2.1 Cost of the simple network. Compute the cost of our simple network using the data in Tables 2.1 and 2.2.
2.7 Effects of a larger butterfly on dropping. If we add more stages to our example butterfly network (and increase the number of nodes accordingly), will the fraction of packets dropped increase? How will the fraction dropped change if the degree of the switches is increased instead? Considering only the dropping probability, is it more efficient to expand the degree of the switches or the number of stages when adding nodes?
3.1 Tornado traffic in the ring. Consider an 8-node ring network in which each node sends traffic to the node 3 hops around the ring. That is, node isends traffic to i +3 (mod 8). Each channel has a bandwidth of 1 Gbit/s and each input offers traffic of 512 Mbits/s. What is the channel load, ideal throughput, and speedup if minimum routing is used on this network? Recalculate these numbers for the case where non-minimal routing is allowed and the probability of taking the non-minimal route is weighted by its distance so that a packet takes the three-hop route with probability 5/8 and the five-hop route with probability 3/8
3.6 Impact of serialization latency on topology choice. A system designer needs to build a network to connect 64 processor nodes with the smallest possible packet latency. To minimize cost, each router is placed on the same chip as its corresponding processor (a direct network) and each processor chip has 128 pins dedicated to the network interface. Each pin’s bandwidth is 2 Gbits/s and the average packet length is L = 512 bits. The hop latency of the routers is tr = 15 ns. Ignore wire latency (Tw = 0).
(a) The designer first considers a fully connected topology. That is, each node has a dedicated channel to every other node. What is the average router latency Trmin and serialization latency Ts of this network? That is the average, zero-load message latency T0?
(b) Re-compute the latencies for a ring topology. Hmin for this ring is 16. (See Section 5.2.2.)
4.3 Packaging a butterfly topology. You need to connect 210 nodes in a packaging technology withWn = 128 andWs = 1024. Choose a butterfly topology that first maximizes the throughput of the network and then minimizes latency. What is this throughput and the corresponding latency? Assume L = 512 bits, f = 1 GHz, and tr = 10 ns. Also, ignore wire latency.
5.2 Tradeoffs in a 4,096-node torus. Examine the tradeoff between k and n for a 4,096- node torus. For each combination of k and n where kn = 4, 096, what is the ideal throughput and average zero-load message latency?Assume each node has 120 signal pins, the bisection width of the system is 1,500 signals, thesignalling frequency is f = 2.5 GHz, the packet length is L = 512 bits, and the router hop delay is 20 ns. Ignore wire latency (Tw = 0).