Problem $3$: $(25$ Points$)$

END TO END THROUGHPUT AND BOTTLENECK LINKS

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 $R=100Mbps.$ The four links from the servers to the shared link have a transmission capacity of $R_S=10Mbps.$ Each of the four links from the shared middle link to a client has a transmission capacity of $R_C=30Mbps.$