What is the best page size if using a modern disk with a 3 ms latency and 100 MB/s transfer rate? Explain why future servers are likely to have larger pages.

For a high-performance system such as a B-tree index for a database, the page size is determined mainly by the data size and disk performance. Assume that on average a B-tree index page is 70% full with ix-sized entries. The utility of a page is its B-tree depth, calculated as log2(entries). The following table shows that for 16-byte entries, and a 10-year-old disk with a 10 ms latency and 10 MB/s transfer rate, the optimal page size is 16K.

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Page Utility or B-Tree Depth Page Size (KB) (Number of Disk Accesses Saved) 6.49 (or log₂ (2048/16x0.7)) 2 4 8 16 32 64 128 256 7.49 8.49 9.49 10.49 11.49 12.49 13.49 Index Page Access Cost (ms) 10.2 10.4 10.8 11.6 13.2 16.4 22.8 35.6 Utility/Cost 0.64 0.72 0.79 0.82 0.79 0.70 0.55 0.38