96
Network-on-Chip
4.6.2 Network Aspect ratio
Besides the channel width and flit size, the network aspect ratio also has
an important role in determining the overall performance and cost of NoC.
In general, for an M × ⎢ ⎡C / M⎤ ⎥ Mesh-1 network (M is the number of nodes
in each row and C is the total number of cores attached in the network),
Equations 4.9 and 4.10 give the average distance (D) and the number of
directed edges (E) as mentioned in the work of Pavlidis and Friedman (2007):
M + ⎡ ⎢ C / M⎤ ⎥
D =
(4.9)
3
⎪ ⎧
⎛ ⎡ C
⎤ ⎞ ⎡ C
⎤
⎪ ⎫
E
=
2
×
⎨ M
×
⎜
− 1
⎟ +
×(
M
−
1)
(4. )
⎥
⎢
⎬
10
⎢
⎥
⎪ ⎩
⎝
⎢ M
⎥ ⎠
⎢ M
⎥
⎪ ⎭
E
⎛
6C
⎞
=
−
2 × ⎜
3 ⎟
⎜
⎟
(4.11)
D
M + C M
⎝
⎢ ⎡ / ⎥ ⎤
⎠
The ratio of E to D is shown in the above equation. The E/D ratio is a good
indicator of network throughput (Decina et al. 1991). It can be shown that for
the Mesh-1 network, the value of E/D reaches its maximum and the value of D
reaches its minimum when the condition M = ⎡ ⎢ C / M ⎥ ⎤ holds. This signifies that
a square mesh network with an equal number of rows and columns is expected
to show the best performance. The performance will degrade as the network
becomes more and more rectangular in nature. Thus, to connect 2 n cores, where
n is odd, a mesh network that connects single core to each router may not be the
ideal choice to the NoC designers due to its rectangular shape. This statement
is also true for a Mesh-2 network for 2 n cores, where n is even.
Table 4.7 shows different topological parameters such as diameter, average distance in hops (D), number of directed edges (E), number of destination cores in the local cluster, and bisection width of all the networks under
consideration for connecting 32 IP cores. It may be observed that although
Mesh-1 has the highest E/D ratio, its diameter is also the highest among all.
TABLe 4.7
Topological Parameters of Different Networks with 32 Cores
Networks
Number of
Destination Core
in Local Cluster
Number
of Edges
(E)
Average
Distance (D)
Edges/
Avg. Dist.
Bisection
Width
Diameter
Mesh-1
Mesh-2
2, 3, 4
1
104
48
4.000
2.645
26.00
18.15
4
4
10
6
BFT
3
40
2.840
14.08
4
4
MoT
1
96
5.161
18.60
4
8
Network-on-Chip
4.6.2 Network Aspect ratio
Besides the channel width and flit size, the network aspect ratio also has
an important role in determining the overall performance and cost of NoC.
In general, for an M × ⎢ ⎡C / M⎤ ⎥ Mesh-1 network (M is the number of nodes
in each row and C is the total number of cores attached in the network),
Equations 4.9 and 4.10 give the average distance (D) and the number of
directed edges (E) as mentioned in the work of Pavlidis and Friedman (2007):
M + ⎡ ⎢ C / M⎤ ⎥
D =
(4.9)
3
⎪ ⎧
⎛ ⎡ C
⎤ ⎞ ⎡ C
⎤
⎪ ⎫
E
=
2
×
⎨ M
×
⎜
− 1
⎟ +
×(
M
−
1)
(4. )
⎥
⎢
⎬
10
⎢
⎥
⎪ ⎩
⎝
⎢ M
⎥ ⎠
⎢ M
⎥
⎪ ⎭
E
⎛
6C
⎞
=
−
2 × ⎜
3 ⎟
⎜
⎟
(4.11)
D
M + C M
⎝
⎢ ⎡ / ⎥ ⎤
⎠
The ratio of E to D is shown in the above equation. The E/D ratio is a good
indicator of network throughput (Decina et al. 1991). It can be shown that for
the Mesh-1 network, the value of E/D reaches its maximum and the value of D
reaches its minimum when the condition M = ⎡ ⎢ C / M ⎥ ⎤ holds. This signifies that
a square mesh network with an equal number of rows and columns is expected
to show the best performance. The performance will degrade as the network
becomes more and more rectangular in nature. Thus, to connect 2 n cores, where
n is odd, a mesh network that connects single core to each router may not be the
ideal choice to the NoC designers due to its rectangular shape. This statement
is also true for a Mesh-2 network for 2 n cores, where n is even.
Table 4.7 shows different topological parameters such as diameter, average distance in hops (D), number of directed edges (E), number of destination cores in the local cluster, and bisection width of all the networks under
consideration for connecting 32 IP cores. It may be observed that although
Mesh-1 has the highest E/D ratio, its diameter is also the highest among all.
TABLe 4.7
Topological Parameters of Different Networks with 32 Cores
Networks
Number of
Destination Core
in Local Cluster
Number
of Edges
(E)
Average
Distance (D)
Edges/
Avg. Dist.
Bisection
Width
Diameter
Mesh-1
Mesh-2
2, 3, 4
1
104
48
4.000
2.645
26.00
18.15
4
4
10
6
BFT
3
40
2.840
14.08
4
4
MoT
1
96
5.161
18.60
4
8