Mathematical Model of a Three-Dimensional Optical Interconnection Network

With the improving performance of microprocessors, their bandwidth and latency requirements have increased at a rate much faster than the network's ability to provide them. The performance bottleneck has gradually shifted from the processors to the interconnection network. Traditional electrical interconnection, because of its low bandwidth, high delay and low interconnection density, becomes one of the constraints of high-performance computer(HPC)'s further improvement. Due to the inherent limitations of the electrical interconnection network, optical interconnection has become a feasible way to improve the performance. A Three-Dimensional Optical Interconnection Network (TDOIN) with low latency and high throughput was put forward in our previous work. An accurate mathematical model can help us design and optimize the optical networks. However, there is not a mathematical model which can provide an accurate analysis for TDOIN. To make better use of the network, we propose a steady-state model to evaluate TDOIN's network characteristics in this paper. This mathematical model is constructed by using Probability Theory. The results of the model analysis and the simulation shows that our model can accurately depict behaviors of TDOIN at steady state.