Consider the data center network with | sr2jr

Authors:

James F. Kurose, Keith W. Ross

Chapter:

The Link Layer: Links,access Networks, And Lans

Exercise:

Problems

Question:32 | ISBN:9780132856201 | Edition: 6

Question

Consider the data center network with hierarchical topology in Figure 5.30. 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 5.31.

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

Answer

a)

Link capacity=10 Gbps

=10000 Mbps (Since, 1Gbps=1000Mbps)

Flow pairs count=80

Formula of the maximum rate of a flow to given data:

$\large The \ maximum \ rate \ of \ a \ flow=\frac{Link \ capacity}{Flow \ pairs \ c ount}$

$\large The \ maximum \ rate \ of \ a \ flow=\frac{10000}{80} =125 Mbps$

b)

Refer the Figure 5.31 in the textbook.

Each host contains number of paths from a tier-1 to tier-2 is 4. So, Path count=4

$\large The \ maximum \ rate \ of \ a \ flow=Path count \times Link capacity$

$\large The \ maximum \ rate \ of \ a \ flow=4 \times 10000 =40000 Mbps$

c)

Take 20 hosts on each hosts and 160 pairs of flows.

So, flow pair count=160 for first topology like the data center network with hierarchical topology in Figure 5.30.

next, flow pair count =20 for second topology like the highly interconnected topology in Figure 5.31.

First topology: Data center network using Hierarchical topology

$\large The \ maximum \ rate \ of \ a \ flow=\frac{Link \ capacity}{Flow \ pairs \ c ount}$

$\large The \ maximum \ rate \ of \ a \ flow=\frac{10000}{160} =62.5 Mbps$

Second topology: Highly interconnected network:

Here, flow pair count =20

$\large The \ maximum \ rate \ of \ a \ flow=20\times10000 =200000 Mbps$

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