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. Required:
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.
c. Now suppose there is a similar traffic pattern, but involving 20 hosts on each rack and 160 pairs of flows. Determine the maximum flow rates for the two topologies.

Explanation:

Given that:

The no of flow pairs = 80

Each link's capacity = 10 Gbps

Link capacity amongst TOR switches and hosts = 1 Gbps

Because each connection is distributed among all flows, each flow crossing the same link distributes the link's capacity with the other flows. The connection capacity needed by each flow in the network is determined by the highest flow rate.

Maximum rate flow =

Since 1 Gbps = 1000 Mbps

= 125 Mbps

Hence, maximum rate flow = 125 Mbps

b.

Each switch at Tier-1 is connected to each and every switch at Tier-2 in the highly integrated structural topology. As a result, there are n-disjoint routes between tier-2 and tier-1 switches.

Number of paths between tier-1 and tier-2 is 4, thus, there exist four paths from tier-1 switch to tier 2.

The capacity whereby all data routes convey is determined by the maximum rate of flow.  

number of available paths = 4  

Each link's capacity = 10 Gbps

Maximum flow rate = 4 × 10 Gbps

Maximum flow rate = 40 Gbps

c.

Because each connection is distributed between all flows, each flow crossing a similar link distributes the link's capacity with other flows.

number of flow pairs = 160

Each link's capacity = 10 Gbps

maximum rate of flow = 10000 Mbps / 160

= 62.5 Mbps

For 160 flow pairs, maximum flow rate = 62.5 Mbps

Each switch in Tier-1 communicates with each switch in Tier-2 in the highly linked topology network. As a result, n-disjoint routes between tier-2 and tier-1 switches are possible. As there exist 20 hosts engaged in the network around each host, the number of routes from either a tier-1 switch or tier-2 switches is 20.

here;

no of paths = 20

each link's capacity = 10 Gbps

Maximum flow rate = 20 × 10  

= 200 Gbps

As such, with 160 pairs of flow, maximum flow rate = 200 Gbps