A Model for Estimating Trace-Sample Miss Ratios

Unknown references, also known as cold-start misses, arise during trace-driven simulation of uniprocessor caches because of the unknown initial conditions. Accurately estimating the miss ratio of unknown references, denoted by ¯, is particularly important when simulating large caches with short trace samples, since many references may be unknown. In this paper we make three contributions regarding ¯. First, we provide empirical evidence that ¯ is much larger than the overall miss ratio (e.g., 0.40 vs. 0.02). Prior work suggests that they should be the same. Second, we develop a model that explains our empirical results for long trace samples. In our model, each block frame is either live, if its next reference will hit, or dead, if its next reference will miss. We model each block frame as an alternating renewal process, and use the renewal-reward theorem to show that ¯ is simply the fraction of time block frames are dead. Finally, we extend the model to handle short trace samples an..