Consider the data center network with hierarchical topology in Figure 1. Suppose now there are 80 pairs of flows, with ten flows between the first and ninth rack, ten flows between the second and tenth rack, and so on. Further suppose that all links in the network are 10 Gbps, except for the links between hosts and TOR switches, which are 1 Gbps.

a. Each flow has the same data rate; determine the maximum rate of a flow.

b. For the same traffic pattern, determine the maximum rate of a flow for the highly interconnected topology in Figure 2.

Internet Load balancer Border router Access router Tier-2 switch Tier-1 switch TOR switch Rack of Servers 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Figure1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Figure 2 Tier-2 switch Tier-1 switch TOR switch Rack of Servers