A Fuzzy Approach for Variation Aware Buffer Insertion and Driver Sizing

In nanometer regime, the effects of process variations are dominating circuit performance, power and reliability of circuits. Hence, it is important to properly manage variation effects at the design stage to avoid excessive performance and power penalties. Buffer insertion and driver sizing (BIDS) techniques are widely used in design flow due to their simplicity and effectiveness in improving metrics such as power, performance and noise. In this paper, we propose a fuzzy optimization technique to perform variation aware Buffer insertion and driver sizing at the network level. Previous variation aware techniques for buffer insertion, processes individual nets in a critical first fashion, which can result in severe over-buffering. Hence, we formulate the variation aware BIDS problem as a fuzzy piece-wise linear program to maximize variation resistance in the presence of delay, power and noise constraints. The uncertainty due to process variations in circuit delay is modeled using fuzzy numbers and the fuzzy approach performs pre-processing deterministic optimizations with the worst and average case values to convert the uncertain problem into a crisp problem. The proposed approach evaluated on ITCpsila99 benchmarks shows a 45% reduction in resource (buffer, driver) cost compared to deterministic worst case approach.