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I'm reading about fat tree and data center topologies, but I have doubts.

To lower cost, "normal" tree is used sharing bandwidth to many hosts. 1:1 is not common, so we see something between 2.5:1 and 8:1. Is this thinking right?

How can fat tree ensure a large bandwidth to hosts? There is a way to tell a host in Pod0 can send a package to another host in Pod1 like 1:1?

Assuming 1 GigE switch for all tree.

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A fat tree topology "ensures" bandwidth by utilising thicker links closer to the core or root, compared to a normal "skinny" tree where you have the same links everywhere.

So for an example, imagine that you have a network with access, distribution and core layers. The 4 access switches each connect 4 hosts using 1 GigE and you're designing a fat tree. The access switches connect to 2 distribution switches which are connected to a single root switch.

For a fat tree, designed 1:1, you'd make sure that the access <-> distribution trunks are 4 GigE, and the core <-> distribution trunks would need to be 8 GigE.

As you can see, you're not ensuring anything, you're just making sure that along every path of the network, every host has it's own 1 GigE of bandwidth.

Here's a good article if you want to learn more; http://clusterdesign.org/fat-trees/

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