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

Abstract

Performance analysis and design space exploration of bufferless Networks-on-Chip is done mainly through time-consuming cycle-accurate simulation, due to the chaotic nature of packet deflections, which have thus far prevented the development of an accurate analytical model. In order to raise the level of abstraction as well as capture the inherently probabilistic behavior of deflection routing, this paper presents a methodology for employing Markov chain models in the analysis of the behavior of bufferless Networks-on-Chip. A formal way of describing a bufferless NoC topology as a set of discrete-time Markov chains is presented. It is demonstrated that by combining this description with the network average distance, it is possible to obtain the expectation of the number of hops between any pair of nodes in the network as a function of the flit deflection probability. Comparisons between the proposed model and cycle-accurate simulation demonstrate the accuracy achieved by the model, with negligible computational cost. The useful range of the proposed model is quantified, demonstrating that it has an error of less than 10% for a significant proportion (between 33 and 75%) of the injection rate range below saturation. Finally, a simple equation for comparing mesh topologies with a “back-of-the-envelope” calculation is introduced.