Usually it will switch once the mobility is shown as down. The foreign wlc will then have to send the traffic to the other anchor WLC and if your using webauth or possibly a different subnet, then that is the amount of time it will take. WebAuth, the clients will have to authenticate again.
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If the mobility anchor config is using default setting, ie 3 pings with 10 sec interval, it will take approximately 30 seconds to detect the anchor is unreachable and send traffic to the other anchor. Is it correct?
No problem. I think there is nothing you really can do especially with WebAuth. If a failure requires the foreign to put traffic to another WLC, then clients have to login again. May times they will not know until they open a browser. So nothing really simple.