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row-wise adjacent tiles such that the breadth of the layer increases just
because of channel width. The length of the layer will increase by the
length of the routers that occupy maximum area in each column. Thus,
in a 3D NoC having eight cores in each layer, the dimension of the middle layer of 2 × 4 × 4 Mesh-1 network considering unidirectional opposite
links gets incremented from 10 mm × 5 mm to 11.5 mm × 5.064 mm, and
that of 2 × 2 × 4 Mesh-2 network becomes 10.678 mm × 5.064 mm. For a
BFT-based network, the length of the middle layer increases due to leaf,
stem, and root routers, whereas its breadth increases just because of channel width. The dimension of the middle layer of a four-layered BFT network having eight cores in each layer becomes 11.017 mm × 5.064 mm. For
a 3D MoT-based network, all routers and repeaters of a row tree in each
layer are also placed between row-wise adjacent tiles such that they do
not increase the breadth of the layer. For a 2 × 2 × 4 MoT network having eight cores in each layer, the dimension of the middle layer becomes
10.684 mm × 5.064 mm. For larger number of cores in each layer, it can
be noted that only the stem routers of the column trees of each 2 × 2
MoT subnetwork will increase the breadth of the layer. The length of the
layer will be increased due to the routers and repeaters of the row tree.
Taking all these factors into account, the dimension of the middle layer
of a 4 × 4 × 4 MoT network having 32 cores in each layer increases from
20 mm × 10 mm to 21.624 mm × 10.404 mm. Assuming each router to be
a perfect square, the length of each side of the stem router is found to be
200 µm which is almost 6 times wider than the cross section of two opposite unidirectional 32-bit links. Thus, unlike mesh and BFT networks, MoT
network connects up to 16 cores in a single row tree in each layer, and
its channel width will not increase the breadth of the layer. In the same
way, it can be shown that the dimension of the middle layer of a 4 × 8 × 4
Mesh-1 and a 4 × 4 × 4 Mesh-2 (both having 32 cores in each layer) network
becomes 22.856 mm × 10.128 mm and 21.5 mm × 10.128 mm, respectively.
For a four-layered BFT based network, the dimension of the middle layer
having 32 cores becomes 22.33 mm × 10.128 mm. For a 1024-core system
where 256 cores are residing in each layer, the area of 16 × 16 × 4 Mesh1, 16 × 8 × 4 Mesh-2, 16 × 8 × 4 MoT, and BFT networks are incremented
from 40 mm × 40 mm to 45.76 mm × 40.512 mm, 43.048 mm × 40.512 mm,
43.504 mm × 41.616 mm, and 46.38 mm × 40.768 mm, respectively.
Table 11.3 depicts the area overhead of underlying networks for 32-,
128-, and 1024-core-based systems where the number of cores residing in
each layer is 8, 32, and 256, respectively. It may be noted that in all cases
the area occupied by the MoT network is lesser than that of Mesh-1 and
BFT-based networks, but higher than that of Mesh-2 network. Although
there exists a possibility of trading-off this additional area for energy/
performance benefits, in this work, this avenue has not been explored as
it goes deep into the physical design issues of systems involving these
NoC topologies.