Distance Vector Routing Basics

"In simple networks, it is common to use a metric that simply counts how many gateways a message must go through. In more complex networks, a metric is chosen to represent the total amount of delay that the message suffers, the cost of sending it, or some other quantity which may be minimized. The main requirement is that it must be possible to represent the metric as a sum of 'costs' for individual hops.

"Formally, if it is possible to get from entity i to entity j directly (i.e., without passing through another gateway between), then a cost, d(i,j), is associated with the hop between i and j. In the normal case where all entities on a given network are considered to be the same, d(i,j) is the same for all destinations on a given network, and represents the cost of using that network. To get the metric of a complete route, one just adds up the costs of the individual hops that make up the route. For the purposes of this memo, we assume that the costs are positive integers.

"Let D(i,j) represent the metric of the best route from entity i to entity j. It should be defined for every pair of entities. d(i,j) represents the costs of the individual steps. Formally, let d(i,j) represent the cost of going directly from entity i to entity j. It is infinite if i and j are not immediate neighbors. (Note that d(i,i) is infinite. That is, we don't consider there to be a direct connection from a node to itself.) Since costs are additive, it is easy to show that the best metric must be described by

and that the best routes start by going from i to those neighbors k for which d(i,k) + D(k,j) has the minimum value. (These things can be shown by induction on the number of steps in the routes.) Note that we can limit the second equation to k's that are immediate neighbors of i. For the others, d(i,k) is infinite, so the term involving them can never be the minimum."