wolfgang miller / 02.07.2009 / 1 concurrency controll algorithms concurrency control algorithms...

Wolfgang Miller / 02.07.2009 / 1

Concurrency Controll Algorithms

Concurrency Control Algorithms

Chapter 4



Overview

I. Introductiono Basics

II. Locking schedulerso Two-Phase Locking

• Non-Two-Phase Locking Protocols

o Write-Only Tree Locking

o Read/Write Tree Locking

III. Non-locking schedulers

o Timestamp Ordering

IV. Optimistic schedulerso BOCC



Overview

I. Introduction Basics

II. Locking schedulerso Two-Phase Locking









CSR – Class of conflict-serializable schedules

Definition: Conflict Equivalence

Schedules s and s‘ are conflict equivalent (denoted s c s‘), if: op(s) = op(s‘) and conf(s) = conf(s‘).

Definition: Conflicts and Conflict RelationsLet s be a schedule, t, t‘ trans(s), t t‘.

(i) Two data operations p t and q t‘ are in conflict in s ifthey access the same data item and at least one of them is a write. i.e.,(p = r(x) ˄ q = w(x)) ˅ (p = w(x) ˄ q = r(x)) ˅ (p = w(x) ˄ q = w(x))

(ii) {(p, q)} | p, q are in conflict and p occurs before q in s} is the conflict relation of s.



CSR – Class of conflict-serializable schedules

Definition: Conflict Serializability:

Schedule s is conflict serializable if there is a serial schedule s‘ such that s c s‘.CSR denotes the class of all conflict serializable schedules.

Example:

s1 = r1(x) r2(x) r1(z) w1(x) w2(y) r3(z) w3(y) c1 c2 w3(z) c3 CSR

s2 = r2(x) w2(x) r1(x) r1(y) r2(y) w2(y) c1 c2 CSR

t2 writes on x before t 1 read x



Scheduler Actions and Transaction States

Definition: CSR SafetyFor a scheduler S, Gen(S) denotes the set of all schedules that S can generate. A scheduler is called CSR safe if Gen(S) CSR

All of the following algorithms are CSR safe



Scheduler Classification

Schedulers can be classified as pessimistic or optimistic:

optimistic Schedulers:

- also called „aggressiv“, because they mostly let steps pass and rarely block. This bears the danger of „getting stuck“ eventually when the serializability of the output can no longer be guaranteed

pessimistic Schedulers:

- also called „conservative“, because they mostly block, in extreme, albeit unlikely case, the output could become a serial schedule, if all transactions but one were blocked.



Scheduler Classification – Algorithms Overview



Overview

I. Introduction basics

II. Locking schedulersTwo-Phase Locking









Locking Schedulers

In a nuthsell this means that if a transaction holds a lock on a specific data item, this item is not available to other, concurrent transactions

The Idea behind locking schedules is to synchronize access to shared data by using locks.

lock notation:

rl(x) read lock xwl(x) write lock xru(x) write unlock xwu(x) write unlock x

compatibility of locks:



Rules for well-formed locking

LR1:If ti contains a step of the form ri (x)[wi (x)], then the schedule s also contains a step of the form rli (x)[wli (x)] before the data operation. Moreover s contains a step of the form rui (x)[wui (x)] somewhere after the operation.

LR2:For each x accessed by ti, schedule s has at most one rli (x) and at most one wli (x) step.

locks of the same type are set at most once per transaction and per data item.LR3:No step of the form rui (.) or wui (.) is redundant (i.e., executed per transaction more than once)

LR4:If x is held locked by both ti and tj for ti, tj trans(s), i ≠ j, then these locks are not in conflict (i.e., they are compatible)



Two-Phase Locking (2PL) - Definition

Definition: Two-Phase Locking

A locking protocol is two-phase if for every output s and every transaction ti trans(s) is true that no qli step follows the first oui step (o ,q {r, w}).

A locking protocol is two-phase if for every transaction a phase during which locks are set is distinguished from and strictly followed by a phase during which locks are released.



Two-Phase Locking (2PL) - Example

2PL Example :s = w1(x) r2(x) w1(y) w1(z) r3(z) c1 w2(y) w3(y) c2 w3(z) c3

wl1(x) w1(x) wl1(y) w1(y) wl1(z) w1(z) wu1(x) rl2(x) r2(x) wu1(y) wu1(z) c1

rl3(z) r3(z) wl2(y) w2(y) wu2(y) ru2(x) c2 wl3(y) w3(y) wl3(z) w3(z) wu3(z) wu3(y) c3

A 2PL output could be:



Overview




Write-Only Tree Locking

Read/Write Tree Locking




V. Hybrid Schedulers



Non-Two-Phase Locking Protocols

The following two tree-based protocols are geared for transactions that exhibit treelike access patterns . In other cases they are susceptible to degradation.

The data items are viewed as nodes of a tree and accesses have to follow a path down the tree.

On the next slides we will have a look at those two tree-based locking schedulers:

Write-Only Tree Locking Read/Write Tree Locking



Write-Only Tree Locking (WTL)

Note:the tree is a virtual data organization only, the relationship between the data items can be quite different

Under the write-only tree locking protocol, lock requests and releasesmust obey the locking rules LR1-LR4 and the following two rules on the next slide:

The Write-Only Tree Locking protocol uses a tree to organize the data items. In its model read operations are missing, they wouldcause problems we will see later.

Thus a transaction can only write data (or read and write are applied to the same item as collapsed into one operation) .




WTL1:If x is any node in the tree other than the root, wli (x) can be set only if ti currently holds a write lock on y, where y is parent of x

WTL2:After a wui (x), no further wli (x) is allowed (on the same data item x)

Example:

if a transaction t = w(c)w(e) wants to acquire wl(c) or wl(e) it has to hold wl(b)




Sample Transaction under the WTL protocol:

transaction t = w(d)w(i)w(k)

wl(a)wl(b)wu(a)wl(d)wl(e)wu(b)w(d)wu(d)wl(i)wu(e)w(i)wl(k)wu(i)w(k)wu(k)



Read/Write Tree Locking (RWTL)

The Read/Write Tree Locking is a generalization of the Write-Only Tree Locking protocol.

Unlike the the Write-Only Tree Locking protocol it supports seperate read operations, too.




Problem: ti locks root before tj does, but tj passes ti within a “read zone”

Example: rl1(a) rl1(b) r1(a) r1(b) wl1(a) w1(a) wl1(b) ul1(a) rl2(a) r2(a) w1(b) rl1(e) ul1(b) rl2(b) r2(b) ul2(a) rl2(e) rl2(i) ul2(b) r2(e) r1(e) r2(i) wl2(i) w2(i) wl2(k) ul2(e) ul2(i) rl1(i) ul1(e) r1(i) ...

Solution: formalize “read zone” and enforce two-phase property on “read zones”.This zones are called pitfall.

appears to follow TL rules but CSR




Definition: Read-Write Tree Locking

Under the RWTL lock requests and releases must obey LR1 - LR4, WTL1, WTL2, and the two-phase property within each pitfall.

Definition: pitfallFor transaction t with read set RS(t) and write set WS(t) let C1, ..., Cm be the connected components of RS(t).

A pitfall of t is a set of the form Ci {x WS(t) | x is a child or parent of some y Ci}.




Example:transaction t with RS(t) = {f, i, g} and WS(t) = {c, l, j, k, o}

has pitfalls pf1={c, f, i, l, j} and pf2={g, c, k}.



Overview







Timestamp Ordering





Nonlocking Schedulers

The next two protocols are alternatives to locking schedulers.They guarantee safety of their output without using locks.

The first one is the Basic Time Stamp Ordering, which counts tothe pessimistic protocols and with the BOCC protocol we will alsosee an optimistic scheduler



Timestamp Ordering (TO)

Timestamp Ordering Rule (TO rule):Each transaction ti is assigned a unique timestamp ts(ti) (e.g., the time of ti‘s beginning).

If pi(x) and qj(x) are in conflict, then the following must hold:

pi(x) is executed before qj(x) iff ts(ti) < ts(tj).

Timestamp Ordering protocols get rid of locks and use timestamps instead.



Basic Timestamp Odering (BTO)

Basic timestamp ordering protocol (BTO):

For each data item x maintain • max-r-scheduled(x): the value of the largest timestamp of a read operation on x

already sent to the scheduler• max-w-scheduled(x): the value of the largest timestamp of a write operation on

x already sent to the scheduler

Operation pi(x) is compared to max-q (x) for each conflicting q:

• if ts(ti) < max-q (x) for some q then abort ti

• else schedule pi(x) for execution and set max-p (x) to ts(ti)



Basic Timestamp Ordering (BTO)

BTO Example:s = r1(x) w2(x) r3(y) w2(y) c2 w3(z) c3 r1(z) c1

r1(x) w2(x) r3(y) a2 w3(z) c3 a1



Scheduler Classification – Algorithms Overview



Overview







Timestamp Ordering

IV. Optimistic schedulers BOCC




Optimistic Protocols

In some scenarios optmistic protocols can do a better job then pessimistic.

A product catalog application where 99% of the transactions are just read price information and descriptions of products. From time to time prices are updated or new products are added, but this occurs with a very low frequency compared to the read events.

A 2PL protocol for example would waste a considerable amount of time for managing locks, instead of reading data items.

optimistic schedulers do a good job in cases were conflicts aren‘t frequent



The three phases of a optimistic scheduler

1. Read phase:The transaction is executed, but all writes applied to a workspace private to the transaction only (not the database)

2. Validation phase:The scheduler tests if its execution has been „correct“ in the sense of conflict serializability and whether the result can be copied to database – if not the transaction is aborted, otherwise the next phase is entered

3. Write phase:The workspace contents are transferred into the database to conclude the transaction



BOCC

BOCC validation of tj:compare tj to all previously committed ti

accept tj if one of the following holds• ti has ended before tj has started, or• RS(tj) WS(ti) = and ti has validated before tj

Under backward-oriented optimistic concurrency control (BOCC),a transaction under validation executes a conflict test against all those transactions that are already committed.



BOCC

Example:Execution of BOCC



Overview

I. Introduction Basics






Timestamp Ordering

IV. Optimistic schedulers BOCC



Thank you for your attention.

Any questions?

wolfgang miller / 02.07.2009 / 1 concurrency controll algorithms concurrency control algorithms...

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