# Transactions: Definition. Transactional properties of DBS. Transactions: Management in DBS. Transactions: Read/Write Model

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2 Concurrent transactions: Schedule TA 1 = r1[x], r1[y], w1[y], r1[z], w1[x], c1 TA 2 = r2[y], r2[z], w2[y], r2[x], w2[x], r2[s], c2 Schedule: r1[x], r2[y], r2[z], w2[y], r2[x], r1[y], w2[x], w1[y], r1[z], r2[s], c2, w1[x], c1 No schedule: r1[x], r2[y], r1[y], w2[y], w1[y], r1[z], r2[z], r2[x], w2[x], c2, w1[x], c Serial schedule The execution of the TAs one after the other, in an arbitrary order, is called a serial execution TA 1 = r1[x], r1[y], w1[y], r1[z], w1[x], c1 TA 2 = r2[y], r2[z], w2[y], r2[x], w2[x], r2[s], c2 T1 then T2: r1[x], r1[y], w1[y], r1[z], w1[x], c1, r2[y], r2[z], w2[y],r2[x], w2[x], r2[s], c2 T2 then T1 : r2[y], r2[z], w2[y], r2[x], w2[x], r2[s], c2, r1[x], r1[y], w1[y], r1[z], w1[x], c Correctness criterion for schedules: Serializability A schedule S of a transaction set T is called serializable, if it is equivalent to a serial execution of T Serializable schedules are defined as correct Equivalence of schedules 1. Resultequivalence: Equivalent if same result on database not really useful, used in some books 2. Conflictequivalence: Equivalent if same same order of conflict operations typically applied 12.9 Conflicts: Lost update, dirty read, nonrepeatable read, phantoms Only if different transactions operate on the same object and at least one is a write operation Possible conflicts between two TAs No conflict: r1[x], r2[x] Possible: r1[x], w2[x] Possible: w1[x], r2[x] Possible: w1[x], w2[x] Conflict pairs: Pairs of conflicting operations in different TAs on the same data object Example: r1[x], r2[y], w1[x], w1[y], w2[y], c1, c Conflicting operations op i [x] and op j [y] are in conflict, if x = y i!= j op = w or op = w Conflict relation Ordered conflict relation C of a schedule S: C(S) = {(op, op ) op and op conflicting operations, op < S op in S} Example: C(S) = {(r2[y], w1[y]), (w1[y], w2[y])} Conflictserializable schedules Same conflict pairs as some serial schedule Same order of conflict pairs as in some serial schedule A Schedule S of a transaction set T is conflictserializable if it has the same conflict relation as some serial execution SER of T: C(S) = C(SER) S: r1[x], r2[x], r1[y], r2[z], w2[y], w2[x], c2, c1 C(S): {(r1[x], w2[x]), (r1[y], w2[y])} SER: r1[x], r1[y], c1, r2[x], r2[z], w2[y], w2[x], c2,

3 Example S: r 1 [x], r 2 [x], r 1 [y], r 2 [z], w 2 [y], w 2 [x], w 1 [y], r 1 [z], c 2, w 1 [x], c 1 C(S) = { (r1[x], w2[x]), (r2[x], w1[x]), (r1[y], w2[y] ), (w2[y], w1[y]), (w2[x], w1[x]) } Not conflictserializable Requires T1 before T2 in a serial schedule Requires T2 before T1 in a serial schedule Conflict Graph (Precedence or dependency graph) Directed graph Shows conflicts between transactions Nodes: transactions of S Arc TA i TA j : conflicting pair (op i [x], op j [x] ) C(S) = { (r1[x], w2[x]), (r2[x], w1[x]), (r1[y], w2[y] ), (w2[y], w1[y]), (w2[x], w1[x]) } T1 x,y x,y T Concurrent transactions: Serializability Theorem Serializability Theorem: A schedule S is conflict serializable, if and only if its conflict graph does not contain a cycle S: r1[y], r3[u], r2[u], w1[y], w2[x], w1[x], w2[z], w3[x], c1, c2, c3 C(S): {(w2[x], w1[x]), (w2[x], w3[x]), (w1[x], w3[x])} SER: r2[u], w2[x], w2[z], c2, r1[y], w1[y], w1[x], c1, r3[u], w3[x], c3 T1 T3 Serializable T Intuitive correctness idea: Determine "conflictequivalent serial schedule from graph Exchange operations in S without switching conflict pairs Proof: " " The nodes of a connected directed graph without cycles can be sorted topologically: a < S b iff there is a path from a to b in the graph. Results in a serial schedule if nonconflicting TAs are added arbitrarily. " " Suppose there is a cycle TA i TA j in the graph. Then there are conflicting pairs (p i,q j ) and (q j ',p i '), No serial schedule will contain both (p i,q j ) and (q j ',p i '). Induction over length of cycle proves the "only if" Concurrent transactions: Scheduling Conflict serializability sometimes too restrictive S: w1[y], w2[x], r2[y], w2[y], w1[x], w3[x], c1, c2, c3 C(S1) = {(w1[y],r2[y]), (w1[y],w2[y]), (w2[x], w1[x]), (w2[x],w3[x]), (w1[x], w3[x])} But effect of S is the same as from the serial Schedule: T1, T2, T3! T1 T3 T Serializability Theoretical model which defines correctness of executions Often not implemented No realtime scheduling control Goal: effective realtime scheduling of operations with guaranteed serializability of resulting execution sequence TA 1 TA n Transaction manager Controls transactions Scheduler Controls execution of DB calls

4 Concurrent transactions: Scheduling Concurrency control: Locking Concurrency control in DBS methods which schedule the operations of different TAs in a way which guarantees serializability Principle concurrency control methods Locking (most important) Optimistic concurrency control Time stamps Transactions not known in advance Locking: Access on data only if TA has lock on data Transactions request and release locks Scheduler allows or defers operations based on lock table Implicit locking by scheduler Explicit locking in application programs error prone additionally allowed for in most DBS Not considered here: transaction independent locking, e.g. page lock while writing Concurrency control: Locking Concurrency control: Lock Protocols Locking is pessimistic: Assumption: during operation op[x] of a (potentially) conflicting operation op'[x] of will access object x Avoid by locking x before accessing x Lock protocols Simplistic Preclaiming Two Phase Locking (2PL) Strict 2PL Simplistic Lock each object before writing Unlock afterwards schedule will not be serializable T1: r1[x], w1[x], c1 T2: r2[x], w2[x], c2 lock1(x), r1[x], unlock1(x), lock2(x), r2[x], unlock2(x), lock1(x), w1[x], unlock1(x), lock2(x), w2[x], unlock2(x) Concurrency control: Lock Protocols Concurrency control: Lock Protocols 2PL Preclaiming Acquire all locks TA needs before performing an operation Release locks if TAs does not get all try again Execute transaction Release locks Lock acquisition phase # locks Begin TA End TA Problems: Racing situation Objects to access may not be known in advance Not used in DBS Work phase time Two phase locking (2PL) 1. Lock each object accessed by TA before usage 2. Respect existing locks of other TAs 3. No TA requests lock which it already holds: if T holds a read lock for x, it will not request a write lock for x 4. No lock after unlock: No lock is requested by a TA, after a lock has been released by same TA 5. Locks are released at least at commit time # locks Begin TA Lock acquisition phase Release phase time End TA Important method

5 Concurrency control: Lock Protocols 2PL Concurrency control: Lock Protocols 2PL Locked objects accessible in lock acquisition phase Rule 3 is essential (see "select... for update") Example: Example: rlock1(x), r1[x], x=x*10, rlock2(x), r2[x], x:=x1, wlock1(x), w1[x], unlock1(x), wlock2(x), w2[x], unlock2(x) Lock after unlock may result in a lost update Rule 4 is essential lock1(x), r1[x], x=x*10, unlock1(x), lock2(x), r2[x], x:=x1, w2[x], unlock2(x), lock1(x), w1(x), unlock1(x) Phase locking theorem If all transactions follow the 2phase locking protocol, the resulting schedule is serializable Proof sketch: Suppose a resulting schedule is not serializable after 2PL conflict graph contains a cycle TA 1 and TA 2 with conflict pairs (p 1,q 2 ) and (q 2 ', p 1 ') p 1,q 2 access the same object x, and q 2 ', p 2 ' an object y (assuming a cycle of length 1, induction for the general case) Let e.g. (p 1,q 2 ) = (r1[x], w2[x]), (q 1 ', p 2 ') = (w2[y], w1[y]) Analyze all possible sequences of execution Concurrency control: Lock Protocols 2PL Concurrency control: Lock Protocols 2PL Proof sketch (continued) Analyze <p 1, q 2, q 2 ', p 1 > Analyze <p 1, q 2 ', q 2, p 1 > Analyze <q 2 ', p 1, p 1 ', q 2 > Analyze <q 2 ', p 1 ', p 1, q 2 > Analyze <q 2 ', p 1, q 2, p 1 > T2: Lock y, T1: Lock x, T2: Lock x, T1: Lock y T1 must have released lock on x and acquired one on y (or T2 must have acquired after release) Hurts 2phase rule! Contradiction to assumption. Similar argumentation for the other possible sequences Theorem Serializability does not imply 2PL serializable schedule not resulting from a 2PL scheduler Cascading abort: Possible access of to object x which was unlocked by in release phase if aborts, used wrong state of x to be aborted by the system # locks Begin TA Release phase abort time May happen recursively: cascading abort Concurrency control: Lock Protocols S2PL Concurrency control: Lock Protocol S2PL Strict 2phase locking Prevents cascading abort Release all locks at commit point # locks Begin TA Lock acquisition phase Release all locks at commit End TA time S: r1[x], r2[y], w1[x], w1[y], w2[y], c1, c2 Lock(x) Lock(y)? Lock(y) w[y] c1 Unlock(x) Unlock(y) Lock(y) w[y] c2 Unlock(y)

7 Concurrency control: Lock Modes Concurrency control: Locking granularity Increment locks Useful for TAs incrementing or decrementing stored values Examples: Money transfer, ticket selling, Commutative increment actions Noncommutative to read or write Equivalent schedules: S: r1[x], r2[x], inc2[y], inc1[y], c1, c2 S: r1[x], inc1[y], r2[x], inc2[y], c1, c2 S: r1[x], r2[x], inc1[y], inc2[y], c1, c2 requester S X I holder S X I Single lock granularity insufficient Overhead: many record locks vs. one table lock Phantoms: not prevented by record locks Granularities: Tuple, page, block, relation, At least two lock granularities in most DBS Problem: TA requests lock on table R Some rows of R locked by different TAs Lock conflict: TA ing for release of all record locks Danger of starvation of TA Concurrency control: Hierarchical locking Concurrency control: Hierarchical locking Object hierarchy: Record Block B1 Record Relation R1 Intention locks Intention to request lock For each lock mode: e.g., IS and IX Block B2... Locking: Start at root of hierarchy Before right element place intention locks At the right element in hierarchy request lock Lock situation: IS, IX signal locks deeper in hierarchy Element locks lock all subordinate elements in hierarchy Goal: Lock on block B1 Warning on upper elements (Intention lock on relation R) Locks on block and records in B1 lock Record lock lock Block B1 Record! Relation R1 Block B Concurrency control: Hierarchical locking Concurrency control: Deadlocks Advantage: one lookup to check if lock on higher level can be granted Compatibility of locks: Exclusive lock not compatible Intended exclusive only compatible to intention locks requester holder IS IX IS IX S X Lock escalation Convert many locks on level i into one lock on level i1 Only for locks by single TA Efficiency reasons (large locktables) S X Lock conflict TA s for lock held by other TA Conflict solved when TA finished and lock released Deadlocks inherent to 2PL Deadlock: at least two pairing conflicts Releasing lock would break Rule 4 Keeping lock would lead to deadlock Resolving deadlocks Cycle check in Waitsforgraph Timeout

9 Concurrency control: Optimistic Concurrency control: Optimistic Optimistic concurrency control Locks are expensive, Conflict solving hopefully is cheaper Several types (backward, forward, ) Backward oriented concurrency control (BOCC) Idea: TAs work on copies, check for conflicts at the end, commit (or abort) BOT Read phase: Copy data to private workspace Execute operations on copy Validation phase: resolve conflicts EOT Commit phase: write data into DB BOCC Implementation ReadSet R(TA) = data set read by TA in read phase WriteSet W(TA) = data set changed during read phase Assumption: W(T) R(T) TA3 w[z] Commit or rollback of T2? EOT w[y] EOT x,y R(T2) z W(T1) x,y W(T3) Concurrency control: Optimistic Concurrency control: Optimistic BOCC Validation for TA: for all transactions (TA') which committed after BOT(T) : if R(TA) W(TA') = then T.commit else T.abort TA3 w[z] EOT w[y] EOT R(T2) W(T3) abort x,y R(T2) z W(T1) x,y W(T3) Could result in unnecessary aborts Fast and atomic commit processing Fast validation Only one TA can validate at a time Useful in situation with few expected conflicts Concurrency control: Timestamps Concurrency control: Timestamps Optimistic concurrency control based on timestamps Each TA timestamp assigned Idea: record timestamps of TA last access on element, compare order of timestamps with transaction schedule For each database element x RT(x): timestamp of youngest TA that read x WT(x): timestamp of youngest TA that wrote x C(x): commit bit, true if lastwriting TA has committed Goal: synchronize TAs such that resulting schedule is equivalent to serial schedule according to timestamp order Scheduler actions Grant request Abort TA, restart TA with new timestamp Delay TA Scheduling TA for reading: If ts(ta) < WT(x): abort TA If ts(ta) >= WT(x): read and RT(x):= max(ts(ta), RT(x)) Scheduling TA for writing: If ts(ta) < RT(x): abort TA If ts(ta) < WT(x): abort TA Else: write and WT(x):= ts(ta) and RT(x):= ts(ta)

10 Concurrency control: Timestamps Concurrency control: Multiversion timestamps Access on object x delayed until TA committed Timestamp method: resulting schedule equivalent serial schedule in timestamp order Older TAs aborted and restarted Younger TAs succeed 2PL: resulting schedule equivalent serial schedule in commit order Requesting TAs have to until commit of other TAs Allows reads that would otherwise cause aborts Hold multiple versions of an object The latest consistent version (in DB) The updated, but not committed version (as copy) TA3 access would have to abort since ts() < WT(x)=ts(TA3) Multiversion: give access to copy of older state Concurrency control: Deadlock resolving Transactions and Concurrency: Short summary Oracle: Variant of Multiversioning Table and row level locks Deadlock detection: sforgraph in central systems Deadlock detection: Timeout in distributed environment (cycles hard to detect) User influence: lock modes MySQL: Multiversioning and twophase locking Table and row level locks Deadlock detection: sfor graph Spaceefficient lock table: lock escalation not needed User influence: set priority of statement types ACID properties of transactions Schedules: Serial, (conflict) serializable Correctness of schedules: Serializability theorem Locking: Preclaiming, 2PL, strict 2PL, lock modes Optimistic concurrency control Timestampmethods Serializability Cascading rollback Deadlocks Detection (Waitsforgraph) Avoidance (Waitsforgraph, Wait/Die, Wound/Wait)

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