Networking Reference
In-Depth Information
4. HIGH-RADIX TOPOLOGIES
Figure 4.8 (b), if the details of the intra-group is ignored, a group can be viewed as a virtual high-radix
router. This very high radix, k >> k enables the system level network to be realized with very low
global diameter (the maximum number of expensive global channels on the minimum path between
any two nodes). Up to g = ah +
1 groups ( N = ap(ah +
1 ) terminals) can be connected with a
global diameter of one. In contrast, a system-level network built directly with radix k routers would
require a larger global diameter.
In a maximum-size ( N = ap(ah + 1 ) ) dragonfly, there is exactly one connection between
each pair of groups. In smaller dragonflies, there are more global connections out of each group
than there are other groups. These excess global connections are distributed over the groups with
each pair of groups connected by at least
ah
+
1
channels. The dragonfly parameters a , p , and h
can have any values. However, to balance channel load on load-balanced traffic, the network should
have a
g
2 h . Because each packet traverses two local channels along its route (one at each
end of the global channel) for one global channel and one terminal channel, this ratio maintains
balance. Additional details of routing and load-balancing on the dragonfly topology will be discussed
in Chapter 5 . Because global channels are expensive, deviations from this 2:1 ratio should be done
in a manner that overprovisions local and terminal channels, so that the expensive global channels
remain fully utilized. That is, the network should be balanced so that a
=
2 p
=
2 h .
The scalability of a balanced dragonfly is shown in Figure 4.9 . By increasing the effective
2 h , 2 p
1,000,000
100,000
10,000
1,000
100
10
1
0
20
40
60
80
Router radix (k)
Figure 4.9: Scalability of the dragonfly topology as router radix increases. 1D flattened butterfly is
assumed for both the intra- and the inter-group networks.
radix, the dragonfly topology is highly scalable - with radix-64 routers, the topology scales to over
256k nodes with a network diameter of only three hops. In comparison, a 2D flattened butterfly
using radix-64 routers can scale to approximately 10k nodes while a 3D flattened butterfly can only
scale up to 64k nodes. Arbitrary networks can be used for the intra-group and inter-group networks
in Figure 4.8 . However, to minimize the network cost, a flattened butterfly with the smallest number
of dimensions will be appropriate. A simple example of the dragonfly is shown in Figure 4.10 with
 
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