It has been shown through various studies that BGP convergence can be roughly given by the following formula:

Convergence = (Maximum AS_PATH – Minimum AS_PATH) x MRAI *(MinimumRouteAdvertisementInterval)*

MRAI as per the specification is the amount of time that a BGP speaker will wait before passing on successive route updates for the same prefix – it defaults to 30 seconds, and applies to all announcements, with no exemption for withdrawals. Since there can be some variance in the MRAI across different BGP implementations the convergence time is roughly given by the above formula.

Lets see how we arrive at this. Consider the topology as show in the fig 1 below:

A, B, C, D and E are all routers in ASes A, B, C, D and E respectively. Assume that A has announced its reachability to 10/8 and all routers have converged. This implies that E has the following paths for 10/8 in its adj-RIBs-In:

p(B) -> AS_PATH {B A} (path learnt from B)

p(C) -> AS_PATH {C B A} (path learnt from C)

p(D) -> AS_PATH {D C B A} (path learnt from D)

In steady state E would advertise 10/8 with AS_PATH {E B A}

Lets see what happens when A loses its connection to the network 10/8.

A announces a withdrawal for 10/8 to B as shown in figure 2.

B runs its decision process and finds that there is no other route to 10/8, and thus sends an explicit withdrawal to its peers C and E.

E upon receiving the withdrawl runs its decision process and finds that the best route, now available for 10/8 is the one that it learnt from C – the one with the AS_PATH {C B A}. It installs this route in the FIB and advertises this, as shown in figure 3.

E switches to the next best route (via C) and continues to forward traffic for 10/8. It should however be noted, that E at this point of time, has absolutely no idea that C too has received a withdrawal for 10/8.

C meanwhile runs its decision process and decides to send an explicit withdrawal to its peers D and E.

E upon receiving the withdrawal from C runs its decision process and finds that it still has a valid path to reach 10/8 – the one via D (refer to figure 4). It switches to this path, again unaware that D too has received an withdrawal for 10/8.

D now sends a withdrawal to E, and thereby removing all possible paths to 10/8 from E (fig 5). Its now that the network is converged.

What we just saw happening above on E is “BGP Path Hunting”. i.e., BGP “hunts” though all possible AS paths, starting from the shorter ones to the longer ones, until it finally converges.

It can be easily proven that the amount of path hunting will increase as the meshiness of the topology increases. In an acyclic topology (say a tree) there is only one possible path so there is no path hunting. An addition of a single link in this topology creates a cycle in the graph and thus at most two possible paths for BGP to “hunt”. Subsequent links can add many more alternate paths for BGP to hunt, depending on where they’re placed in the graph.

In the worst possible case path hunting in BGP can explore every possible path of each path length. More commonly it has been observed that path hunting in today’s Internet can add an additional 2 or 3 BGP updates to a prefix withdrawal.