Exercise 5 9 For a high performance system such as a B tree index for 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 fi x sized entries The utility of a page is its B tree depth, calculated as log2 (entries) The following table shows for 16 byte entries, and a 10 year old disk with a 10ms latency and 10 MB s transfer rate, the optimal page size is 16K Page size (KB) Page utility or B tree depth (number of disk accesses saved) Index page Access Cost (ms) Utility cost 2 6 49 (or log2(2048 160 7)) 10 2 0 64 4 7 49 10 4 0 72 8 8 49 10 8 0 79 16 9 49 11 6 0 82 32 10 49 13 2 0 79 64 11 49 16 4 0 70 128 12 49 22 8 0 55 256 13 49 35 6 0 38 5 9 1 10 5 4 What is the best page size if entries now become 128 bytes 5 9 2 10 5 4 Based on Exercise 5 9 1, what is the best page size if pages are half full 5 9 3 20 5 4 Based on Exercise 5 9 2, what is the best page size if using a modern disk with 3ms latency and 100 MB s transfer rate Explain why future servers are likely to have larger pages Keeping frequently used (or hot) pages in DRAM can save disk accesses, but how do we determine the exact meaning of frequently used for a given system Data engineers use the cost ratio between DRAM and disk access to quantify the reuse time threshold for hot pages The cost of a disk access is $Disk accesses per sec, while the cost of keep a page in DRAM is $DRAM MB page size The typical DRAM and disk costs, and typical database page sizes at several time points are listed below Year DRAM cost ($ MB) Page size (KB) Disk cost ($ disk) Disk access rate (access sec) 1987 5000 1 15000 15 1997 15 8 2000 64 2007 0 05 64 80 83 5 9 4 10 5 1, 5 4 What are the reuse time thresholds for these three technology generations 5 9 5 10 5 4 What are the reuse time thresholds if we keep using the same 4K page size Whats the trend here 5 9 6 20 5 4 What other factors can be changed to keep using the same page size (thus avoiding software rewrite) Discuss their likeliness with current technology and cost trends

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Exercise 5 9 For a high performance system such as a B tree index for 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 fi x sized entries  The utility of a page is its B tree depth, calculated as log2 (entries)  The following table shows for 16 byte entries, and a 10 year old disk with a 10ms latency and 10 MB s transfer rate, the optimal page size is 16K  Page size (KB) Page utility or B tree depth (number of disk accesses saved) Index page Access Cost (ms) Utility cost 2 6 49 (or log2(2048 160 7)) 10 2 0 64 4 7 49 10 4 0 72 8 8 49 10 8 0 79 16 9 49 11 6 0 82 32 10 49 13 2 0 79 64 11 49 16 4 0 70 128 12 49 22 8 0 55 256 13 49 35 6 0 38 5 9 1  10   5 4  What is the best page size if entries now become 128 bytes  5 9 2  10   5 4  Based on Exercise 5 9 1, what is the best page size if pages are half full  5 9 3  20   5 4  Based on Exercise 5 9 2, what is the best page size if using a modern disk with 3ms latency and 100 MB s transfer rate  Explain why future servers are likely to have larger pages  Keeping frequently used (or hot) pages in DRAM can save disk accesses, but how do we determine the exact meaning of frequently used for a given system  Data engineers use the cost ratio between DRAM and disk access to quantify the reuse time threshold for hot pages  The cost of a disk access is $Disk accesses per  sec, while the cost of keep a page in DRAM is $DRAM MB page size  The typical DRAM and disk costs, and typical database page sizes at several time points are listed below  Year DRAM cost ($ MB) Page size (KB) Disk cost ($ disk) Disk access rate (access sec) 1987 5000 1 15000 15 1997 15 8 2000 64 2007 0 05 64 80 83 5 9 4  10   5 1, 5 4  What are the reuse time thresholds for these three technology generations  5 9 5  10   5 4  What are the reuse time thresholds if we keep using the same 4K page size  Whats the trend here  5 9 6  20   5 4  What other factors can be changed to keep using the same page size (thus avoiding software rewrite)  Discuss their likeliness with current technology and cost trends

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Question: Exercise 5.9 For a high-performance system such as a B-tree index for database, the page size is determined mainly by the data size and disk

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