Ben Bitdiddle and Louis Reasoner are examining a 3.5-inch magnetic disk that spins at 7,500 RPM, with an average seek time of 6.5 milliseconds and a data transfer rate of 10 megabytes per second. Sectors contain 512 bytes of user data.

a. On average, how long does it take to read a block of eight contiguous sectors when the starting sector is chosen at random?

b. Suppose that the operating system maintains a one-megabyte cache in RAM to hold disk sectors. The latency of this cache is 25 nanoseconds, and for block transfers the data transfer rate from the cache to a different location in RAM is 160 megabytes per second. Explain how these two specifications can simultaneously be true.

c. Give a formula that tells the expected time to read 100 randomly chosen disk sectors, assuming that the hit ratio of the disk block cache is h.

d. Ben’s workstation has 256 megabytes of RAM. To increase the cache hit ratio, Ben reconfigures the disk sector cache to be much larger than one megabyte. To his surprise he discovers that many of his applications now run slower rather than faster. What has Ben probably overlooked?

e. Louis has disassembled the disk unit to see how it works. Remembering that the centrifuge in the biology lab runs at 36,000 RPM, he has come up with a bright idea on how to reduce the rotational latency of the disk. He suggests speeding it up to 96,000 RPM. He calculates that the rotation time will now be 625 microseconds. Ben says this idea is crazy. Explain Ben’s concern.