clocks and global state.ppt

8/19/2019 Clocks and Global State.ppt

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1

Synchronization & clocks



2

Synchronization

Synchronization: coordination of actionsbetween processes.

Processes are usually asynchronous,

(operate without regard to events in otherprocesses)

Sometimes need to cooperatesynchronize

!or mutual e"clusion !or event ordering (was message " from

process P sent before or after message y fromprocess #$)



3

Synchronization in centralized systems isprimarily accomplished through sharedmemory

%vent ordering is clear because all events aretimed by the same cloc&

Synchronization in distributed systems isharder



4

Fundamental Limitations of aDistributed System

'istributed systems are assumed tohave no global cloc&

'istributed systems have no sharedmemory

hese limitations force us to be creativein solving the following fundamental

problems rdering events

*apturing a global state

%nsuring mutual e"clusion



5

Model

Distributed system model: n processes connected by a communications

networ&

imperfectly synchronized cloc&s, thus noe"act notion of +what time it is at otherprocesses

reliable message delivery

may or may not bound message deliverytime

no shared memory



6

Time in Distributed Systems

ime is an important and interesting issue indistributes systems. %"ample: e-commerce transaction timestamp for

auditing and accountability purposes. eed time for maintaining consistency of databases.

hree notions of time: ime seen by e"ternal observer: / global cloc& of

perfect accuracy ime seen on cloc&s of individual hosts: %ach has its

own cloc&, and cloc&s may drift out of sync 0ogical time: event a occurs before event b and this is

detectable because information about a may havereached b b is causally dependent on a


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Logical Time

/bstraction 'oesnt provide a cloc& in the sense of wall

cloc& time

!ocus is on definition of the +happens beforerelationship between events +*ould whats happening in this event have

been influenced by what happened in that event$

%vents are: message sends message receptions local events



8

Logical Clocks

bservation: if two processes (running onseparate processors) do not interact, it doesntmatter if their cloc&s are not synchronized.

bservation: 2hen processes do interact, theyare usually interested in event order , instead ofe"act event time.

3ence 0ogical cloc&s are sufficient for manyapplications



9

Logical Time: The Picture

a

c

e

d

p0

p1

p2

p3

a,b and a,c are concurrent

c happens after b

e happens after a, b, c, d

b



10

a!!ened"#efore $elation

he happened before relation ( ) captures thecausal relationships between events: a b if a and b are events in the same process

and a occurred before b

a b if a is the send event of a message m and b is the corresponding receive event

is a transitive relation %vent a potentially causally affects event b if a b %vent a is concurrent with event b if neither

a b nor b a



11

Three %m!ortant Schemes

0amports logical cloc&s cloc& is a single integer

4ector cloc&s cloc& is a vector of integers with length n n 5 number of processes

6atri" cloc&s cloc& is an n " n matri" of integers n 5 number of processes



12

Lam!orts Clocks

0amports cloc&s captures partialordering defined by the relation

0amports logical cloc&s: %ach process i maintains a counter Ci whose

current value is attached to each message sent

7nternal events in a process cause the counterCi to be incremented

2hen a message is received by a process i , Ci isset to ma"(m.Cj, Ci) + 1



13

3appened before relation: a -8 b : %vent a occurred before event b. %vents in

the same process.

a -8 b : 7f a is the event of sending a message min a process and b is the event of receipt of thesame message m by another process.

a -8 b, b -8 c, then a -8 c. +-8 is transitive.

*ausally rdered %vents a -8 b : %vent a +causally affects event b

*oncurrent %vents nly one is true: a -8 b (or) b -8 a (or) a 99 b.

Lam!orts Clock



14

S!ace"time Diagram

Time

Space P1

P2

e11 e12 e13 e14

e21 e22 e23 e24



15

Logical Clocks *onditions satisfied:

*i is cloc& in Process Pi.

7f a -8 b in process Pi, *i(a) *i(b)

a: sending message m in Pi; b : receiving message m in P<;then, *i(a) *<(b).

7mplementation =ules: R1: Ci = Ci + d (d > 0); cloc& is updated

between two successive events at a process.

R2: Cj = max(Cj, tm + d); (d > 0); 2hen P<receives a message m with a time stamp tm

(tm assigned by Pi, the sender; tm 5 *i(a), abeing the event of sending message m).



16

S!ace"time Diagram

Time

Space P1

P2

e11 e12 e13 e14

e21 e22 e23 e24

e15 e16 e17

e25

(1) (2) (3) (4) (5) (6) (7)

(1) (2) (3) (4) (7)



17

Limitation of Lam!ortsClock

Time

Space P1

P2

e11 e12 e13 e14

e21 e22 e23 e24

P3 e31 e32 e33



18

Limitation of Lam!orts Clock



19

Lam!orts Clocks: Total 'rder

defines a partial order rather than a totalorder

3ow to impose a total order$

>se process 7's to brea& ties 7mportant: otal order is +artificial--it has

nothing to do with the cloc& on the wall?



20

(ector Time

4ector time correctly captures the causalityrelationship between distributed events (capturesthe transitive closure of the relation)

%ach process i maintains a vector of state numbers

Si to &eep trac& of transitive dependencies amongprocesses [email protected]: is a +vector cloc& at process Pi whose

entries are the +assumedbest guess cloc& valuesof different processes.

Si@<A (< 8i) is the best guess of Pi for P<s cloc&. Si@iA contains the current state number for process

i; Si@nA, n ≠ i, contains the most recent statenumber of process n upon which i currently depends



22

(ector Time: The Picture

p0

p1

p2

p3

1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1 0 0 0

1 2 0 0 1 3 2 0 1 4 2 0

1 4 2 00 1 0 0

0 1 1 0

0 1 0 0

0 1 2 0

0 1 2 0

1 4 2 1



24

#irman"Schi!er"Ste!hensonProtocol

(i) o broadcast m from process i, increment *i(i),and timestamp m with 4m 5 *i@iA

(ii) 2hen < G i receives m, < delays delivery of muntil

1. * <@iA 5 4m@iA E1 andC. * <@&A H 4m@&A for all & G i

1. says m is the ne"t msg P < was e"pecting from Pi

C. says P < has seen all msgs seen by Pi when Pi sentm.'elayed messaged are Iueued in < sorted byvector time. *oncurrent messages are sorted byreceive time. 2hen m is delivered at <, * < isupdated according to vector cloc& rule



25

Causal Messageordering-contd.

" ot#er $ords, i% a messa&e m is re'eived%rom i, you s#ould also #ave re'eived every

messa&e t#at P i re'eived be%ore it set m;

e&,

if m is sent by P 1 and ts(m) is (J, K, L) and

you are P 3, you should already have received

e"actly C messages from P1 and at least K

from PC

if m is sent by PC and ts(m) is (K, M, 1, J)

and if you are PJ and 4*J is (J, J, K, J) then

you need to wait for a fourth message from

PC and at least one more message from P1.



26

P0

P1

P2

(1, 0, 0)

P1 received message m from P0 before sending

messagem*

to P2; P2 must wait for delivery ofm

before receiving m*

(ncrement own cloc! only on message send)

"efore sending or receiving any messages, one#s

own cloc! is (0, 0, $0)

%&2

(1, 0, 0) (1, 1, 0)

(1, 1, 0)%&1

m

m'

%&0

%&2

nforcing &ausal &ommunication

%&0

(1, 1, 0)

(0, 0, 0)%&2



27

(ector Time: Com!arison

4ector timestamps are compared in thefollowing manner:– TSi ! TS" i#

∀ k, TSi[k] ≤ TS"[k] and k, TSi[k] ! TS"[k].

eg @ (J,J,M) (J,K,M) A

– $n event e causa%%& de'ends on an evente) i#

e).TS ! e.TS

– Two events e and e) are concurrent

i* neither e).TS ! e.TS nor e.TS ! e).TS

∃



29

Matri/ Clocks

6otivation 6y vector cloc& describes what 7 +see

7n some applications, 7 also want to &now what other people see

6atri" cloc&: %ach event has n vector cloc&s, one for each process

he i th vector on process i is called process i s principle vector i.e. its own vector cloc& as before



30

Matri/ Time

7n a system of matri" cloc&s, the time is representedby a set of n N n matrices of non-negative integers.

/ process pi maintains a matri" mti @1..n, 1..nA where, mti*i , i denotes the local logical cloc& of pi and

trac&s the progress of the computation at processpi . mti*i , j denotes the latest &nowledge that process

pi has about the local logical cloc&,mt <@< , < A, of process p< .

mti*j , represents the &nowledge that process pihas about the latest &nowledge that p< has about thelocal logical cloc&, mt& @&, &A, of p&

he entire matri" mti denotes pi s local view of theglobal logical time.



31

Process pi uses the following rules =1 and =C to update itscloc&:

=1 : Oefore e"ecuting an event, process pi updates its locallogical time as follows:

mti*i , i := mti*i , i + d (d > 0)

=C: %ach message m is piggybac&ed with matri" time mt.2hen pi receives such a message (m,mt) from a process p<, pi e"ecutes the following seIuence of actions:

>pdate its global logical time as follows:

(a) 1 -= -= : mti *i , := max(mti*i , , mt*j , )

(hat is, update its row mti @i , A with the p< s row in thereceived timestamp,mt.)

(b) 1 -=,l -= : mti*, l:= max(mti*, l , mt*, l )

%"ecute =1. 'eliver message m.



32

.atri/ &loc! /amle

user1 (rocess1)

user2 (rocess2)

user3 (rocess3)

(1,0,0)

(0,0,0)

(0,0,0)

(0,0,0)

(0,1,0)

(0,0,0)

(0,0,0)

(0,0,0)

(0,0,1)

(2,0,0)

(0,0,0)

(0,0,0)

(3,0,0)

(0,0,0)

(0,0,0)

(0,0,0)

(0,0,0)

(0,0,2)

(0,0,0)

(0,2,2)

(0,0,2)

(2,0,0)

(2,3,2)

(0,0,2)

(2,0,0)

(2,3,2)

(2,3,3)



33

Pro!erty of matri/ clocks:

7f min& (mti@&, l A) H t

hen process pi &nows that every other process p&

&nows that pl s local time has progressed till t.

7f this is true, it is clear that process p i &nowsthat all other processes &now that pl will never

send information with a local time t.

7n many applications, this implies that processes

will no longer reIuire from pl certain informationand can use this fact to discard obsoleteinformation.



34

0hy the need for global staterecording,

2hen it is &nown that local computations havestopped and that there are no more messages intransit, the system has obviously entered a statein which no more progress will be made.

deadloc&ed$

correctly terminated$



35

1lobal state of a distributedsystem

/bsence of global cloc& leads to a problemin global state recording

2hat is global state$ 0ocal state of each process and

he state of communication channels i.e.

messages that are currently in transit(sent but not received)



36

1lobal State

$500 $200

AB

C1: Empty

C2: Empty

G!"a State 1

$450 $200

A B

C1: T# $50

C2: Empty

G!"a State 2

$450 $250

A B

C1: Empty

C2: Empty

G!"a State 3



37

o* to record the global state

'istributed snapshot reflects a state in which the distributed systemmight have been

reflects a consistent global state 7f we have recorded that process P has

received a msg from another process #, thenwe should also have recorded that process #had actually sent the msg

he reverse condition (# has sent a msg that Phas not yet received) is allowed.



38

Cut2

/ 'ut represents the last event that hasbeen recorded for each of severalprocesses.

/ll recorded msg receipts have a correspondingrecorded send event

/n inconsistent cut would have a receipt ofa msg but no corresponding send event



39

3/am!leProducer Consumer !roblem

p records its state

m

p



40

3/am!le

p

m



41

3/am!le

I records its state

p

m



42

3/am!leThe recorded state

m

p

m



43

0here did *e err,

2hat did we do$

p

m



44

3rror22

he sender has no record of the sending

he receiver has the record of the receipt

=esult Qlobal state has record of the receive event

but no send event violating the happenedbefore concept??



45

$ecording 1lobal State

Send(6i<): message 6 sent from Si to S<

rec(6i<): message 6 received by S<, from Si

time("): ime of event "

0Si: local state at Si send(6i<) is in 0Si iff (if and only if)

time(send(6i<)) time(0Si)

rec(6i<) is in 0S< iff time(rec(6i<)) time(0S<)

transit(0Si, 0S<) : set of messagessentrecorded at 0Si and receivedrecorded at 0S<



46

$ecording 1lobal State 4

inconsistent(0Si,0S<): set of messages sentrecorded at 0Si and receivedrecorded at0S<

Qlobal State, QS: D0S1, 0SC,R., 0SnF

*onsistent Qlobal State, QS 5 D0S1, ..0SnF/' for all i in n, inconsistent(0Si,0S<) is null.

ransitless global state, QS 5 D0S1,R,0SnF/' for all 7 in n, transit(0Si,0S<) is null.



47

$ecording 1lobal State 55

S1

S2

%1 %2&S1

&S2

%1: t'ait

%2: ic!itet



48

$ecording 1lobal State555

Strongly consistent global state: consistentand transitless, i.e., all send and thecorresponding receive events are recorded inall 0Si.

&S11

&S21

&S31

&S12

&S22 &S23

&S32 &S33



49

Chandy"Lam!ort 6lgorithm

'istributed algorithm to capture a consistentglobal state. *ommunication channels assumed tobe !7!.

>ses a marer to initiate the algorithm. Sending 6ar&er by P:

P records its state. !or each outgoing channel *, Psends a mar&er on * with the state info.

=eceiving 6ar&er by #: 7f # has recorded its state: a. =ecord the state as

an empty seIuence, S%' mar&er (use above rule).

%lse (# has recorded state before): =ecord the state of* as seIuence of messages received along *, after #sstate was recorded and before # received the mar&er.



50

Chandy"Lam!ort 6lgorithm

7nitiation of mar&er can be done by anyprocess, with its own uniIue mar&er:process id, seIuence number8.

Several processes can initiate state recording

by sending mar&ers. *oncurrent sending ofmar&ers allowed.

ne possible way to collect global state: allprocesses send the recorded state information

to the initiator of mar&er. 7nitiator process cansum up the global state.



51

6lgorithm in 6ction

p

S

0 S1 S

2 S3

S p0 S p

1 S p2 S p

3

m1 m2 m3



52

6lgorithm in 6ction

p

S

0 S1 S

2 S3

S p0 S p

1 S p2 S p

3

m1 m2 m3

'ec!'* tate a S1 + e* ma',e' t! p



53

6lgorithm in 6ction

p

S

0 S1 S

2 S3

S p0 S p

1 S p2 S p

3

m1 m2 m3

p 'ec!'* tate a S p2+ c-ae tate a empty



54

6lgorithm in 6ction

p

S

0 S1 S

2 S3

S p0 S p

1 S p2 S p

3

m1 m2 m3

'ec!'* c-ae tate a m3



6lgorithm in 6ction

p

S

0 S1 S

2 S3

S p0 S p

1 S p2 S p

3

m1 m2 m3

.ec!'*e* G!"a State / ((S p2+ S

1)+ (0+m3) )

clocks and global state.ppt

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