D64 Assignment #1

Due Monday, January 24, 2000 at 4:00pm.

The assignment should be turned in before class on Monday.

Problem Set

1. (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:

   1. How many sectors are there on a track? What is the capacity of each surface? What is the capacity of the disk?
   2. How many cylinders does the disk have?
   3. What is the maximum rotational latency?
   4. 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?
   5. What is the worst case seek time? What is the average seek time?

2. (20 pts.) For this problem, use the drive described in problem 1 and assume that blocks are 4096 bytes.

   Answer the following questions:

   1. What is the worst case time to read 1 block? What is the best case time? What is the average time?
   2. Repeat part 1 but assume we want to read 4 contiguous blocks.
   3. 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.
   4. 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.

3. (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:

   1. What will be the value of sector 0 in redundant disks 5,6, and 7?
   2. 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.

4. (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?