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Fat tree network topology looks like a tree topology like below figure. In tree topology, we have same terminologies like Root, parent, child etc. This is mainly used to connect a large number of physical servers/computers in a large data center. enter image description here

In the tree structure topology, leaf nodes are physical servers or computers. Rest other nodes are switches. Switches are basically 3 types: Core switches, Aggregation switches, and Edge switches. My question is what's the purpose of such a structure, and i want to know the functionality of each layer (ex: which layer has a routing role ...).

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The purpose of a "fat tree" structure is to provide uniform bandwidth between any two nodes. Compare this to a traditional core-distribution-access model, where traffic gets oversubscribed at the core.

There are different ways of implementing a fat tree. You can have all the layers perform routing.

The article you copied this picture from has a good, if technical, explanation.

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If all your links use the same bandwidth (e.g. 1 Gbit/s), all nodes hanging off an aggregation switch must share this limited bandwidth of their uplink. Since the hierarchy enables a high level of aggregation with a large number of end nodes, that aggregated links will very quickly become a bottleneck. From another point of view, you're running a very high oversubscription ratio (sum of edge-node bandwidths : sum of uplink bandwidth), potentially many hundreds to one.

Instead, you increase link bandwidth higher up in the tree. Depending on the number of edge nodes and their workloads, you could e.g. increase the link speed between edge and aggregation to 10 Gbit/s and accordingly the speed between aggregation and core to 40 Gbit/s. That's a fat tree where links grow faster the closer they come to the root/core.

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