[PPT] - Synchronous Ordering 1 Goals of the lecture Hiera rchy of PowerPoint Presentation

SLIDE 1 Synchronous Ordering 1 Goals

f

the lecture

Hiera

rchy

f

communication mo des

Motivation

fo r synchronous

rdering
Cro

wn

Sucient

conditions fo r synchronous

rdering
Implementation

rules

Safet

y theo rem

Liveness

c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 2 Synchronous Ordering 2 Comm unicatio n Mo des

FIF0

s 1

s

2 = ) :(r 2

r

1 ) P 1 P 2 P 3

sequence

numb ers a re sucient to implement FIF O.

Causally

Ordered s 1 ! s 2 = ) :(r 2

r

1 ) P 1 P 2 P 3

matrix

clo cks a re sucient to implement Causal

rdering.

c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 3 Synchronous Ordering 3 Comm unicatio n Mo des [Contd.]

Synchronous

Ordering (SYNC) 9T : E ! 1 N : 8s; r ; e; f 2 E s ; r = ) T(s) = T(r ) e

f

= ) T(e) < T(f )

6

6 ? 1 1 2 2 3 3

time

diagram

f

a synchronous computation can b e dra wn such that all message a rro ws a re vertical.

any
rder

clo ck is insucient to implement synchronous

rdering.

c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 4 Synchronous Ordering 4 Motivation fo r Synch. p 1 p 2 1: insert (queue q 1 , c) 1: insert (queue q 2 , a) 2: insert (queue q 2 , d) 2: insert (queue q 1 , b).

queue

q 1 queue q 2 pro cess p 1 pro cess p 2

*
*

@ @ @ @ @ @ @ @ @ @ I s in (queue q 2 , a) s in (queue q 1 , c) s in (queue q 1 , b) s in (queue q 2 , d)

queue

q 1 queue q 2

6

s p 1 : 1 s p 1 : 2 6 s p 2 : 1 6 s p 2 : 2

6

s p 1 : 1 s p 1 : 2 6 s p 2 : 1 6 s p 2 : 2

6

s p 1 : 1 s p 1 : 2 6 s p 2 : 1 6 s p 2 : 2 State q 1 c b q 2 d a q 1 c b q 2 a d q 1 b c q 2 a d c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 5 Synchronous Ordering 5 Cro wns in Distributed Computation

A

computation is synchronous i there do es not exist a se- quence

f

send and co rresp

nding

receive events such that s ! E r 1 ; s 1 ! E r 2 ; : : : ; s k 2 ! E r k 1 ; s k 1 ! E r :

such

a structure is called cro wn.

Example:

P 1 P 2 P 3 s 1 r 1 s 2 r 2 s r s 1 r 1 s 3 r 3 s 2 r 2 (A) (B) s 1 ! r 2 ; s 2 ! r 1 s 1

r

2 ; s 2

r

3 ; s 3

r

1 (A) : Cro wn

f

size 2 (B) : Strong Cro wn

f

size 3 c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 6 Synchronous Ordering 6 Algo rithm

Commit

P

int
f

a Message P 1 P 2 e s 1 r 1 s 2 r 2

Prio

rit y Rule (RP) P 1 P 2 P 3 s r s r s r e (a) The message along with the underlying message P 1 P 2 P 3 s r r s e (b) The resulting message

rdering

c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 7 Synchronous Ordering 7 Algo rithm [Contd.]

Send

Condition s 1

s

2 = ) r 1 ! r 2

Receive

Condition s 1

s

2 = ) s 1 :ack

s

2 c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 8 Synchronous Ordering 8 Implem entati

n

P i P j e

passiv

e

f

f :ack e:ack

activ

e

activ

e

Send

Condition (SC) s 1

s

2 = ) r 1 ! r 2 (SP) s 1

s

2 = ) s 1 :ack

s

2 (W ait fo r ack)

Receive

Condition (R C) s 1

r

2 = ) :(r 2 ! r 1 ) (RP) s 1

r

2 = ) s 1 :ack

r

2 :ack (Send ack if no ack p ending ) c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 9 Synchronous Ordering 9 Basic Lemma Lemma 1 (s 1 ! r 2 ) and (SC) = ) (r 1 ! r 2 ) _ (s 1

r

2 ) Pro

f:

s s s

s

s 1

s

3 = ) r 1 ! r 3 = ) r 1 ! r 2 Case 1 Case 2 s 1 r 1 r 2 s 1 r 1 r 2 Case 3 s 1 r 1 s 3 r 2 r 3 ! r 2 2 c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 10 Synchronous Ordering 10 Cro wn and Strong Cro wn Lemma 2 Given SC and R C. 2 CR = ) 2 SCR. Pro

f:

s 1 ! r 2 ; s 2 ! r 1 Let :(s 1

r

2 ) = ) r 1 ! r 2 S C = ) :(s 2

r

1 ) R C :(s 2

r

1 ) ^ (s 2 ! r 1 ) = ) r 2 ! r 1 2 Lemma 3 Given SC, R C. CR(k ) = ) SCR (k ) Pro

f:

s i1 ! r i ; s i ! r i+1 s.t. :(s i

r

i+1 ) = ) r i ! r i+1 Therefo re, s i1 ! r i ; s i ! r i+1 reduced to s i1 ! r i+1 . 2 c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 11 Synchronous Ordering 11 Safet y :S Y N C H , C R ) S C R s

r

1 ; s 1

r

2 ;

;

s k 1

r

i.e. P (s i ) = P (r (i+1) mo d k ) F rom PR : P (s i ) > P (r i ) w e get P (s ) < P (r ) c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 12 Synchronous Ordering 12 Liveness

If

P k w ants to send a message then it can eventually succeed.

k

smallest p ro cesses will eventually b e in active state. c Vija y K. Ga rg Distributed Systems F all 94

SLIDE 13 Synchronous Ordering 13 Overhead

Prio

rit y Rule

fo

r every message (s; r ) if P(s) < P(r ): +

ne

control message and + dela y

f

less than 2t units

f

time.

fo

r every message (s; r ) if P(s) > P(r ): + no control message and + no dela y .

Send

and Receive Proto col +

ne

control message and + dela y is upp er b

unded

b y nt, where n is equal to the numb er

f

p ro cesses. c Vija y K. Ga rg Distributed Systems F all 94