Increasing the radix of networks monotonically reduces the overall cost of a network. Network
cost is largely due to router pins and connectors and hence is roughly proportional to total router
bandwidth: the number of channels times their bandwidth. For a fixed network bisection bandwidth,
this cost is proportional to hop count. Since increasing radix reduces hop count, higher radix networks
have lower cost as shown in Figure 4.3 (b). Power dissipated by a network also decreases with
increasing radix. The network power is roughly proportional to the number of router nodes in
the network. As radix increases, hop count decreases, and the number of router nodes decreases. The
power of an individual router node is largely independent of radix as long as total router bandwidth
is held constant. Router power is largely due to SerDes (serializer/deserializer) I/O circuits and
internal switch datapaths. The arbitration logic, which becomes more complex as radix increases,
represents a negligible fraction of total power [ 67 ].
4.2.2 ECONOMICAL OPTICAL SIGNALING
Migrating from low-radix topology to high-radix topology increases the length of the channels
as described earlier in Section 4.1 . For low-radix routers, the routers are often only connected to
neighboring routers - e.g., with a radix-6 router in a 3-D torus network, each router is connect to
two neighbors in the x , y , and z dimensions. The long wraparound link of a torus topology can be
removed by creating a “folded” torus, as shown in Figure 4.1 (a). As a result, the cable lengths are
reasonably short and only need to cross one or two cabinets at most and thus often under a few
meters in length. The benefit of short cables, under say five meters, is that they can be driven using
low-cost passive electrical signaling. With a high-radix router, such as a radix-64 router, each router
is now connected to a larger number of routers which can be either centrally located or physically
distributed, yet far away. Although high-radix reduces the network diameter, it increases the length
of the cables required in the system as demonstrated in Figure 4.1 (b).
Historically, the high cost of optical signaling limited its use to very long distances or applica-
tions that demanded performance regardless of cost. Recent advances in silicon photonics and their
application to active optical cables such as Intel Connects Cables [ 23 ] and Luxtera Blazar [ 46 , 47 ]
have enabled economical optical interconnect. These active optical cables have electrical connections
at either end and EO and OE 5 modules integrated into the cable itself.
Figure 4.4 compares the cost of electrical and optical signaling bandwidth as a function of
distance. The cost of Intel Connects Cables[ 23 ] is compared with the electrical cable cost model
presented in [ 41 ]. 6 Optical cables have a higher fixed cost (y-intercept) but a lower cost per unit
distance (slope) than electrical cables. Based on the data presented here, the crossover point is at
10m. For distances shorter than 10m, electrical signaling is less expensive. Beyond 10m, optical
signaling is more economical. By reducing the number of global cables it minimizes the effect of
the higher fixed overhead of optical signaling, and by making the global cables longer, it maximizes
5 EO : Electrical to Optical, OE : Optical to Electrical
6 The optical cost was based on prices available at http://shop.intel.com at the time this analysis was done in 2008 [ 38 ]. If purchased
in bulk, the prices will likely be lower. The use of multi-mode fiber instead of single-mode fiber may also result in lower cost.
Subsequently, the Connects Cables were acquired from Intel by EMCORE Corporation.