An upgraded version of IEEE's STP called RSTP (Rapid Spanning Tree 802.1w) cuts the convergence time of STP to about one second. One disadvantage to RSTP (and STP) is that only one of the redundant links can be active at a time in an "active standby" configuration, and STP also changes the active path to another router, so the gateway addresses of the clients must change as well. To avoid these problems, you must run VRRP along with STP and RSTP on your routers, which emulates one virtual router address for both core routers and takes about three seconds to fail over.
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But because VRRP and RSTP work independently, it's possible VRRP will designate one router as master and RSTP would determine the path to the backup router as the preferred path. Worst case, this means if the backup VRRP router receives traffic, it will immediately forward it to the master router for processing, adding a router hop.
Another router redundancy option is to run OSPF in the core router as well as on the aggregator switches. OSPF is a link state protocol, so if one of the links goes down, it usually fails over in less than one second. You don't need VRRP with OSPF if you don't have redundant aggregator switches, because the clients would use the single aggregator switch as their gateway address. Most OSPF router and switch implementations now support ECMP (Equal Cost Multipath), a newer version of OSPF that load balances traffic equally across two links. Both links are always active in an active/active configuration and, if there is a failure, only half the traffic will be affected.
Load balancing also means that, theoretically, you have the total bandwidth of both links available. But, if you're depending upon both links for your bandwidth requirements, you don't get full redundancy. If a failure occurs, the traffic will oversubscribe the remaining link with unpredictable results. You can mitigate this to some extent with QoS but, given the low cost of LAN bandwidth, it's better to upgrade the link speeds and get true redundancy.