Networking Reference
In-Depth Information
1000
2010
100
2003
1996
10
1991
1
10
100
1000
10000
Aspect Ratio
Figure 4.2: Relationship between the optimal radix for minimum latency and router aspect ratio. The
labeled points show the approximate aspect ratio for a given year's technology with a packet size of L =128
bits
2003 technology
2010 technology
2003 technology
2010 technology
300
8
7
250
6
200
5
4
150
3
100
2
50
1
0
0
0
50
100
150
200
250
0
50
100
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250
radix
radix
(a)
(b)
Figure 4.3: Latency (a) and cost (b) of the network as the radix is increased for two different technologies.
A plot of the minimum latency radix versus aspect ratio is shown in Figure 4.2 annotated with
aspect ratios from several years. These particular numbers are representative of large supercomputers
with single-word network accesses 4 , but the general trend of the radix increasing significantly over
time remains. Figure 4.3 (a) shows how latency varies with radix for 2003 and 2010 aspect ratios. As
radix is increased, latency first decreases as hop count, and hence T h , is reduced. However, beyond a
certain radix, serialization latency begins to dominate the overall latency and latency increases. As
bandwidth, and hence aspect ratio, is increased, the radix that gives minimum latency also increases.
For 2004 technology (aspect ratio = 652), the optimum radix is 45 while for 2010 technology (aspect
ratio = 3013) the optimum radix is 128.
4 The 1996 data is from the Cray T3E [ 55 ]( B =48Gb/s, t r =40ns, N =2048), the 2003 data is combined from the Alpha 21364 [ 49 ]
and Velio VC2002 [ 20 ] (1Tb/s, 10ns, 4096), and the 2010 data was estimated as (20Tb/s, 2ns, 8192).
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