A Theoretical Model for FPGA Routing

Abstract

The previous chapter presented an experimental study of the effect of the flexibility of the routing architecture in a symmetrical FPGA on the routability of circuits. Flexibility was defined to be a function of the total number of routing switches and wire segments and routability was measured as the percentage of a circuit’s connections that could be successfully routed by CAD tools. This chapter presents a similar study of symmetrical FPGAs, but uses theory rather than experiments. The approach taken is to develop a mathematical model based on probability theory to represent routing in FPGAs as a random process. The model uses simple parameters for the FPGA itself and a circuit to be routed, and allows a range of routing architectures to be specified. Two purposes are served by this study: it confirms the experimental results that were presented, and it provides a basis for future studies of FPGA routing architectures. The latter goal is the most significant one since a theoretical study is often much easier to perform than one that involves time-consuming experiments and possibly the need to develop new CAD programs.