Problem $3$

Consider the scenario shown below, with four different servers connected to four different clients over four three$-$hop paths. The four pairs share a common middle hop with a transmission capacity of $\backslash ($ R$=\backslash )400$ Mbps $.$ The four links from the servers to the shared link have a transmission capacity of $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$s$\}\}=20\backslash )$ Mbps $.$ Each of the four links from the shared middle link to a client has a transmission capacity of $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$c$\}\}=\backslash )60$ Mbps$.$

Answering the following questions $($next page$)$:

a$)$ What is the maximum achievable end$-$end throughput $($in Mbps$)$ for each of the four client$-$toserver pairs, assuming that the middle link is fair$-$shared $($i$.$e$.,$ divides its transmission rate equally among the four pairs$)?$

b$)$ Which link is the bottleneck link $($Rc$,$ Rs$,$ or R$)$ for each session?

c$)$ Assuming that the senders are sending at the maximum rate possible, what are the link utilizations for the sender links $($Rs$),$ client links $($Rc$),$ and the middle link $($R$)?$