Q$2$:

Consider the scenario shown below, where at $\backslash ($ t$=1\backslash ),$ node $\backslash ($ u $\backslash )$ receives distance vectors $($DVs$)$ from neighboring nodes $\backslash ($ v $\backslash )$ and x $.$ The $($old$)$ DV at u $($before receiving the new DVs from its neighbors$)$ is shown, as well as the DVs being sent from $\backslash ($ v $\backslash )$ and $\backslash ($ x $\backslash ).$

$```$

Initial DV i

Du$($u$)=$

Du$($D$)=$

Dit$\}(\backslash$boldsymbol$\{$w$\})$

Du$($x$)=$

Duty$)=$

Du$($x$)=\text{'}$

$```$

$($a$)$ Determine the new distance vector components at u $.$

$($b$)$ Suppose that distance vector calculations have completed in all nodes at time $\backslash ($ t $\backslash ).$ Then, the link between nodes $\backslash ($ w $\backslash )$ and $\backslash ($ z $\backslash )$ is failed $($link cost between $\backslash ($ w $\backslash )$ and $\backslash ($ z $\backslash )$ goes to $\backslash (\backslash$infty $\backslash ))$ at time $\backslash ($ t $\backslash ).$ Assuming that all nodes exchange distance vectors $($DV$)$s at times $\backslash ($ t$+1,$ t$+2,\backslash$ldots $\backslash )($i$.$e$.,$ a clock tick is one time unit$),$ immediately recompute their DVs$,$ and if they transmit a new DV do so at the next integer time value. Is u$\text{'}$s distance vector changed to reflect this link cost change? If your answer is "yes", mention after how many time ticks this happens? If your answer is $"$no$"$ explain the reason for this answer?