Zero-load predictive model for performance analysis in deflection routing NoCs

Abstract

We study a static model for 2-D and 3-D networks that accurately represents the average distance travelled by packets under deflection routing, which is a specific form of adaptive routing. The model captures static properties of the network topology and the spatial distribution of traffic, but does not take into account traffic loading and congestion. Even though this static model cannot accurately predict packet latency under high load, we contend that it is a perfect predictor of deflection routing networks' relative performance under any load condition below saturation, and thus always correctly predicts the optimum network configuration. This is verified through cycle-accurate simulations of congested and uncongested networks with fully adaptive, deflection routing for regular traffic patterns such as uniform random, localized, bursty, and others, as well as irregular patterns in both regular and irregular networks. As the networks with minimal average distance perform best even under high traffic load, the average distance model establishes a robust relation between a static network property, average distance, and network performance under load, providing new insight into network behaviour and an opportunity to identify the optimal network configuration without timeconsuming simulations.

Performance Analysis of 2D and 3D Bufferless NoCs Using Markov Chain Models

“…The chaotic nature of deflections in bufferless routing makes the quest for an analytical model for deflection routing even more challenging. Previous work has identified that the most important parameter in bufferless networks is the mean distance between the source and destination node, based on the topology and the spatial distribution of traffic [21]. The authors demonstrate how this single metric can be used to compare candidate architectures.…”

“…The reason is that the above approach, while surprisingly accurate and efficient, does not take into account the probabilistic and, therefore, difficult-to-predict nature of deflections. In fact, the authors in [21] state without exaggeration that "Due to the exceedingly complex spatial and temporal interference patterns of packets across the network in adaptive routing networks, an accurate analytic latency model seems to be out of reach". Simulation remains the only method for determining network latency under non-zero load conditions.…”

“…For example, in uniform random traffic, each node sends to all other nodes with equal probability, and is therefore a uniform probability distribution. Essentially, we use the average distance model proposed in [21], formulated as vector and matrix operations in order to combine it with our model. Since this probability distribution determines the number of packets exchanged among source-destination pairs, we model it as a vector of weights w. The elements of the vector are essentially the probabilities of the distribution, normalized so that the inner product w•v divided by N is equal to one, in order to be consistent with the definition of probability.…”

“…The first is the number of flits injected per clock cycle per node (flit distribution in time) and the second is the rate at which a source node sends to other nodes (flit distribution in space). As already mentioned, we take the traffic pattern into account by adopting the average distance model [21].…”

“…Figures 5-7 show the average latency in hops for three typical 3D NoC topologies, 4 × 4 × 4 (Figure 5), 8 × 4 × 2 (Figure 6) and 8 × 8 × 1 (Figure 7), for rising injection rates comparing simulation, the average distance model [21] and the proposed model under the assumption that P d = γ, for uniform random traffic. As shown in Figures 5-7, our results are almost surprisingly accurate in the network's high-performance injection rate region.…”