Copyright © K.Goseva 2008 CS 757 Distributed Systems Slide 1
West Virginia
University
Synchronization
Chapter 6
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Lamport Timestamps & Election Algorithms for Clock Sync & Mutual Exclusion, Study notes of Computer Science
An overview of clock synchronization and mutual exclusion techniques in distributed systems, focusing on lamport timestamps and election algorithms. The slides cover topics such as reference broadcast synchronization (rbs), lamport timestamps, mutual exclusion, and election algorithms in the context of west virginia university's cs 757 distributed systems course.
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Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Synchronization
Chapter 6
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Outline
- Clock synchronization • Logical clocks • Mutual exclusion • Election algorithms
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Physical Clocks
Computation of the mean solar day
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Physical Clocks
- Atomic clock (1948) counts transitions of the cesium 133 atom• International Atomic Time (TAI)• TAI seconds are of constant length, unlike solar seconds• Leap seconds are introduced when necessary to keep in phase with the
sun - Universal Coordinated Time (UTC)–UTC replaced the old standard – Greenwich Mean Time which is an astronomical
time
- OS must have special software to account for leap seconds
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Clock Synchronization Algorithms
Relation between clock time and UTC when clocks tick at different rates•^
ρ
is the maximum drift rate
- If two clocks are drifting from
UTC in opposite directions at atime
Δ
t after they were synchronized,
they may be 2
ρΔ
t apart
- To assure that clocks will not
differ more than
δ
, they must be
resynchronized at least every
δ
/(
ρ
) seconds
ρ
ρ
≤
≤
−
1
1
dC dt
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Global Positioning System
Related problem: Determining one’s position anywhere inthe world
GPS is a satellite-based distributed system launched in 1978^ – 29 satellites, each circulating in an orbit at ~20,
km
- Each satellite has up to four atomic clocks – A satellite continuously broadcasts its position and timestamps
each message with its local time
- Three satellites are needed to determine the longitude, latitude, and
altitude of a receiver on Earth
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Global Positioning System
- When a message is received from satellite
i
with
timestamp
T
,i
the delay
i^
measured by the receiver is
- As signals travel with the speed of light
c,
the measured
distance from the satellite is
- The real distance is computes as• If we have four satellites, we have to solve four equations
for the coordinates of the receiver
and
Δ
r
r
i
now
i^
T
T
r
i
r
i
now
i^
c d c T T c c
Δ ⋅ + = Δ ⋅ + − ⋅ = Δ
⋅^
)
(
2
2
2
) ( ) ( ) ( r i r i r i
i^
z z y y x x d − + − + − = )
,
,
(
r
r
r^
z
y
x
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Global Positioning System
Many things are not perfect^ – GPS does not take leap seconds into account. The deviation from
UTC can easily be taken care in software.
Atomic clocks in satellites are not always in sync – The position of the satellite is not known precisely – The receiver’s clock has a finite accuracy – The signal propagation speed is not constant – The Earth is not a perfect sphere
Relatively cheap GPS receivers: precision within 1-5 metersfor the location
Professional receivers, hooked up in a computer network:less than 10-35 nanoseconds error for the time
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Network Time Protocol
If
A
’s clock is fast
θ
< 0, which means
A
should set its clock
backward
However, time is not allowed to run backward
Changes are introduced gradually^ – Assume the timer is set to generate 100 interrupts per second, i.e.,
interrupts are 10
msec
apart
- Slow down: each interrupt adds 9
msec
until the correction is made
- Speed up: each interrupt adds 11
msec
until the correction is made
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Network Time Protocol
Network Time Protocol (NTP) allows set-up pairwisebetween servers
Eight pairs of (
θ
,δ
) values are buffered. The minimum
δ
is
adopted as the best estimate for the delay and the associated θ
as the best estimate of the offset
NTP divides servers into strata^ – a server with a reference clock is startum-1 server
When
A
contacts
B,
it will adjust its time only if its stratum
level is higher than the stratum level of
B.
After the
synchronization
A’
s stratum level will become by one
higher than
B
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Use of synchronized clocks
In the last few years, hardware and software forsynchronizing clocks on a wide scale (i.e., over the entireInternet) has become available^ – With this new technology, it is possible to keep millions of clocks
synchronized to within a few milliseconds of UTC
New algorithms that utilize synchronized clocks are startingto appear^ – Enforce at-most-once message delivery to a server, even in the
face of crashes
- Achieve cache consistency – Handle commitment to atomic transaction
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
The Berkeley Algorithm
a)
The time daemon polls all the other machines for their clock values b) The machines answer c)
The time daemon tells estimates an average time and tells everyone how toadjust their clocks
Suitable when no machine has a WWV receiver. The time server (i.e., daemon) is active.
Copyright © K.Goseva 2008
CS 757 Distributed Systems
West VirginiaUniversity
Clock Synchronization in Wireless
Networks
- When a sender broadcasts a reference message
m,
each
node
p
records the time when it receives the message
T
p,m
from its local clock
- Two nodes
p
and
q
exchange their corresponding times, so
they can estimate their relative offsetwhere
M
is the total number of reference messages sent
p
will know the value of
q
’s clock relative to its own
M
T
T
q p
Offset
M k
k q
k p
∑
=
−
=
1
,
,^
)
(
] , [
Copyright © K.Goseva 2008
CS 757 Distributed Systems
Slide 20
West VirginiaUniversity
Clock Synchronization in Wireless
Networks
- The previous estimate works only if the clocks do not drift
apart
- If the clocks of
p
and
q
drift apart, the later values will be
less accurate than the earlier values and simple average asin the previous slide will not work
- Algorithm that uses linear regression to compute the offset
The constants
α
and
β
are computed from the pairs
β
α
=
t
t
q
p
Offset
)
](
,
[
)
,
(
,
,^
k q
k p^
T
T