lecture08-disk-array-systems.md

Lecture 8 Disk Array Systems

Reconstructing Failed Drive Data

Reliability of Disk Arrays with No Repair

• $MTBF = \frac{\Sigma{t_{down}-t_{up}}}{Number of failures}$
• $MTBF_{MDS} = \frac{\Sigma{t_{down}-t_{up}}}{Number of failures}$
• Striped array of N disks
  • $MTBF_{striped-array} = MTBF_{drive} / N$
• Stripped+Mirrored array of N+N disks
  • $MTBF_{striped-mirrored-array} = MTBF_{pair} / N$
  • $MTBF_{pair} = (MTBF_{drive}/2) + MTBF_{drive} = 1.5 * MTBF_{drive}$
• 4N data disks and N parity disks
  • $MTBF_{p-array} = MTBF_{stripe} / N$
  • $MTBF_{stripe} = (MTBF_{stripe}/5) + (MTBF_{drive}/4) = 0.45 * MTBF_{drive}$

Disk Rebuild and Disk Sparsing

• Goal: restore array redundancy after a failure
• After first failure, data still available for degraded access
• Second failure would result in data loss
• Trade-off: reliability vs. performance

Reliability of Disk Arrays with Rebuild

• Mean Time To Rebuild (MTTR)
  • No data loss if repair completes before 2nd failure
• Mean Time To Data Loss (MTTDL)
  • Canonical way: solve Markov model of array states
• There is a huge difference between MTTR between with/without rebuild

Three Modes of Operation

• Normal mode
  • everything working; maximum efficiency
• Degraded mode
  • some disk unavailable
  • must use degraded mode operations
• Rebuild mode
  • reconstructing lost disk's contents onto space
  • degraded mode operations plus competition with rebuild