Time Synchronization in Distributed Systems: Clocks, Algorithms, and Logical Clocks, Study notes of Electrical and Electronics Engineering

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Lecture

time,

clocks,

and

synchronization

distributed

systems

CS

/^ ECE

/^ CSE

acknowledgment

These^ slides

are^ based

on^ ideas

and^ material

from^ the

following

sources:

-^ slides

prepared

by^ Professors

M.^ T.^ Harandi and

J.^ Hou and

subsequently

modified

by^ Professors

Indranil Gupta,

Nitin Vaidya,

and^ Yih

‐Chun^

Hu at

University

of^ Illinois

-^ slides

from^ Professor

S.^ Ghosh’s course

at^ University

of^ Iowa

plan

for

today

• sources

of^ time

• how

to^ synchronize

clocks?

• can

we^

define

sequence

of^ events

without

using

physical

clocks

time

sources

-^ primary

standard

=^ rotation

of^ the

earth

-^ not^ a

stable

-^ de^ facto^ primary

standard

=^ International

Atomic

Time^

(TAI)

-^1 atomic

second

=^ 9,192,631,

orbital

transitions

(^133) of Cs

-^86400

atomic

seconds

=^1 solar

day^ – 3ms

-^ Coordinated

Universal

Time^

(UTC)

=^ international

standard

-^ derived

from^ TAI

by^ adding

leap^ seconds

to^ keep

it^ close

to^ solar

time

-^ UTC

source

signals

are^ synchronized

-^ UTC

time^ is

re‐transmitted

by^ GPS

satellites

(0.1‐^10

mS)

ρ^ for

some

real

oscillators

PPM^

stability

over

oscillator

0 ‐^70 °

C^

years

NCXO

5 ‐^100

1 ‐^10

TCXO

0.1‐^5

0.1‐^2

OCXO

‐^1

0.02‐^2

MCXO

‐^2

0.02‐^2

Source:^ http://www.isotemp.com/

‐010.html

terminology

-^ a^ distributed

system

consists

of^ N^ processes

p^ ,^ p^ ,^1

…,^ p^ N

-^ process

p^ ,^ i^ œ i^

{1,…,^

N}

-^ state:

values

of^ local

variables

including

time

-^ c^ (t):^ i^ the^ reading

of^ the^ software

clock^ at

process

i^ when^

the^ real^

time^ is^ t

.

-^ actions:

send,^ receive,

compute

-^ occurrence

of^ an^

action^

is^ called

an^ event t^1

t^2

m^

m’

send(m)

send(m’) recv(m)

recv(m’)

p^2 p^1

comp

real^ time

ƒ^ uses

an^ elected

leader^

process

to^ ensure

that^ maximum

skew^

is^ δ

ƒ^ leader

broadcasts

to^ all^ machines

for^ their

time

ƒ^ adjusts

times^

received

for^ transmission

delay &^ latency

ƒ^ averages

times^

after^ removing

outliers

ƒ^ tells

each^ machine

how^ to

adjust.

ƒ^ in^ some

systems

multiple

time^ servers

are^ used

ƒ^ avg.

time^ is

more^

accurate,

but^ still

drifts

ƒ^ failure

of^ the

leader

requires

some^

time^ for

re‐election,

so^ accuracy

cannot internal^ be^ guaranteed

synchronization:

Berkeley

algorithm

mr mt

pi^

Time server,S

external

synchronization:

Cristian’s

method

• suppose

we^ know

the^ minimum

client

‐server

one‐ way^

transmission

delay:

min

• then,

the^ actual

time^

could

be^ between

[T+min,

T+RTT— min] • accuracy

RTT/

‐^ min

external

synchronization:

Cristian’s method

t^1

t^2

Server^ Client

mr^

T m(T)t

secondary servers,synched by theprimary server

Primary server, direct synch.

Strata 3,synched by thesecondaryservers

ƒ^ uses

a^ network

of^ time

servers

to^ synchronize

all^ processes

on^ a

network. ƒ time^ servers

are^ connected

by^ a^ synchronization

subnet

tree

ƒ^ the^

root^ is

adjusted

directly

ƒ^ each

node^ synchronizes

its^ children

nodes. 1 2

2

2

3

3

3

3

3

3

Network

Time

Protocol

(NTP)

T^ i-1 Ti T^ i-2 Ti- 3 Server B Server A

m^

m'

Time Time

-^ o :^ true

skew^ of

clock^ at

B^ relative

to

that^ at^

A^ =^ c– cA^

B

-^ t^ and

t’:^ actual

transmission

times

for^ m^ and

m’

-^ o :^ estimated i

skew

-^ d^ =^ t^ i^

+^ t’^ :^ estimate

of^ accuracy

of^ oi

Theoretical

Base

for

NTP

T=^ Ti‐^2

+^ t^ +^ i‐ 3 o T=^ Ti^ i‐^1

+^ t’^ – o addingt^ +^ t’^ =^ T

‐^ Ti‐ 2 i‐^3 +^ T‐^ T i^ i‐^1

subtractingo^ =^ ½^ [T

‐^ Ti‐ 2 i‐^3 ‐^ T+^ T i^

]^ +^ ½i‐ 1 [t’^ – t]

let^ o=^ ½i^

[T‐^ i‐^2

T‐^ T^ i‐^3 i^

+^ T]i‐^1

|o^ – o|i^

§^ ½^ |t’

- t|^ §^

½^ [t’^ +^ t]^ =^ ½^ d

i

summary

• several

algorithms

for^

internal

and

external

clock

synchronization

• accuracy

depends

on^ uncertainty

in

message

delays

• we

have

not

discussed

failures

– there

are^ algorithms

for^ synchronization

with

a^ fraction

of^ failed

clocks

[e.g.,

Lamport,

Melliar

‐Smith

algorithm]

ƒ^ is

it^ always

necessary

to^ give

absolute

time

to^ events?

ƒ^ suppose

we^

can^

assign

relative

time

to

events,

in^ a

way

that

does

not

violate

their

causality

logical

clocks

happens

‐before

relation

on

events

ƒ^ define

a^ relation

→^ on

the^ events as

follows

ƒ^ on^

the^ same

process:

a^ →^ b ,^

iff^ time(a)

<^ time(b)

ƒ^ if^ p

sends 1 m^ to^ p

:^ send(m) 2

→^ receive(m)

ƒ^ (transitivity)

if^ a^ →

b^ and^

b^ →^ c^ then

a^ →^ c

ƒ^ →^

is^ called

the^ Happens

‐Before

relation

ƒ^ events

a^ and b^ are^ concurrent if

not^ (a

→^ b^

or^ b^ →

a)

t^1

t^2

m^

m’

send(m)

send(m’) recv(m)

recv(m’)

p^2 p^1

comp

real^ time