Question

Consider a network with three routers P, Q, R shown in the figure below. All the links have cost of unity.
 

The routers exchange distance vector routing information and have converged on the routing tables, after which the link Q-R fails. Assume that P and Q send out routing updates at random times, each at the same average rate. The probability of a routing loop formation (rounded off to one decimal place) between P and Q, leading to count-to-infinity problem, is \(\underline{\hspace{1cm}}\).

Hint:

In distance-vector routing, the count-to-infinity problem can cause prolonged instability due to incorrect routing information. Random update rates influence the likelihood of routing loops.

Answer 1

Correct Answer: 0.5

In the distance-vector routing protocol, the count-to-infinity problem arises when a network partition or link failure occurs, causing incorrect routing tables to persist for an extended period. The probability of a routing loop formation between two routers is influenced by several factors, such as the rate at which they exchange updates and the convergence time after a failure. Given that the routers send out updates at random times, and the link Q-R fails, the probability of a routing loop forming between P and Q is generally approximated as 0.5 in such cases of random updates. Thus, the probability of a routing loop formation is: \[ \boxed{0.5}. \]