Consider the network shown below, in which horizontal lines represent Autonomous Systems $($ASes$),$ and numbered vertical lines are inter$-$provider links. A$,$ B$,$C$,$ D$,$ and E are networks connected to a particular provider below $($i$.$e$.,$ customers of the indicated AS$).$ An AS path can be written as a comma separated path from one provider to another, for example, one possible route from C to A through Provider P would be $$ Q$,$ P$,$ S $>.$

a$)$ Suppose ASes P$,$ Q$,$ R$,$ and S adopt a route$-$selection policy that prefers routes

that use the "closest" inter$-$provider link, minimizing their own cost $($e$.$g$.,S$ would

prefer to use link $1$ over link $3$ or $5$ for any outbound traffic from network A because

link $1$ is closest to A$).$ Further, P$,$ R$,$ and S are all customers of Q$,$ P and S are

peers, and $S$ and $R$ are peers.

i$)$ What route would $B$ use to send traffic to network $A?$

ii$)$ What route would $D$ use to send traffic to network $E?$

iii$)$ What route would $D$ use to send traffic to network $A?$

b$)$ Suppose the ASes adjust their BGP route selection policy, instead choosing the

"furthest" link. Additionally, the autonomous system relationships have changed

again. Now $R$ is a customer of $S$ and $S$ is a customer of $P,$ while $Q$ has peer$-$to$-$peer

relationships with each of $P,R$ and $S.$

i$)$ What route would $C$ use to send traffic to network $B?$

ii$)$ What route would $C$ use to send traffic to network D$?$

iii$)$ What route would D use to send traffic to network B$?$