The principle of writing data near the current disk head position is most effective when the head is always on a free sector. This is not always possible. In this section, we develop a number of analytical models to estimate the amount of time needed to locate free sectors under various utilizations. These models will help us evaluate whether eager writing is a sound strategy, set performance targets for real implementations, and predict future improvements as disks improve. We also use the models to motivate new file system allocation and reorganization algorithms. Because we are interested in the theoretical limits of eager writing latency, the models are for the smallest addressable unit: a disk sector (although the validity of the formulas do not depend on the sector size).