The assignment should be turned in before class on Monday.

- (25
*pts.*) Consider a disk with the following characteristics:- There are seven platters, each of which has two surfaces.
- There are 5000 tracks per surface.
- Each track stores (on average) 102400 bytes of data.
- A sector contains 512 bytes.
- The gaps occupy 7% of a track.
- The disk platters rotate at 10400RPM.
- It takes 0.8ms to start or stop the head assembly, and 1ms to travel every 600 cylinders once the assembly is moving.

Answer the following questions:

- How many sectors are there on a track? What is the capacity of each surface? What is the capacity of the disk?
- How many cylinders does the disk have?
- What is the maximum rotational latency?
- Assuming that only 1 track can be read at a time, what is the maximum throughput of the drive? What if an entire cylinder can be read at once?
- What is the worst case seek time? What is the average seek time?

- (20
*pts.*) For this problem, use the drive described in problem 1 and assume that blocks are 4096 bytes.Answer the following questions:

- What is the worst case time to read 1 block? What is the best case time? What is the average time?
- Repeat part 1 but assume we want to read 4 contiguous blocks.
- What is the worst case time to write 1 block? What is the best case time? What is the average time? Assume that we want to verify the block has been written correctly.
- What is the worst case time to modify 1 block? What is the best case time? What is the average time? Assume
that we want to verify the block has been written correctly.

- (15
*pts.*) Suppose we are using RAID level 6 as shown in Figure 2.16. Further, suppose that sector 0 of the four data disks contains the following:**Disk #****Sector 0 Value**1

1100001011

2

0110111001

3

1000010111

4

1011011001

Answer the following two questions:

- What will be the value of sector 0 in redundant disks 5,6, and 7?
- If data disk 3 and redundant disk 7 fail, what are the steps to restore them? Show the step by step results
for sector 0 in each replaced disk.

- (15 pts.) Consider the stable storage algorithm as described in section 2.5.3. Suppose that there is a sector
X that is very rarely written (i.e. it is a sector that stores schema information for a mature database application).
Our concern is that if X
_{R}decays before X_{L}, when X_{L}finally decays we will have completely lost the sector. Consider changing the book's algorithm to alternatively read X_{R}and X_{L}instead of always reading X_{L}. Will this address our concern? Does it introduce any new problems?