Time Synchronization
Chapter 9
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/1
Rating
• Area maturity
First steps
Text book
• Practical importance
No apps
Mission critical
• Theoretical importance
Not really
Must have
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/2
Overview
•
•
•
•
•
Motivation
Clock Sources
Reference-Broadcast Synchronization (RBS)
Time-sync Protocol for Sensor Networks (TPSN)
Gradient Clock Synchronization
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/3
2. Time Synchronization in
Distributed Systems
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/4
Assumptions
• Process can perform three kinds of atomic actions/events
– Local computation
– Send a single message to a single process
– Receive a single message from a single
process
• Communication model
– Point-to-point
– Error-free, infinite buffer
– Potentially out of order
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/5
Motivation
• Many protocols need to impose an ordering among events
– If two players open the same treasure
chest “almost” at the same time, who
should get the treasure?
• Physical clocks:
– Seems to completely solve the problem
– But what about theory of relativity?
– Even without theory of relativity – efficiency
problems
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/6
Physical Clock Synchronization
The relation between clock time and UTC
when clocks tick at different rates.
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/7
Classification
•
Types of Synchronization
External Synchronization : Keep as close to
UTC as possible
Internal Synchronization : Mutual
synchronization is important
•
Types of clocks
• Unbounded 0, 1, 2, 3, . . .
Bounded 0,1, 2, . . . M-1, 0, 1, . . .
•
Phase Synchronization
Unbounded clocks are not realistic, but are easier to
deal with in algorithms. Real clocks are always bounded.
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/8
Terminology
c
l
o
c
k
Š
clock 1
clock 2
t drift rate= 
i
m
e
R
R
Newtonian time
•
Drift rate  : Max rate two clocks
can differ, < 10^-6 for Xtal clocks
•
Clock skew  : Max. Allowed drift
•
Resynchronization interval R :
Depends on clock skew
•
Challenges
•
•
•
•
(Drift is unavoidable)
Accounting for propagation delay
Accounting for processing delay
Faulty clocks
Ad Hoc and Sensor Networks – Roger Wattenhofer –
9/9
Internal synchronization
•
A simple averaging algorithm
c
c-
i
c+
j
•
Assume n clocks, at most t are
faulty
•
•
Step 1. Read every clock in the system.
Step 2. Discard outliers and substitute
them by the value of the local clock.
Step 3. Update the clock using the
average of these values.
•
c-2
k
Some clocks may be faulty.
Exhibits 2-faced behavior
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/10
Network Time Protocol (NTP)
•
Level 1
Tiered architecture
Time
server
Level 0
Level 1
Level 1
•
•
•
•
•
•
Broadcast mode
- least accurate
Procedure call
- medium accuracy
Peer-to-peer mode
- upper level servers use this for max
accuracy
Level 2
Level 2
Level 2
The tree can reconfigure itself if some node fails.
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/11
P2P mode of NTP
T2
Q
T3
•
Let Q’s time be ahead of P’s time by . Then
•
•
T2 = T1 + TPQ + 
T4 = T3 + TQP - 
•
y = TPQ + TQP = T2 +T4 -T1 -T3 (RTT)
•

= (T2 -T4 -T1 +T3) / 2 - (TPQ - TQP) / 2
•
P
T1
T4
x
Between y/2 and -y/2
So, x- y/2 ≤  ≤ x+ y
Ping several times, and obtain the smallest value of y. Use it to calculate 
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/12
Cristian’s Algorithm
• 1. Client gets data from a time server.
• 2. It computes the round trip time (RTT), and compensates for this
• delay while adjusting its own clock
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/13
Berkeley Time Protocol (FromTanenbaum 2007)
a) The time daemon
asks all the other
machines for their
clockvalues.
b) The machines
answer
The time daemon
tells everyone how
to adjust their
clock.
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/14
Software “Clocks”
• Software “clocks” can incur much lower overhead than
maintaining (sufficiently accurate) physical clocks
• Allows a protocol to infer ordering among events
• Goal of software “clocks”: Capture event ordering that are visible
to users
– But what orderings are visible to users
without physical clocks?
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/15
Visible Ordering to Users
•
•
•
A  B (process order)
B  C (send-receive order)
A  C (transitivity)
A
A?D
B?D
C?D
B
user1 (process1)
C
user2 (process2)
user3 (process3)
D
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/16
“Happened-Before” Relation
• “Happened-before” relation captures the ordering that is visible to
users when there is no physical clock
– A partial order among events
– Process-order, send-receive order, transitivity
• First introduced by Lamport – Considered to be the first fundamental
result in distributed computing
• Goal of software “clock” is to capture the above “happened-before”
relation. Formally, a logical clock C is a map from the set of events
E to N (the set of natural numbers) with the following constraint:
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/17
1: Logical Clocks
• Each event has a single integer as its logical clock value
– Each process has a local counter C
– Increment C at each “local computation” and “send” event
– When sending a message, logical clock value V is attached
to the message. At each “receive” event, C = max(C, V) + 1
3 = max(1,2)+1
1
4 = max(3,3)+1
3
4
2
user1 (process1)
user2 (process2)
user3 (process3)
1
1
3
2
4
5
5
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/18
Logical Clock Properties
• Theorem:
– Event s happens before t  the logical clock value of s is
smaller than the logical clock value of t.
• The reverse may not be true
1
2
3
4
user1 (process1)
user2 (process2)
user3 (process3)
1
1
3
2
4
5
5
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/19
Lamport’s Logical Clock Algorithm
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/20
2: Vector Clocks
• Logical clock:
• Vector clock:
– Event s happens before event t  the vector clock value of s
is “smaller” than the vector clock value of t.
• Each event has a vector of n integers as its vector clock value
– v1 = v2 if all n fields same
– v1  v2 if every field in v1 is less than or equal to the
corresponding field in v2
– v1 < v2 if v1  v2 and v1 ≠ v2
Relation “<“ here is
not a total order
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/21
Vector Clock Protocol
•
•
•
Each process i has a local vector C
Increment C[i] at each “local computation” and “send” event
When sending a message, vector clock value V is attached to the message. At
each “receive” event, C = pairwise-max(C, V); C[i]++;
C = (0,1,0), V = (0,0,2)
pairwise-max(C, V) = (0,1,2)
(1,0,0)
(2,0,0)
(3,0,0)
user1 (process1)
user2 (process2)
user3 (process3)
(0,1,0)
(0,0,1)
(0,2,2)
(0,0,2)
(2,3,2)
(2,3,3)
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/22
Vector Clock Properties
•
•
Event s happens before t  vector clock value of s < vector clock value of t:
There must be a chain from s to t
Event s happens before t  vector clock value of s < vector clock value of t
– If s and t on same process, done
– If s is on p and t is on q, let VS be s’s vector clock and VT be t’s
– VS < VT  VS[p] ≤ VT[p]  Must be a sequence of message from p to q
after s and before t
p
q
s
t
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/23
Example Application of Vector Clock
• Each user has an order placed by a customer
– Want all users to know all orders
• Each order has a vector clock value
I have seen all orders whose vector clock is smaller than (2,3,2):
I can avoid linear search for existence testing
D1, (1,0,0)
(2,0,0)
(3,0,0)
user1 (process1)
user2 (process2)
user3 (process3)
D2, (0,1,0)
D3, (0,0,1)
(0,2,2) D1
D3
(0,0,2)
(2,3,2)
D1, D2, D3
(2,3,3)
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/24
Vector Clock Algorithm
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/25
A sample execution of the vector clock algorithm
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/26
Summary
• Goal : Define “time” in a distributed system
• Logical clock
– “happened before”  smaller clock value
• Vector clock
– “happened before”  smaller clock value
• Matrix clock
– Gives a process knowledge about what
other processes know
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/27
Motivation
• Time synchronization is essential for many applications
–
–
–
–
–
Coordination of wake-up and sleeping times (energy efficiency)
TDMA schedules
Ordering of collected sensor data/events
Co-operation of multiple sensor nodes
Estimation of position information (e.g. shooter detection)
• Goals of clock synchronization
– Compensate offset between clocks
– Compensate drift between clocks
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/28
Properties of Synchronization Algorithms
• External versus internal synchronization
– External sync: Nodes synchronize with an external clock source (UTC)
– Internal sync: Nodes synchronize to a common time
– to a leader, to an averaged time, or to anything else
• Instant versus periodic synchronization
– Periodic synchronization required to compensate clock drift
• A-priori versus a-posteriori
– A-posteriori clock synchronization triggered by an event
• Local versus global synchronization
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/29
Clock Sources
• Radio Clock Signal:
– Clock signal from a reference source (atomic clock)
is transmitted over a longwave radio signal
– DCF77 station near Frankfurt, Germany transmits at
77.5 kHz with a transmission range of up to 2000 km
– Accuracy limited by the distance to the sender,
Frankfurt-Zurich is about 1ms.
– Special antenna/receiver hardware required
• Global Positioning System (GPS):
– Satellites continuously transmit own position and
time code
– Line of sight between satellite and receiver required
– Special antenna/receiver hardware required
Clock Devices in Sensor Nodes
• Structure
– External oscillator with a nominal frequency (e.g. 32 kHz)
– Counter register which is incremented with oscillator pulses
– Works also when CPU is in sleep state
• Accuracy
Measured Time
– Clock drift: random deviation from the nominal rate dependent on power
supply, temperature, etc.
– E.g. TinyNodes have a maximum drift of 30-50 ppm at room temperature
Oscillator
Clock with
Drift
Perfect
Clock
This is a drift of up to
50 μs per second
or 0.18s per hour
Jittering
Clock
Clock
with Offset
Actual Time
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/31
Sender/Receiver Synchronization
• Round-Trip Time (RTT) based synchronization
t2
B
T
im
e
a
c
c
o
r
d
in
g
t
o
B
A
n
s
w
e
r
fr
o
m
B
R
e
q
u
e
s
t
fr
o
m
A
A
t1
t3
T
im
e
a
c
c
o
r
d
in
g
t
o
A
t4
• Receiver synchronizes to the sender‘s clock
• Propagation delay  and clock offset  can be calculated
(t 4  t1 )  (t3  t2 )
2
(t  (t + δ))  (t 4  (t3 + δ)) (t 2  t1 ) + (t3  t4 )
θ= 2 1
=
2
2
δ=
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/32
Disturbing Influences on Packet Latency
• Influences
–
–
–
–
–
Sending Time S
Medium Access Time A
Transmission Time T
Propagation Time PA,B
Reception Time R
S
A
(up to 100ms)
(up to 500ms)
(tens of milliseconds, depending on size)
(microseconds, depending on distance)
(up to 100ms)
T
Timestamp TA
PA,B
R
Timestamp TB
Critical path
• Asymmetric packet delays due to non-determinism
• Solution: timestamp packets at MAC Layer
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/33
Reference-Broadcast Synchronization (RBS)
• A sender synchronizes a set of receivers with one another
• Point of reference: beacon’s arrival time
t2
t2
t

S
A
P

R
1
S
S
S
,A
A
t
t

S
A
P

R
3
1
S
S
S
,B
B

t2
t
(
P

P
)
(
R

R
)
3
S
,A
S
,B
A
B
A

S
t1
B
t3
• Only sensitive to the difference in propagation and reception time
• Time stamping at the interrupt time when a beacon is received
• After a beacon is sent, all receivers exchange their reception times to
calculate their clock offset
• Post-synchronization possible
• Least-square linear regression to tackle clock drifts
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/34
Time-sync Protocol for Sensor Networks (TPSN)
• Traditional sender-receiver synchronization (RTT-based)
• Initialization phase: Breadth-first-search flooding
– Root node at level 0 sends out a level discovery packet
– Receiving nodes which have not yet an assigned level set their level
to +1 and start a random timer
– After the timer is expired, a new level discovery packet will be sent
– When a new node is deployed, it sends out a level request packet after
a random timeout
0
1
1
1
2
2
2
2
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/35
Time-sync Protocol for Sensor Networks (TPSN)
• Synchronization phase
– Root node issues a time sync packet which triggers a random timer at
all level 1 nodes
– After the timer is expired, the node asks its parent for synchronization
using a synchronization pulse
– The parent node answers with an acknowledgement
– Thus, the requesting node knows the round trip time and can calculate
its clock offset
– Child nodes receiving a synchronization pulse also start a random timer
themselves to trigger their own synchronization
0
Time Sync
1
B
Sync pulse
A
1
ACK
2
2
2
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/36
Time-sync Protocol for Sensor Networks (TPSN)
t

t

S

A

P

R
2
1
A
A
A
,
B
B
0
t

t

S

A

P

R
4
3
B
B
B
,A
A
(
S

S
)

(
A

A
)

(
P

P
)

(
R

R
)
,
B
B
,A
B
A

A B A B A
2
•
•
•
•
t2 B
t1
A
1
t3
t4
1
2
2
2
Time stamping packets at the MAC layer
In contrast to RBS, the signal propagation time might be negligible
Authors claim that it is “about two times” better than RBS
Again, clock drifts are taken into account using periodical
synchronization messages
• Problem: What happens in a non-tree topology (e.g. ring)?!?
– Two neighbors may have exceptionally bad synchronization
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/37
Theoretical Bounds for Clock Synchronization
•
Network Model:
– Each node i has a local clock Li(t)
– Network with n nodes, diameter D.
– Reliable point-to-point communication with minimal delay µ
– Jitter ε is the uncertainty in message delay
•
Two neighboring nodes u, v cannot distinguish whether message is faster
from u to v and slower from v to u, or vice versa. Hence clocks of
neighboring nodes can be up to  off.
v
0
1
2
µ+
µ
•
•
1
0
1
µ+
u
0
v
3
2
3
u
0
1
2
3
µ
2
3
Hence, two nodes at distance D may have clocks which are D off.
This can be achieved by a simple flooding algorithm: Whenever a node
receives a new minimum value, it sets its clock to the new value and
forwards its new clock value to all its neighbors.
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/38
Gradient Clock Synchronization
1. Global property: Minimize clock skew between any two nodes
2. Local (gradient) property: Small clock skew between two nodes if
the distance between the nodes is small.
3. Clock should not be allowed to jump backwards

You don’t want new events to be registered earlier than older events.
Root node
• Example: Ring topology
0
1
1
Small clock skew
2
2
3
3
4
Large clock skew
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/39
Trivial Solution: Let t = 0 at all nodes and times
1. Global property: Minimize clock skew between any two nodes
2. Local (gradient) property: Small clock skew between two nodes if
the distance between the nodes is small.
3. Clock should not be allowed to jump backwards
• To prevent trivial solution, we need a fourth constraint:
4. Clock should always to move forward.
•
•
Sometimes faster, sometimes slower is OK.
But there should be a minimum and a maximum speed.
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/40
Gradient Clock Synchronization
• Model
– Each node has a hardware clock Hi(∙) with a clock rate hi (t )  L,U 
where 0 < L < U and U ≥ 1
t
– The time of node i at time t is Hi (t )   hi (t )dt
0
– Each node has a logical clock Li(∙) which increases at the rate of Hi(∙)
– Employ a synchronization algorithm A to update the local clock with
fresh clock values from neighboring nodes (clock cannot run
backwards)
– Nodes inform their neighboring nodes when local clock is updated
Time is 152
Time is 142
Time is 140
Time is 150
???
Ad Hoc and Sensor Networks – Roger Wattenhofer – 9/41
Goals of this chaper
• Understand the importance of time synchronization in WSNs
• Understand typical strategies for time synchronization and how they
are applied in WSNs
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer42
– 9/42
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Overview
•
•
•
•
The time synchronization problem
Protocols based on sender/receiver synchronization
Protocols based on receiver/receiver synchronization
Summary
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer43
– 9/43
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Overview
•
•
•
•
The time synchronization problem
Protocols based on sender/receiver synchronization
Protocols based on receiver/receiver synchronization
Summary
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer44
– 9/44
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Example
•
•
•
Goal: estimate angle of arrival of a
very distant sound event using an
array of acoustic sensors
From the figure,  can be estimated
when x and d are known:
d is known a priori, x must be
estimated from differences in time
of arrival
– x = C Dt where C is the speed of
sound
– For d=1 m and Dt=0.001 we get  =
0.336 radians
– When Dt is estimated with 500 ms
error, the  estimates can vary
between 0.166 and 0.518
•
Morale: a seemingly small error in
time synch can lead to significantly
different angle estimates
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer45
– 9/45
Ad hoc & sensor Ad
networs
- Ch
8: –Time
The role of time in WSNs
• Time synchronization algorithms can be used to better synchronize
clocks of sensor nodes
• Time synchronization is needed for WSN applications and protocols:
– Applications: AOA estimation, beamforming
– Protocols: TDMA, protocols with coordinated wakeup, ...
– Distributed debugging: timestamping of distributed events is needed to
figure out their correct order of appearance
• WSN have a direct coupling to the physical world, hence their notion
of time should be related to physical time:
– physical time = wall clock time, real-time, i.e. one second of a WSN
clock should be close to one second of real time
– Commonly agreed time scale for real time is UTC, generated from
atomic clocks and modified by insertion of leap seconds to keep in
synch with astronomical timescales (one rotation of earth)
– Other concept: logical time (Lamport), where only the relative ordering
of events counts but not their relation to real time
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer46
– 9/46
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Clocks in WSN nodes
• Often, a hardware clock is present:
– An oscillator generates pulses at a fixed
nominal frequency
– A counter register is incremented after a fixed
number of pulses
– Only register content is available to software
– Register change rate gives achievable time resolution
– Node i’s register value at real time t is Hi(t)
– Convention: small letters (like t, t’) denote real physical times,
capital letters denote timestamps or anything else visible to nodes
• A (node-local) software clock is usually derived as follows:
– Li(t) = i Hi(t) + fi (not considering overruns of
the counter-register)
SS 05
47
Hoc and Sensor
Networks
Roger Wattenhofer
Ad hoc & sensor Ad
networs
- Ch
8: –Time
– 9/47
Synchronization accuracy / agreement
• External synchronization:
– synchronization with external real time scale
like UTC
– Nodes i=1, ..., n are accurate at time t within
bound  when
|Li(t) – t|< for all i
– Hence, at least one node must have access to the external time
scale
• Internal synchronization
– No external timescale, nodes must agree on
common time
– Nodes i=1, ..., n agree on time within bound 
when |Li(t) – Lj(t)|< for all i,j
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer48
– 9/48
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Sources of inaccuracies
• Nodes are switched on at random times, phases θi hence can be
random
• Actual oscillators have random deviations from nominal frequency
(drift, skew)
– Deviations are specified in ppm (pulses per million), the ppm value
counts the additional pulses or lost pulses over the time of one million
pulses at nominal rate
– The cheaper the oscillators, the larger the average deviation
– For sensor nodes values between 1 ppm (one second every 11 days) and
100 ppm (one second every 2.8 hours) are assumed, Berkeley motes have
an average drift of 40 ppm
• Oscillator frequency depends on time (oscillator aging) and
environment (temperature, pressure, supply voltage, ...)
– Especially the time-dependent drift rates call for frequent resynchronization, as one-time synchronization is not sufficient
– However, stability over tens of minutes is often a reasonable
assumption
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer49
– 9/49
Ad hoc & sensor Ad
networs
- Ch
8: –Time
General properties of time synchronization algorithms
• Physical time vs. logical time
• External vs. internal synchronization
• Global vs. local algorithms
– Keep all nodes of a WSN synchronized or only a local neighbourhood?
• Absolute vs. relative time
• Hardware vs. software-based mechanisms
– A GPS receiver would be a hardware solution, but often too
heavyweight/costly/energy-consuming in WSN nodes, and in addition a
line-of-sight to at least four satellites is required
• A-priori vs. a-posteriori synchronization
– Is time synchronization achieved before or after an interesting event?
 Post-facto synchronization
• Deterministic vs. stochastic precision bounds
• Local clock update discipline
– Should backward jumps of local clocks be avoided? (Users of make say
yes here ....)
– Avoid sudden jumps?
SS 05
Hoc and Sensor
Networks
Roger Wattenhofer50
– 9/50
Ad hoc & sensor Ad
networs
- Ch
8: –Time
Performance metrics and fundamental structure
• Metrics:
– Precision: maximum synchronization error for deterministic algorithms,
error mean / stddev / quantiles for stochastic ones
– Energy costs, e.g. # of exchanged packets, computational costs
– Memory requirements
– Fault tolerance: what happens when nodes die?
• Fundamental building blocks of time synchronization algorithms:
– Resynchronization event detection block: when to trigger a time
synchronization round? Periodically? After external event?
– Remote clock estimation block: figuring out the other nodes clocks with
the help of exchanging packets
– Clock correction block: compute adjustments for own local clock based
on estimated clocks of other nodes
– Synchronization mesh setup block: figure out which node synchronizes
with which other nodes
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Constraints for Time Synchronization in WSNs
•
•
•
•
•
An algorithm should scale to large networks of unreliable nodes
Quite diverse precision requirements, from ms to tens of seconds
Use of extra hardware (like GPS receivers) is mostly not an option
low mobility
Often there are no fixed upper bounds on packet delivery times (due
to MAC delays, buffering, ...)
• Negligible propagation delay between neighboring nodes
• Manual node configuration is not an option
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Post-facto synchronization
• Basic idea:
– Keeping nodes synchronized all the time
incurs substantial energy costs due to need
for frequent resynchronization
– Especially true for networks which become active only rarely
– When a node observes an external event at
time t, it stores its local timestamp Li(t),
achieves synchronization with neighbor node
/ sink node and converts Li(t) accordingly
• Can be implemented in different ways, to be discussed later
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Overview
•
•
•
•
The time synchronization problem
Protocols based on sender/receiver synchronization
Protocols based on receiver/receiver synchronization
Summary
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Protocols based on sender/receiver synchronization
• In this kind of protocols, a receiver synchronizes to the clock of a
sender
• We have to consider two steps:
– Pairwise synchronization: how does a single receiver
synchronize to a single sender?
– Networkwide synchronization: how to figure out who
synchronizes with whom to keep the whole network / parts of it
synchronized?
• The classical NTP protocol [Mills, RFC 1305] belongs to this class
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LTS – Lightweight Time Synchronization
• Overall goal: synchronize the clocks of all sensor nodes / of a
subset of nodes to one reference clock (e.g. equipped with GPS
receivers)
• It allows to synchronize the whole network, parts of it and it also
supports post-facto synchronization
• It considers only phase shifts and does not try to correct different
drift rates
• Two components:
– pairwise synchronization: based on sender/receiver technique
– networkwide synchronization: minimum spanning tree
construction with reference node as root
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LTS – Pairwise Synchronization
i
j
Trigger resynchronization
Format synch packet
Timestamp packet with
Hand over packet for transmission
Operating system,
channel access
Start packet transmission
Propagation delay
Packet transmission time
Packet reception interrupt
Timestamp with
Format synch answer packet
Timestamp with
Hand over packet
for transmission
OS, Channel access
Start packet transmission
Packet reception interrupt
Timestamp with
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LTS – Pairwise Synchronization
• Node i wants to synchronize its clock to node j’s clock
• Timeline:
– Node i triggers resynchronization at time t0, formats packet,
timestamps it at t1 with Li(t1) and hands it over to transmission
(with Li(t1) as payload)
– At t2 the first bit appears on the channel, at t3 the receiver
receives last bit, packet reception is signaled at t4, and at t5 node
j timestamps it with Lj(t5)
– Node j formats answer packet, timestamps it at time t6 with Lj(t6)
and hands it over for transmission – as payload the timestamps
Li(t1), Lj(t5) and Lj(t6) are included
– The arrival of the answer packet is signaled at time t7 to node i,
and i timestamps it afterwards with Li(t8)
• After time t8, node i possesses four values: Li(t1), Lj(t5), Lj(t6) and
Li(t8) and wants to estimate its clock offset to node j – but how?
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LTS – Pairwise Synchronization
• Assumptions:
– Node i’s original aim is to estimate the true offset O=D(t1)=Li(t1) – Lj(t1)
– During the whole process the drift is negligible
 the algorithm in fact estimates D(t5) and assumes D(t5) = D(t1)
– Propagation delay t the same in both directions, request and answer
packets have duration tp, both parameters are known to i
• Approach:
– Node i estimates D(t5)=Li(t5)-Lj(t5) and therefore needs to estimate Lj(t5),
which is generated “somewhere” between t1 and t8
– When t8 – t1 is very small, we might be willing to approximate O Li(t1) –
Lj(t5) or as Li(t8) – Lj(t5)
• But we can reduce uncertainty:
– after t1 we have at least one propagation delay and packet transmission
time (for the request packet)
– before t8 we have another propagation delay and packet transmission
time (for the response packet)
– There passes also time between Lj(t5) and Lj(t6), and Li(t5) must be
before this interval
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LTS – Pairwise Synchronization
• Under the assumption that the remaining uncertainty is allocated
equally to both i and j, node i can estimate Lj(t5) as
• This means:
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LTS – Pairwise Synchronization -- Discussion
• Node i can figure out the offset to node j based on the known values
Li(t1), Lj(t5), Lj(t6), Li(t8)
• This exchange takes two packets – if node j should also learn about
the offset, a third packet is needed from i to j carrying O
• The uncertainty is in the interval
I = [Li(t1)+t+tp, Li(t8) - t – tp – (Lj(t6) – Lj(t5)],
and by picking the mid-point of the interval as Li(t5), the maximum
uncertainty is |I|/2
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LTS – Pairwise Synchronization -- Discussion
• Sources of inaccuracies:
–
–
–
–
MAC delay
interrupt latencies upon receiving packets
Delays between packet interrupts and timestamping operation
Delay in operating system and protocol stack
• Improvements:
– Let i timestamp its packet after the MAC delay, immediately before
transmitting the first bit
– This would remove the uncertainty due to i’s operating system / protocol
stack and the MAC delay!!
– Let j timestamp receive packets as early as possible, e.g. in the
interrupt routine
– this removes the delay between packet interrupts and timestamping from
the uncertainty, and leaves only interrupt latencies
 these things are hard to do when COTS hardware is used, but easy
when full source code of MAC and direct access to hardware are
available
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LTS – Pairwise Synchronization – Error Analysis
•
•
Elson et al measured pairwise
differences in timestamping
times at a set of receivers when
timestamping happens in the
interrupt routine (Berkeley
motes)
Estimated distribution:
– normal random variable (rv) with
zero mean/stddev of 11.1 ms
•
•
Additional assumption: uncertainty on the transmitter side has
same distrib. and is independent
Hence:
– total uncertainty is a zero-mean
normal rv with variance 4 s2
– For a normal rv 99% of all
outcomes have maximum
distance of 2.3s to mean
 the maximum synchronization
error is with 99% probability
smaller than 2.3 * 2 * s
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LTS – Networkwide Synchronization
• We are given one reference node R, to which all other nodes / a
subset of nodes want to synchronize
– R’s direct neighbors (level-1 neighbors) synchronize with R
– Two-hop (level-2) neighbors synchronize with level-1 neighbors
– ....
• This way a spanning tree is created
• But one should not allow arbitrary spanning trees:
– Consider a node i with hop distance hi to the root node
– Assume that:
– all synchronization errors are independent
– all synch errors are identically normally distributed with zero
mean and variance 4s2
– Then node i’s synchronization error is a zero-mean normal rv
with variance hi 4 s2
– Hence, a minimum spanning tree minimizes synchronization
errors
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LTS – Centralized Multihop LTS
• Reference node R triggers construction of a spanning tree, it first
synchronizes its neighbors, then the first-level neighbors
synchronize second-level neighbors and so on
• Different distributed algorithms for construction of spanning tree can
be used, e.g. DDFS, Echo algorithm
• Communication costs:
– Costs for construction of spanning tree
– Synchronizing two nodes costs 3 packets,
synchronizing n nodes costs 3n packets
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LTS – Distributed Multihop LTS
• No explicit construction of spanning tree needed, but each node
knows identity of reference node(s) and routes to them
• When node 1 wants to synchronize with R, an appropriate request
travels to R – following this, 4 synchronizes to R, 3 synchronizes to
4, 2 synchronizes to 3, 1 synchronizes to 2
– By-product: nodes 2, 3, and 4 are synchronized with R
1
2
3
5
4
7
R
8
6
• Minimum spanning tree constructed implicitly: node 1 should know
shortest route to the closest reference node
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LTS – Distributed Multihop LTS -- Variations
• When node 5 wants to synchronize with R, it can:
– issue its own synchronization request using route over 3, 4 and
put additional synchronization burden on them
– ask in its local neighborhood whether someone is synchronized
or has an ongoing synchronization request and benefit from that
later on
– Enforce usage of path over 7, 8 (path diversification) to also
synchronize these nodes
• Discussion:
– Simulation shows that distributed multihop LTS needs more
packets (between 40% and 100%) when all nodes have to be
synchronized, even with optimizations
– Distributed multihop LTS allows to synchronize only the
minimally required set of nodes  post-facto synchronization
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Other Sender-/Receiver-based Protocols
• These protocols work similar to LTS, with some differences in:
– Method of spanning tree construction
– How and when to take timestamps
– How to achieve post-facto synchronization
• One variant: TPSN (Timing-Sync Protocol for Sensor Nets)
– Pairwise-protocol similar to LTS, but timestamping at node i happens
immediately before first bit appears on the medium, and timestamping
at node j happens in interrupt routine
– Spanning tree construction based on level-discovery protocol:
– root issues level_discovery packet with level 0
– neighbors assign themselves level 1 + level value from level_discovery
– neighbors wait for some random time before they issue level_discovery
packets indicating their own level
– Nodes missing level_discovery packets for long time ask their neighborhood
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Roger Wattenhofer68
– 9/68
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8: –Time
Overview
•
•
•
•
The time synchronization problem
Protocols based on sender/receiver synchronization
Protocols based on receiver/receiver synchronization
Summary
SS 05
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Roger Wattenhofer69
– 9/69
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8: –Time
Overview
•
•
•
•
The time synchronization problem
Protocols based on sender/receiver synchronization
Protocols based on receiver/receiver synchronization
Summary
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Roger Wattenhofer70
– 9/70
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Summary
• Time synchronization is important for both WSN applications and
protocols
• Using hardware like GPS receivers is typically not an option, so
extra protocols are needed
• Post-facto synchronization allows for time-synchronization on
demand, otherwise clock drifts would require frequent resynchronization and thus a constant energy drain
• Some of the presented protocols take significant advantage of WSN
peculiarities like:
– small propagation delays
– the ability to influence the node firmware to
timestamp outgoing packets late, incoming
packets early
• Of course, there are many, many more schemes ....
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