Empirical models for net-length probability distribution and applications

In this paper, we propose a novel, empirical, and parameterizable model for estimating the probability distribution of wire length for each net in a placed netlist. The model is simple and fast to compute. We did extensive experimentation with state-of-the-art commercial (Cadence) and academic (Parquet and Labyrinth) tools and validated our model. Our distribution model was around three times more accurate than assuming half-perimeter bounding box as the fixed net-length estimate. Since the model is parameterizable it can be easily tailored for different routing tools and benchmarks. This model would be very useful in defining a full fledged probabilistic design automation methodology in which various design metrics are optimized from a probabilistic point of view. We also discuss the application of our model in a novel probabilistic approach to the buffer insertion problem.