Multiple Disks

I. Motivation:

   A. Reliability: Stave off data loss due to disk failure

   B. Performance: Write to multiple disks in parallel

II. Reliability

   A. More disks: Lower mean time to failure

      1. Adding disks increases the probability that one will fail

   B. Prevent n-disk failure from causing data loss

      1. Write n+1 times
      2. Assumes failures are independent
         a) Not necessarily true, ie, disks from same fabrication run will have
            the same defect 
      3. This is essentially just mirroring

III. Performance

   A. Create a virtual disk of many individual disks

   B. Higher bandwidth reads

   C. Linear speedup in data you can read

      1. Doesn't help seeks
      2. Does help bandwidth

   D. Striping

      1. Byte level: Stripe at byte granularity
         _____            _____
        (_____)          (_____)    <-- (Disk drive)
      1 |_    |        2 |_    |
        |     |          |     |
      3 |_    |        4 |_    |
        |     |          |     |
        |_____|          |_____|          

      2. Block level: Stripe at block granularity
         _____            _____
        (_____)          (_____)
        |__   |          |__   |
      1 |__|  |        2 |__|  |
        |__   |          |__   |
      3 |__|  |        4 |__|  |
        |_____|          |_____|          

    
      3. Comparison between byte and block level striping
         a) Byte is better if accessing < 1 block, as a block-level wouldn't 
            help much
         b) Block is better if > 1 block, because it can serve different 
            requests at once

      4. With striping, a failure in *any* disk means a failure in *all* disks

IV. RAID: Redundant Array of Independent (old def: Inexpensive) Disks
   
   A. RAID Level ~= Configuration

   B. RAID 0: Basic Striping
      1. Not reliable
      2. Fast
         _____            _____             _____           
        (_____)          (_____)           (_____)     
     d1 |_    |       d2 |_    |        d3 |_    |
        |     |          |     |           |     |
     d4 |_    |       d5 |_    |        d6 |_    |
        |     |          |     |           |     |
        |_____|          |_____|           |_____|                   

   C. RAID 1: Simple Mirroring
      1. Increased reliability
      2. No speedup

         _____            _____
        (_____)          (_____)
        |__   |          |__   |
     d1 |__|  |       d1 |__|  |
        |__   |          |__   |
     d2 |__|  |       d2 |__|  |
        |_____|          |_____|          



   D. RAID 2: Byte-Level Striping

      1. Use (7, 4) Hamming Code
      2. 4 disks worth of data requires 3 disks of parity data 
      3. 7 disks total
      4. Can survive any 1 disk failure
      5. 75% overhead.
      6. Never used

         Data Disks:
               _____            _____          _____            _____
              (_____)          (_____)        (_____)          (_____)
              |__   |          |__   |        |__   |          |__   |
           a1 |__|  |       a2 |__|  |     a3 |__|  |       a4 |__|  |
      (byte1) |_____|          |_____|        |_____|          |_____|          

         Parity Disks:
               _____            _____          _____
              (_____)          (_____)        (_____)
              |__   |          |__   |        |__   |
           ap |__|  |       aq |__|  |     ar |__|  |
              |_____|          |_____|        |_____|


   E. RAID 3: Byte Level Striping with Parity
      1. One extra disk for parity
      2. Intuition: The disk controller tells you when you read a disk sector
         if it is invalid.  So if a disk fails, you know which disk it is that
         failed.
      3. Simple example: Assume each disk holds one bit:

         ___          ___          ___          ___          ___ 
        |   |        |   |        |   |        |   |        |   |
        | A1|        | A2|        | A3|  ...   |A10|        | Ap| <-- Parity
        |___|        |___|        |___|        |___|        |___|

   Holds: 1            0            1            0            1   <-- Parity

        If we know that it was A2 that failed, then we can reconstruct the 
        contents of A2

        Extrapolate example to a whole disk containing parity for each
        corresponding byte.

      4. Low overhead, fast
      5. Slower than RAID 1 because it has to calculate parity at each write
  
   F. RAID 4: Same as RAID 3 but with block level striping

      1. Advantages: 
         a) Better than RAID 3 because can serve requests in parallel
         b) One disk is involved in each access

      2. Disadvantages:
         a) If a write is smaller than a block, still have to recalculate a
            whole parity block
         b) Parity disk is accessed at every access
            - Parity disk will wear out faster
            - Bottleneck waiting for parity disk

   G. RAID 5: Spread data across multiple disks
      
      1. Block level striping
      2. Distributed parity blocks
      3. Only supports a single disk failure
         a) Window of vulnerability
            - Manually replace disk
            - Rebuild new disk
            - If a second failure occurs during Window of Vulnerability, we
              lose everything
            - Research shows that rebuild process can actually cause another
              disk to fail!
               _____            _____          _____
              (_____)          (_____)        (_____)
              |__   |          |__   |        |__   |
           a1 |__|  |       a2 |__|  |     ap |__|  |
              |__   |          |__   |        |__   |
           b1 |__|  |       bp |__|  |     b2 |__|  |
              |__   |          |__   |        |__   |
           cp |__|  |       c1 |__|  |     c2 |__|  |
              |_____|          |_____|        |_____|

   
   H. RAID 6: RAID 5 with Two "Parity" disks
      1. Call them Ap and Aq - Reed-Solomon codes
      2. Parity disks store different data
      3. Two disk failures do not cause data loss

   I. RAID 1+0: Mirrored and Striped

   J. Hot Spare
      A. Helps with Window of Vulnerability problem
      B. Keep a spare disk live and connected, but don't use it to store data
      C. Window decreased because do not need to manually add a disk
      D. Auto-start rebuild process on failure

   K. Scalability
      A. Ease of scalability depends on RAID configuration
      B. Something to consider when designing a RAID setup