# DB2 - lesson 02
#### Paraboschi
##### 12 October 2015
## Concurrency Control
### Advantages of Concurrency
Modern computers are capable of executing different processes in a concurrent way,
Concurrency is also important in DBMS because it allows multiple Transactions at the same time
ex: Two students enroll contemporarily on the Politecnico site.
Concurrency is made by
- time sharing on a single processor
- or sharing the processes on multiple CPU cores.
### Concurrenct executions
A problem may rise when we heve two or more concurrent operations modifying the same data.
Tens, hundredss, thousands of transactions per second cannot be executed serially
Concurrency need to be controlled to avoid anomalies.
### Types of concurrency
b(Tx) = begin transaction x
e(Tx) = end transaction x
- __serial__ b(T1) e(T1) b(T2) e(T2)
- or b(T2) e(T2) b(T1) e(T1)
- __interleaved__ b(T1) b(T2) e(T1) e(T2)
- __nested__ b(T1) b(T2) e(T2) e(T1)
### Problems due to concurrency
Given these two transactions:
>T1: UPDATE account
SET balance = balance + 3
WHERE client = 'Smith'
>T2: UPDATE account
SET balance = balance + 3
WHERE client = 'Smith'
#### Execution with lost UPDATE
As the name states, one or more changes to the data are lost.
The error is produced by:
- R1 R2 W1 W2
- R1 R2 W2 W1
> D=100
T1: R(D,V1)
V1 = V1 + 3
T2: R(D,V2)
V2 = V2 + 6
T1: W(V1,D)
T2: W(V2,D)
D=103
D=106!
#### Dirty read
The read of the second transaction happen before the rollback of T1,
therefore a wrong value is used for T2.
- R1 W1 R2 abort1 W2
> D=100
T1: R(D,V1)
T1: V1 = V1 + 3
T1: W(V1,D) D=103
T2: R(D,V2)
T1: ROLLBACK
T2: V2 = V2 + 6
T2: W(V2,D) D=109!
#### Nonrepeatable read
The first read (to V1) and the second read (to V3) of the same value D give different results because D is changed in the meantime.
- R1 R2 W2 R1
>D=100
T1: R(D,V1)
T2: R(D,V2)
T2: V2 = V2 + 6
T2: W(V2,D) D=106
T1: R(D,V3) V3<>V1!
#### Ghost update
T1 reads X and Y, T2 writes Y and Z, T1 has still the old value of Y.
- R1 R1 R2 R2 W2 W2 R1
> X+Y+Z=100, X=50, Y=30, Z=20
T1: R(X,V1), R(Y,V2)
T2: R(Y,V3), R(Z,V4)
T2: V3 = V3 + 10, V4=V4-10
T2: W(V3,Y), W(V4,Z) (Y=40, Z=10)
T1: R(Z,V5) (for T1, V1+V2+V5=90!)
#### Phantom insert
This anomaly is due to the insertion of a "phantom" tuple that satisfies the conditions of a previous query.
- R1 W2 (new data) R1
>T1: C=AVG(B:A=1)
T2: Insert (A=1,B=2)
T1: C=AVG(B: A=1)
### Schedule
Sequence of input/output operations performed by concurrent transactions.
es:
>S1: r1(x) r2(z) w1(x) w2
r1,w1
$r_1,w_1\in T_1$
$r_2,w_2\in T_2$
#### Principles of Concurrent Control
- __Goal__: to reject schedules that cause anomalies
- __Scheduler__: component that accepts or rejects the operations requested by the transactions
- __Serial schedule__: the actions of each transaction occur in contiguous sequences
- __Serializable schedule__: Produces the same results as some serial schedule on the same transactions (by *schedule equivalence*)
- The class of acceptable schedules produced by a scheduler depends on the cost of equivalence checking, because scheduling must happen in real-time and the more is optimized my sheduling the more computational power I will need to obtain it.
### CSR and VSR
$CSR\subset VSR$
#### View-serializability
###### NOTE: what is a read-from operation?
- $r_i(x)$ *reads-from* $w_j(x)$ in a schedule S when $w_j(x)$ precedes $r_i(x)$ in S and there is no $w_k(x)$ between $r_i(x)$ and $w_j(x)$ in S
- $w_j(x)$ is a *final write* if it is the last write on x that occurs in S
Two schedules are __view-equivalent__ $S_i {\approx}_v S_j$ if they have the same reads-from relations and the same final writes.
A schedule is __view-serializable__ if it is equivalent to a serial schedule.
__VSR__ is the set of *view-serializable* schedules.
#### VSR
defines the schedules which are:
- serializable
- anomaly-free
But is vast and costly to evaluate
#### CSR
Is a subset of VSR solutions, used because it contains costs.
##### Example of View-serializability
```
S3: w0(x) r2(x) r1(x) w2(x) w2(z)
S4: w0(X) r1(x) r2(x) w2(x) w2(z)
S5: w0(x) r1(x) w1(x) r2(x) w1(z)
S6: w0(x) r1(x) w1(x) w1(z) r2(z)
```
In this example S3 is view serializable to S4 because both schedules have the following properties:
- r2(x) reads from w0(x)
- r1(x) reads from w0(x)
- w2(z) is the final write
Meanwhile S5 and S6 are view serializable because in both schedules:
- r1(x) reads from w0(x)
- r2(x) reads from w1(x)
- w1(z) is the final write
##### Another Example
```
S7: r1(x) r2(x) w1(x) w2(x)
S8: r1(X) r2(x) w2(x) r1(x)
S9: r1(x) r1(y) r2(z) r2(y) w2(y) w2(z) r1(z)
```
- S7 correspond to a lost update
- S8 correspond to a non repeatable read
- S9 correspond to a ghost update
- They are all non view serializable
##### Complexity
Deciding view-equivalence of two given schedules can be done in polynomial time
Deciding View-serializability of a generic schedule is a NP-complete problem
#### CSR
An action ai is conflicting with aj (i!=j) if both are operations on common data and at least one of them is a write operation.
- read-write conflicts (rw, wr)
- write-write conflicts (ww)
Two schedules are conflict-equivalent if they contain the same operations and all conflicting operation pair occur in the same order.
One schedule is conflict-serializable if it is conflict-equivalent to a serial schedule.
CSR is the set of conflict-equivalent schedules.
##### CSR and VSR
Every conflict-serializable schedule is also view-serializable, but the converse is not necessarily true
In order to prove that $\;CSR\subset VSR\;$ we have to prove that conflict-equivalence implies view-equivalence.
Let S1 and S2 be two conflict-equivalent schedules:
- They have the same final writes, if they didn't, there would be at least two writes with a different order
- They have the same reads-from relations, if they didn't, there would be at least one read-write pair with a different order
So this implies that S1 and S2 are also view-equivalent.
#### Testing conflict-serializability
It is done with a conflict graph that has:
- One node for each transaction Ti
- One arc from Ti to Tj if it exists at least one conflict between an action of Ti and an action of Tj such as ai precedes aj.
A schedule is in CSR iff its conflict graph is acyclic.