Problem 2. (20 points)Consider a database buffer manager that uses 1GB of main memory and keeps data on a hard drive which reads 100MB per second and takes 10 milliseconds per disk seek.

(a) (10 points) Assume that (1) the size of each disk block is 10KB and (2) for each block kept in the buffer, the probability that the buffer manager can handle the next data request using that block (i.e., the probability that the block contains the requested data) is 5*10^6 . In this case, calculate the expected data access time (i.e., how much time the buffer manager on average would spend to provide a requested disk block). For this calculation, assume that (1) the buffer manager runs the algorithm explained in Section 13.5.1 of the textbook, (2) the buffer is already full (i.e., the entirety of the 1GB buffer space is already used to hold 105 disk blocks), and (3) no disk blocks are updated (i.e., no need to write dirty blocks back to the hard drive). Also, ignore the time spent for reading/writing data in the main memory.

(b) (10 points) Assume that (1) the size of each disk block is 100KB and (2) for each block kept in the buffer, the probability that the buffer manager can handle the next data request using that block (i.e., the probability that the block contains the requested data) is 10^5 . Calculate the expected data access time as in (a). Also, based on the above calculations, explain whether it is more advantageous to use 10KB disk blocks or 100KB disk blocks.