Final answer:
The routing protocol property that determines the amount of time it takes to fail over from a previously active route to a backup route is convergence time.
Step-by-step explanation:
The name for the routing protocol property that determines the amount of time it takes to fail over from a previously active route to a backup route is convergence time. Convergence time refers to the time it takes for all the routers in a network to synchronize and update their routing tables after changes occur, such as a link failure or a new route becoming available.
Routing protocols, such as OSPF (Open Shortest Path First) and EIGRP (Enhanced Interior Gateway Routing Protocol), have different convergence times based on their algorithms and configuration settings. For example, OSPF typically has a faster convergence time compared to EIGRP.
To illustrate this property, let's consider a scenario where a link fails in a network. If a routing protocol has a fast convergence time, the routers in the network will quickly recognize the link failure and reroute traffic through backup routes. On the other hand, a routing protocol with a slow convergence time may take longer to detect the link failure and update the routing tables, resulting in potential network downtime or suboptimal routing.