In this work we analyze the performance of the largest installation of the Blue Gene/L architecture. This currently has the highest peak performance of any supercomputer. The performance characteristics of this machine are considered that gives rise to achievable application performance. By using a detailed performance model of Sweep3D - a kernel application of interest to Los Alamos National Laboratory we verify that the performance of Blue Gene/L is as expected. In addition the model is used to analyze a possible configuration of a peta-flop version of Blue Gene which contains an increased number of processor cores operating at a higher clock frequency. Uncertainties in the performance characteristics of this future system are captured through a sensitivity analysis on the achievable processing rate, communication latency, and bandwidth. The analysis shows the expected level of performance for Sweep3D that may be achieved on such a system in comparison to current systems.