2 routes to NetX out 2 different interfaces. Metric of 1st route is 10 and the 2nd one is 15.
EIGRP by default does equal cost load balancing. In this case, the routerA would install only the route with a metric of 10.
You could add the command 'variance 2' under EIGRP process and that would cause the router to install both routes in the routing table. The term to describe this feature is called unequal cost load balancing.
In the above scenario, let's say routerA receives 3 packets it will send 2 packets out the 1st link with a metric of 10 and 1 packet out the 2nd link with a metric of 5. The load sharing is proportinate to that of the metric. This is the default behavior.
The command you mentioned above 'traffic-share min across interfaces' would make the RouterA send all 3 packets out the 1st route. Though the 2nd route exists in the routing table it wouldn't be used until the 1st route disappears. This only facilitates quick EIGRP reconvergence.
"In this situation, EIGRP sends packets only through E-C-A, which is the best path to the destination network. This is identical to the forwarding behavior without use of the variance command. However, if you use the traffic-share min command and the variance command, even though traffic is sent over the minimum-cost path only, all feasible routes get installed into the routing table, which decreases convergence times"
Now, my point is:
Why do I may want to use the traffis-blalnce min across-interfaces is the promotion from FS to Successor is immediate?
From my post above:
"If the primary route (Successor) fails the FS is immediately installed from the topology table into the routing table (no recomputation of DUAL)"
There's a slight benefit in using the variance command and having the alternate route in the routing table rather than have to move the feasible successor from the topology table to routing table. Look at the quote from CCO below:
"The feasible successor feature of EIGRP reduces the amount of processor resources used by an autonomous system (AS). It requires only the routers affected by a topology change to perform route re-computation. The route re-computation only occurs for routes that were affected, which reduces search time in complex data structures"
There's some recomputation required in this situation when the successor goes away whereas having an alternate route in the routing table causes seamless reconvergence.
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