Parity Declustering for Continous Operation in Redundant Disk Arrays

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Parity Declustering for Continous Operation in
Redundant Disk Arrays

• Mark Holland, Garth A. Gibson

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Purpose of Parity Declustering

• Parity Declustering is designed to balance
  cost against data reliability and performance
  during failure recovery.
• It improves on standard parity organizations
  by reducing the additional load on surviving
  disks during the reconstruction of a failed
  disks contents. And it yields higher user
  throughput during recovery, and/or shorter
  recovery time.

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Declustered Parity Layout

• RAID is a special case of declustered Parity
  Layout, in RAID GC

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Definition of some terms

• Data unit is the minimum amount of contiguous
  user data allocated to one disk before any data
  is allocated to any other disk.
• Parity unit is a block of parity information that
  is the size of a data stripe unit.
• Parity stripe is the set of data units over
  which a parity unit is computed, plus the parity
  unit itself.
• e.g. An S in the layout is either a data unit or
  parity unit.
• Four Ss together is called parity stripe.

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Example declustered layout

• Di,j represents one of the four data units in
  parity stripe number i,and Pi represents the
  parity unit for parity stripe i.
• Declustering ratio is defined as a(G-1)/(C-1).
  It indicates the fraction of each surviving disk
  that must be read during the reconstruction of a
  failed disk.
• For example, D1.0, D1.1, D1.2, P1 together is a
  parity stripe.
• So G4 , C 5, a 75
• In RAID5, a 100

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Data layout strategy

• How to layout data in parity declustered disk
  arrays?
• Our goals
• Single failure correcting No two stripe units in
  the same parity stripe may reside on the same
  physical disk.
• 2. Distributed reconstructionWhen any disk
  fails, its user workload should be evenly
  distributed across all other disks in the array.
• 3. Distributed parity Parity information should
  be evenly distributed across the array.
• Efficient mappingThe function mapping a file
  systems logical block address to physical disk
  addresses is efficient.
• Large write optimization Dont need 4 access
  operation.
• Maximal parallelism Read of contiguous data can
  have max parallelism.

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Layout strategy

• The distributed reconstrucition criterion
  requires that the same number of unites be read
  from each surviving disk during the
  reconstruction of a failed disk. This will be
  achieved if the number of times that a pair of
  disks contain stripe units from the same parity
  stripe is constant across all pairs of disks.Such
  layout can be implemented by balanced incomplete
  block design.
• A block design is an arrangment of v distinct
  objects into b tuples, each containing k
  elements, such that each object appears in
  exactly r tuples, and each pair of objects
  appears in exactly ?p tuples.

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Complete block design

• Its simpler than incomplete block design.
• A block design is called a complete block design
  which includes all combinations of exactly k
  distinct elements selected from the set of v
  objects. The number of these combinations is
  .

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Example complete block design

• In this example, we arrange 5 distinct
  objects(numbers) into 5 tuples, such that each
  object appears in exactly 4 tuples, and each pair
  of objects appears in exactly 3 tuples.
• e.g. number 0 appears in 4 tuples,
• (0,1) appears in tuple 0, 1, 2.
• (1,4) appears in tuple 1,2,4.
• Its complete because it includes all
  combinations of exactly 4 distinct elements
  selected from the set of 5 elements.

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Layout with complete block design

• Tuple 00,1,2,3
• Tuple 10,1,2,4
• Tuple 20,1,3,4
• Tuple 30,2,3,4
• Tuple 41,2,3,4

• If we associates disks with objects(numbers) and
  parity stripes with tuples. We get
• Although its complete, it violates the design
  goals 3. It doesnt distributed parity evenly.
  Parity on disk 4 is the bottleneck for write
  operation.

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• We duplicate previous layout G times, assigning
  parity to a different element of each tuple in
  each duplication, then we get above full block
  design table.

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Problem with full block design

• The size of the block design table may be very
  large. So its not guaranteed that the layout
  will have an efficient mapping. But its required
  by our fourth criterion.
• Our fifth and sixth criteria depend on the data
  mapping function used by higher levels of
  software.
• Large-write opimization is guaranteed.
• But parallel read cannot achieve maximal
  parallelism.
• Thats, not all sets of five adjacent data
  units from the mapping, D0.0, D0.1, D0.2, D1.0,
  D1.1, D1.2, D2.0 etc., are allocated on five
  different disks. Reading five adjacent data units
  starting at data unit 0 causes disk 0 and 1 to be
  used twice, and disk3 and 4 not at all.

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Problem with full block design

• In addition, in the case the number of disks in
  an array( C ) is large relative to the number of
  stripe units in a parity stripe( G), the full
  block design cannot be implemented.
• e.g. a 41 disk array with 20 parity overhead(G
  5) allocated by a complete block design will
  have about 3,750,000 tuples. It cannot be
  implemented, because even large disks rarely have
  more than a few million sectors.

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Balanced Incomplete block design

• Our goal is to find a small block design on C
  objects with a tuple size of G. Hall presents a
  list containing a large number of known block
  designs, and states that , within the bounds of
  this list, a solution is given in every case
  where one is known to exit
• Sometimes a balanced incomplete block design with
  the required parameters may not be known, we
  resort to choosing the closest feasible design
  point thats the point which yield a value of a
  closest to what is desired.

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Balanced Incomplete block design

• We can choose the closest feasible design point
  from the subset of Halls list of design.

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Average reponse time

• These two figure show that, except for writes
  with a 0.1, fault-free performance is
  essentially independent of parity declustering.

• It may lead to slightly better average response
  time in the degraded rather than fault-free
  mode.(A user write may induces only one write
  access)

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Reconstruction Performance

• Higher user performance during recovery compared
  to RAID 5.
• Simplest Reconstruction involves a single sweep
  through the contents of a failed disk. For each
  stripe unit on a replacement disk, the
  reconstruction process reads all other stripe
  units in the corresponding parity stripe and
  computes an exclusive-or on these units. The
  resulting unit is then written to the replacement
  disk.
• The time needed to entirely repair a failed disk
  is equal to the time needed to replace it in the
  array plus the time needed to reconstruct its
  entire contents and store them on the
  replacement.
• Continuous-operation system require data
  availability during reconstruction.

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Four reconstruction algorithm

• Minial-update algorithm No extra work is sent
  whenever possible user writes are folded into the
  parity unit, and neither reconstruction
  optimization is enabled
• User-writes algorithmAll user writes explicitly
  targeted at the replacement disk are sent
  directly to the replacement.
• Redirection of readsuser accesses to data that
  has already been reconstructed are serviced by
  (redirected to ) the replacement disk, rather
  than invoking on-the-fly reconstruction as they
  would if the data were not yet available.
• Piggybacking of writesUser reads that cause
  on-the-fly reconstruction also cause the
  reconstructed data to be written to the
  replacement disk. This is targeted at speeding
  reconstruction.
• (Redirection of reads and Piggybacking of
  writes are proposed by Muntz and Lui.)

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Comparison of four algorithm

• The testing result showed that Muntz and Luis
  redirection of reads and redirectpiggyback dont
  consistently decrease reconstruction time
  relative to the simpler algorithm.
• The reason is that loading the replacement disk
  with random work penalizes the reconstruction
  writes to this disk more than off-loading
  benefits the surviving disks unless the surviving
  disks are highly utilized.
• Even a small amount of random load imposed on the
  replacement disk may greatly increase its average
  access times because reconstruction writes are
  sequential and dont require long seeks.

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Conclusion

• We demonstrated
• Parity declustering, a strategy for allocating
  parity in a single-failure-correcting redundant
  disk array that trades increased parity overhead
  for reduced user-performance degradation during
  on-line failure recovery, can be effectively
  implemented in array-controlling software.
• Using block design to map parity stripes onto a
  disk array insures that both the parity update
  load and the on-line reconstruction load is
  balanced over all disks in the array.

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Questions

• 1.Whats parity declustering?
• 2. Whats the data layout goals?
• 3. Whats the disadvantage of complete block
  design?