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Let us rst consider reliability The chance that some disk out of a set of N disks will fail is much higher than the chance that a speci c single disk will fail Suppose that the mean time to failure of a disk is 100,000 hours, or slightly over 11 years Then, the mean time to failure of some disk in an array of 100 disks will be 100,000 / 100 = 1000 hours, or around 42 days, which is not long at all! If we store only one copy of the data, then each disk failure will result in loss of a signi cant amount of data (as discussed in Section 1121) Such a high rate of data loss is unacceptable The solution to the problem of reliability is to introduce redundancy; that is, we store extra information that is not needed normally, but that can be used in the event of failure of a disk to rebuild the lost information Thus, even if a disk fails, data are not lost, so the effective mean time to failure is increased, provided that we count only failures that lead to loss of data or to nonavailability of data The simplest (but most expensive) approach to introducing redundancy is to duplicate every disk This technique is called mirroring (or, sometimes, shadowing) A logical disk then consists of two physical disks, and every write is carried out on both disks If one of the disks fails, the data can be read from the other Data will be lost only if the second disk fails before the rst failed disk is repaired The mean time to failure (where failure is the loss of data) of a mirrored disk depends on the mean time to failure of the individual disks, as well as on the mean time to repair, which is the time it takes (on an average) to replace a failed disk and to restore the data on it Suppose that the failures of the two disks are independent; that is, there is no connection between the failure of one disk and the failure of the other Then, if the mean time to failure of a single disk is 100,000 hours, and the mean time to repair is 10 hours, then the mean time to data loss of a mirrored disk system is 1000002 /(2 10) = 500 106 hours, or 57,000 years! (We do not go into the derivations here; references in the bibliographical notes provide the details).

13

The McGraw Hill Companies, 2001

11

CHAPTER 13:

You should be aware that the assumption of independence of disk failures is not valid Power failures, and natural disasters such as earthquakes, res, and oods, may result in damage to both disks at the same time As disks age, the probability of failure increases, increasing the chance that a second disk will fail while the rst is being repaired In spite of all these considerations, however, mirrored-disk systems offer much higher reliability than do single-disk systems Mirrored-disk systems with mean time to data loss of about 500,000 to 1,000,000 hours, or 55 to 110 years, are available today Power failures are a particular source of concern, since they occur far more frequently than do natural disasters Power failures are not a concern if there is no data transfer to disk in progress when they occur However, even with mirroring of disks, if writes are in progress to the same block in both disks, and power fails before both blocks are fully written, the two blocks can be in an inconsistent state The solution to this problem is to write one copy rst, then the next, so that one of the two copies is always consistent Some extra actions are required when we restart after a power failure, to recover from incomplete writes This matter is examined in Exercise 114

Fig 3-6 The circuit shown here is equivalent to the circuit shown in Fig 3-5

The McGraw Hill Companies, 2001

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