NT/PV Model for Long Duration Transaction Systems

1
NT/PV Model for Long Duration Transaction Systems

• Theoretical aspects of concurrency control in
  long-duration transaction systems
• It is based on the following ideas
• nested transactions
• predicate constraints
• multiple version of database states

Reference Formal Aspects of Concurrency
Control in Long-Duration Transaction Systems
Using the NT/PV Model, H.F. Korth and G.
Speegle, ACM TODS Vol 19, No. 3, Pages 492-535,
1994
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Problems

• Traditional transactions
• short, a fraction of a section
• simple
• New applications
• office information systems
• work flow systems
• web-based information systems
• Long-duration transaction systems
• human-interaction
• last very long, hours or days

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Intuitions

• Nested transactions
• a sub-transaction is a collection of database
  access operations ( usually read and write )
  which the rest of transaction views as a single
  operation.
• All the operations in a sub-transaction must be
  executed or none at all
• some operations in a subtransaction may also be a
  sub-transaction of the next lower level
• Nested transaction hierarchy
• leaves are read/write operations
• nonleaf nodes are subtransactions
• root models the execution of the entire system

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Example
Consider a round trip from Austin to Rochester
Trip
Rochester --gt Austin
R-gtC C-gt D D -gt A
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• Criteria for correctness
• Serializability
• A transaction transform the database from one
  consistent state to another consistent state
• the initial empty database is consistent
• execute one transaction at a time
• the final result is thus consistent
• Predicate constraint
• use predicate logic to specify the consistent
  constraints
• each transaction has
• precondition
• postcondition
• it is acceptable if one sub-transaction
  invalidate the consistency constrains but another
  will then restore it
• a transaction can access to an inconsistent state
  only if its precondition accepts it

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• Multiple Versions
• multiple versions of data items can be utilized
  to achieve greater concurrency
• overhead for keeping multiple versions
• mechanisms to determine which version to be read

We hope these mechanisms will help up to
increase concurrency
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Formal Models

• The standard transaction model
• E the set of all data items in the database
• dom(e) the domain of data item e for all e in E
• unique state S a database state with one value
  for all e in E
• D the set of all unique states
• P(D) assume P is a predicate specifying the
  database consistency constraint, P(D) is the set
  of all unique states which satisfy P.
• a transaction t can be represented as a function
• t(P(D) to P(D)

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The NT/PV Model

• A database state S is a set of unique states
• D denotes the set of all database states.
• Given a database state S, a version state Vs is a
  set of unique states which can be generated from
  S.
• A database with two items, each with two
  versions, would have four unique database states
  in the version state.
• A transaction is defined as a mapping from one
  database state to another database state
• a mapping form an element of a version state to a
  unique state

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• A predicate on a database state is satisfied if
  any element in the version state satisfies it.
• A transaction can be specified by two predicates
  I and O such that for any database state S, if S
  is in I(D) ( S satisfied I) then t(S) is in O(D)
  ( t(S) satisfied O).
• Implementation of a transaction t is a pair (T,
  P), where T is a set of transactions or
  operations, and P is a partial order on T.
• this models the nested transactions.

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Definition 1

• A transaction t is defined as a four-tuple
  
  (T, P, I, O)
• where (T, P) is the implementation and (I, O) is
  the specification of t

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Definition 2

• An execution of a transaction T (T, P, I, O) is
  a pair of (R, X), where R is a relation on T x T
  such that
• R is compatible with respect to P, i.e., if Ti lt
  Tj in P, then Tj lt/ Ti in R
• X is a mapping from T to a version state v such
  that if Tk is in T then X(Tk) is the input state
  of Tk.
• X is used to specify which version is used as the
  input for Tk
• The execution of a transaction system T specifies
  
• the order in which all sub-transactions are
  executed
• which version will be used as the input for each
  sub-transactions

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Definition 3

• An execution (R, X) of a transaction
  t (T, P, I, O) is an NT/PV-correct
  execution if
• the last sub-transaction Tf in the execution
  order satisfies O, and
• for each other transaction Ti, X(Ti) satisfied
  the I.

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Example
Consider the transaction Austin --gtRochester
Precondition Greg is not flying anywhere at
the departure time Postcondition Greg has a
series flight from A to R, and
the connecting time gt 30 minutes A-gtR
( T, P, I, O ) where T A-gtD, D -gt C,
C-gt R P an empty set I
Precondition O Postcondition
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Reservation 1
Incorrect because Gregs Flight left Dallas too
soon
Incorrect because the flights are not even
connected
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Standard Transaction
Definition 4 A transaction t (T, P, I, O) is
a standard transaction if (1) T is a
set of READ and WRITE operations (2)
P is a total order on T, (3) I O
All transactions preserve the consistency
A standard transaction is thus defined as a
sequence of database operations and its
operations preserves the consistency
Definition 5 A transaction t ( T, P, I, O )
is a standard transaction set if (1)
every Ti in T is a standard transaction,
(2) P is empty, and (3) I O
true
A standard transaction set is just a set of
standard transactions.
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• Given a transaction (T, P, I, O), and an
  execution (R, X).
• R is a standard relation on T if the order of
  steps within a transaction is preserved in R
• A schedule of a standard transaction set is
  specified by a standard relation R.
• A conflict relation R on T is defined as a
  relation characterizing the conflict pair of
  operators. That is,
• Ti lt Tj if Read(Ti, A) before Write(Tj, A)
  in R, where Read and Write denotes a pair of
  conflict operations
• An execution (R, X) for (T, P, I, O) is conflict
  serializable if and only if R is acyclic.

Theorem An execution (R, X) for (T, P, I, O) is
conflict serializable if and only if R is
acyclic
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A Protocol for NT/PV-Correct Execution

• Version Predicate Correct (VPC) protocol
• Leaf Transaction Execution

Lock Held
Lock Requeste
Lock Compatibility Matrix
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State transition for leaf transactions
Init
Check
Block
Execute
Commit
Abort
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The Protocol

• Init a leaf transaction enters Init when its
  prarent transaction submits a begin transaction
  operation
• specifies I and O
• request Rv ( read for validation) locks
• goto Block or Check, depending on Rv locks
• Block waiting for Rv or Read locks
• waiting is short
• after waiting is over, enter
• Init if it is waiting for Rv
• Execute if it is waiting for Read,
• Check if forced by another transaction

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The Protocol (continued)

• Check to find a correct set of versions to read,
  and it will
• enter Eexcute if this set of versions is found
• ramains in Check if the set cannot be found
• abort in some cases
• Execute
• a write request is always granted and the write
  lock released as soon as possible
• it may cause inconsistency and thus leads to
  re-evaluation
• a read request is granted based on the
  compatibility matrix
• the transaction enters Block if the write lock is
  held by others

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The Protocol (continued)

• Commit
• A transaction may commit if it finishes all its
  steps and releases all its locks
• Abort
• it has to rollback all its operations
• Leaf termination
• only sibling transactions may see the results of
  a transaction even after it commits
• a committed transaction has to abort if its
  parent aborts

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Non-Leaf Transactions

• The transition graph is a subset of that of leaf
  transactions
• the only operation is start subtransactions
• it inherits all read set of it subtransactions
• the transaction cannot precede committed
  subtransactions
• Reeval of a non-leaf transaction will reassign
  the versions to its lower level transactions
  which may cause them to be re-evaluated or even
  aborted.

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Main Results

• The VPC protocol allows only NT/PV-correct
  executions