1 controlled concurrency now we start looking at what kind of concurrency we should allow we first...

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Controlled concurrency

• Now we start looking at what kind of concurrency we should allow

• We first look at uncontrolled concurrency and see what happens– We look at 3 bad examples– We then look at how we can understand whether

concurrency is OK or not.• Then we look at how to control concurrency

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FIGURE 21.3 (a) : The lost update problem.This occurs when two transactions that access the same database items have their operations interleaved in a way that makes the value of some database item incorrect.

• Eg: X = 20, Y = 15, M = 2, N = 3

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FIGURE 21.3 (b) The temporary update (dirty read) problem.When one transaction updates a database item and then the transaction fails : the updated item is accessed by another transaction before it is changed back to its original value

• Here issues of concurrency and recovery

Eg:

X = 20

Y = 15

M = 2

N = 3

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FIGURE 21.3 (c) The incorrect summary problem.If one T is calculating an aggregate summary function on a number of records while another T id updating some of these records, the aggregate function may calculate some values before they are updated and others after they are updated.

Eg: A = 2, N = 3, X = 10, Y = 8

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Serial Schedules• Serial schedule: A schedule S is serial if, for

every transaction T in the schedule, all operations of T are executed consecutively in S– i.e. all of one T has to finish before another T starts– Eg: T2 T1 T3 is serial

• Otherwise, the schedule is called nonserial or interleaved schedule

• S1 = r1(x), w1(x), r2(x), r2(y) : serial: T1 T2

• S2 = r1(x), r2(x), w1(x), r2(y) : interleaved

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Concurrency• How to deal with problems of inconsistency of

data because of concurrency?– Like in the 3 examples we saw earlier

• Only allow serial execution. Problem?• Wasteful:T1 is doing I/O, T2 is forced to wait• Solution: Allow controlled concurrency

– Allow when no conflict– Don’t allow when conflict

• Now we see how to do “controlled concurrency”

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Concurrency Eg– Figure

21.5

• Which of C, D should be allowed?

• Eg: – X= 50

– M = 10

– N = 5

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Different serial schedules• Will 2 diff. serial schedules always give same results ?• No – diff. serial schedules can give diff. results. Eg:

– T1 = r(x), r(y), x = x + y, w(x) – T2 = r(x), r(y), y = x + y, w(y)– x = 20, y = 30– Serial schedule T1T2 : final values of X, Y?– Serial schedule T2T1 : final values of X, Y?

• Any serial execution is OK: why?• o/w we should not allow concurrency at all.• Eg: Suppose T1T2 OK, but T2T1 not OK:

– All of T1has to happen before all of T2

– Makes no sense to talk about T1 and T2 executing concurrently

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Serializability• Implication for concurrent execution?• Want concurrent schedule equivalent to some

serial schedule• Serializable: A schedule S is serializable if it is

equivalent to some serial schedule.• Intuition behind serializability: since any serial

execution OK– allow interleaved execution as long as result will be

same as some serial execution.• Eg: Fig. 17.5 D OK (equivalent to A), C not OK

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Serializability: Result Equivalency• We said schedule S is serializable if it is

equivalent to some serial schedule. – What does “equivalent” mean ?

• Check if concurrent schedule produces the same result as a serial schedule. How ?

• First approach: pick some data values, try.• Result equivalent: Two schedules are result

equivalent if they produce same final state on some data– Is this idea OK?– Saw it with Fig 17.5 Eg

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Serializability: Result Equivalency• Problem: could have happened by accident i.e.

on the data we happened to look at, get the same result but not generally true

• Eg: Look at Fig 17.5 again– Any values of X, M, N which will make C produce

same result as A (or B) ?• When M = 0

– But C should not be allowed• Want stronger guarantee. How ?• Important ops should be in same order as serial

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Conflicting Operations• Order of some pairs of ops are important to

consider for concurrency/recovery, others not.• Two operations are in conflict: When ?• 1. Belong to different transactions. Why?• Within T1 can’t switch: Eg: w1(y), r1 (x) • 2. Access the same data item. Why?• If diff. data, then doesn’t matter:

– w1(x), w2 (y) same as w2(y), w1 (x)

• 3. One of them is a write op. . Why?• r1(x),r2 (x) same as r2(x),r1(x): data unchanged

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Complete Schedules• Complete Schedule : S of T1, T2, … Tn

1. Exactly same ops in S and T1, T2, … Tn

2. Includes abort/commit for each Ti

3. If op1 before op2 in Ti then same order in S

4. For any pair of conflicting operations, one must occur before other in S

– We can leave out internal operations

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Serializability: Conflict Equivalent• Eg: S: r1(x), r2(y), w1(y), w1(x), w2(x)• What are the conflict pairs ?• (r1(x), w2(x))

• (w1(x), w2(x))

• (r2(y), w1(y))• Conflict Equivalent: Two schedules are conflict

equivalent if the order of any two conflicting operations is the same– i.e. have the same conflict pairs

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Serializability: Conflict Equivalent• Eg: T1 = r1(x), w1(y), T2 = r2(y), w2(x)

– S1 = r1(x), r2(y), w2(x), w1(y)– S2 = r2(y), w2(x), r1(x), w1(y)– Are S1, S2 conflict equivalent ?

– are conflict pairs the same ?• What are the conflict pairs of S1• (r1(x), w2(x)), (r2(y), w1(y))• What are the conflict pairs of S2• (w2(x)), r1(x)), (r2(y), w1(y))• Different pairs: not conflict equivalent

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Serializability: Conflict Equivalent• Eg: S3 = r1(x), r2(y), w1(y), w2(x)

S4 = r2(y), r1(x), w1(y), w2(x )• Are S3, S4 conflict equivalent ?

– are conflict pairs the same ?• What are the conflict pairs of S3• (r1(x), w2(x)), (r2(y), w1(y))

• What are the conflict pairs of S4• (r1(x), w2(x)), (r2(y), w1(y))

• Same pairs : are conflict equivalent

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Serializability Eg– Figure

21.5

• Which of C, D should be allowed?

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Serializability: Conflict Equivalency• S is conflict serializable if it is conflict equivalent to

some serial schedule S’• Figure 17.5 : A (T1T2) is serial, so is B (T2T1)• Is D conflict serializable

– D’s conflict pairs equivalent to those of A or B?• Conflict pair of A, B, D ?• A: (r1(x), w2(x)), (w1(x), r2(x)), (w1(x), w2(x))• B: (r2(x), w1(x)), (w2(x), r1(x)), (w2(x),w1(x)) • D: (r1(x), w2(x)), (w1(x), r2(x)), (w1(x), w2(x))• Is C conflict serializable. Conflict pairs ?• C: (r1(x), w2(x)), (w1(x), w2(x)), (r2(x), w1(x))• C not equivalent to A: r2(x) before w1(x)• C not equivalent to B: w1(x) before w2(x)

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Serializability• Serializable not the same as serial.

– What is the difference ?• Serial means no interleaving: T1 T2 T3 etc• Serializable allows interleaving, but has to be

equivalent to a serial schedule • Serializable schedule :

– Will leave the database in a consistent state. – Interleaving is controlled and will result in the same

state as if the transactions were serially executed,– Will achieve efficiency due to concurrent execution.

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Testing For Conflict SerializabilityTesting for conflict serializability Algorithm 17.1: 1. Looks at only read_Item (X) and write_Item (X)

operations : not the internal ops2. Constructs a precedence graph (serialization graph)

- a graph with directed edges 3. An edge is created from Ti to Tj if one of the

operations in Ti appears before a conflicting operation in Tj

4. The schedule is serializable if and only if the precedence graph has no cycles.

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Figure 21.5: draw

precedence graphs

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FIGURE 21.7: precedence graph for Figure 21.5 • Constructing precedence graphs for schedules from Figure 17.5 to test for

conflict serializability. Precedence graphs for (a) serial schedule A. (b) serial schedule B. (c) schedule C (not serializable). (d) schedule D (serializable, equivalent to schedule A).

• How do we interpret the cycles ?

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FIGURE 21.8 (a). • Another example of serializability testing. (a) The

READ and WRITE operations of three transactions T1, T2, and T3.

• We will look at schedules in next 2 slides– And draw the precedence graphs

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FIGURE 21.8 (b). • Schedule E.

– Precedence graph ? Serializable ?

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FIGURE 21.8 (c). • Schedule F.

– Precedence graph ? Serializable ?

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Serializability• Issue: OS controls how ops get interleaved :

– Resulting schedule may or may not be serializable– Problem ?

• If not serializable, then what?• Have to rollback. Problem?• Expensive – not practical! How to solve?• Guarantee serializability. How ?• Locks:

– Current approach used in most DBMSs: • Two phase locking: will study

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View Serializability• We have seen result equivalent and conflict equivalent.• View equivalent: another condition. [RG] eg:

• Schedule S2 is serial• Schedule S1: R1(A), W2(A), W1(A), W3(A). Is this

conflict serializable?• No – precedence graph has a cycle.

– T1 → T2 → T1• Do you think S1 should be allowed ?

Schedule S1:T1: R(A) W(A)T2: W(A)T3: W(A)

Schedule S2:T1: R(A),W(A)T2: W(A)T3: W(A)

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View Serializability• S1 is equivalent (in every situation) to serial

S2 i.e. T1,T2,T3. Why?• Because final value of A written by T3

– This is a blind write so does not matter whether T1, T2 were in serial order or interleaved

• Stronger than result equivalent, weaker than conflict equivalent

• View equivalent: we won’t do formal defn.• View serializability good enough

– but expensive to test (NP-hard)– so use conflict serializability since easier to test

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Other Notions of SerializabilityOther Types of Equivalence of Schedules • Under special semantic constraints

– schedules that are otherwise not conflict serializable may work correctly.

– [SKS Eg] in next slide

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[SKS] Example• A is checking account

• B is savings account

• T1 transferring 50$ from A to B

• T5 transferring 10$ from B to A

• Is this schedule conflict serializable?

• No. Also not view serializable– Though we have not studied definition.

• Should this schedule be allowed ?• Yes : Eg: A = 100, B = 30. In general, OK. Why?• D: debit, C: credit. D D C C same as D C D C

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Recoverability vs Serializability• Both affected by concurrent execution of

transactions, but the two are quite different• Recoverability : How to recover if transaction

aborts or system crashes• Serializability : Even if no system crashes and

all transactions commit– Have to make sure we get correct results

• Equivalent to serial schedule

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Serializability Tests• DBMS has to provide a mechanism to ensure that

schedules are conflict serializable • We have seen how to test a schedule to see if it is (was)

serializable. – How can this be used?

• We could run the transactions without attempting to control concurrency. Then what ?

• Test to see if the schedule which resulted was serializable. If serializable, then what ?

• Everything OK. If not serializable, then what ?• Rollback. Problem ?• Expensive. Alternative ?

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Concurrency Control vs. Serializability Tests

• Develop concurrency control protocols that only allow concurrent schedules which we want– Serializable– Recoverable, cascadeless .

• Connection between concurrency control protocols and serializability tests ?

• Tests for serializability help us understand why a concurrency control protocol is correct– i.e. why protocol guarantees serializability.