The discussion above assumes that the topology of the network is fixed. In practice, gateways and lines often fail and come back up. To handle this possibility, we need to modify the algorithm slightly. The theoretical version of the algorithm involved a minimum over all immediate neighbors. If the topology changes, the set of neighbors changes. Therefore, the next time the calculation is done, the change will be reflected. However, as mentioned above, actual implementations use an incremental version of the minimization. Only the best route to any given destination is remembered. If the gateway involved in that route should crash, or the network connection to it break, the calculation might never reflect the change. The algorithm as shown so far depends upon a gateway notifying its neighbors if its metrics change. If the gateway crashes, then it has no way of notifying neighbors of a change.
In order to handle problems of this kind, distance vector protocols must make some provision for timing out routes. The details depend upon the specific protocol. As an example, in RIP every gateway that participates in routing sends an update message to all its neighbors once every 30 seconds. Suppose the current route for network N uses gateway G. If we don't hear from G for 180 seconds, we can assume that either the gateway has crashed or the network connecting us to it has become unusable. Thus, we mark the route as invalid. When we hear from another neighbor that has a valid route to N, the valid route will replace the invalid one. Note that we wait for 180 seconds before timing out a route even though we expect to hear from each neighbor every 30 seconds. Unfortunately, messages are occasionally lost by networks. Thus, it is probably not a good idea to invalidate a route based on a single missed message.
As we will see below, it is useful to have a way to notify neighbors that there currently isn't a valid route to some network. RIP, along with several other protocols of this class, does this through a normal update message, by marking that network as unreachable. A specific metric value is chosen to indicate an unreachable destination; that metric value is larger than the largest valid metric that we expect to see. In the existing implementation of RIP, 16 is used. This value is normally referred to as "infinity", since it is larger than the largest valid metric. 16 may look like a surprisingly small number. It is chosen to be this small for reasons that we will see shortly. In most implementations, the same convention is used internally to flag a route as invalid.