Chapter 6 Time Synchronization

Chapter 6Time Synchronization

Outline 6.1. The Problems of Time Synchronization 6.2. Protocols Based on Sender/Receiver Synchronization

Network Time Protocol (NTP) Timing-sync Protocol for Sensor Networks (TPSN) Flooding Time Synchronization Protocol (FTSP) 6.2.4. Ratio-based time Synchronization Protocol (RSP)

6.3. Protocols Based on Receiver/Receiver Synchronization Reference Broadcast Synchronization (RBS) Hierarchy Referencing Time Synchronization (HRTS)

6.4. Summary

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6.1 The Problems of Time Synchronization Why Need for Time Synchronization?

Many of the applications of WSN needs the event with time stamp

Ordering of the samples for reporting Events are reported by multiple nodes When WSN is energy save enabled, it need all nodes to be

in sync in order to be in Idle or Active mode Medium Access Layer (MAC) Scheduling (ex: TDMA) Order of messages may change while transmission

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Sources of Inaccuracies A local software clock of node i at time t Li(t) = i Hi(t) + i

Hi(t): hardware clock of node i at time t i :clock drift rate of node i i :phase shift of node i

Actual oscillators have random deviations from nominal frequency (drift, skew) additional pulses or lost pulses over the time of one million

pulses at nominal rate Oscillator frequency is time variable

Long-term variation: oscillator aging Short-term variation: environment (temperature, pressure,

supply voltage, ...)4 112/04/24

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 neighborhood?

Absolute vs. relative time Only accurate time difference Sufficient to estimate the drift instead of phase offset

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General Properties of Time Synchronization Algorithms 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: is triggered by an external event

Deterministic vs. stochastic precision bounds Local clock update discipline

No backward jumps of local clocks No sudden jumps

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Performance Metrics and Fundamental Structure Metrics:

Precision: maximum synchronization error for deterministic algorithms, mean error /stddev /quantiles for stochastic ones

Energy costs, e.g. # of exchanged packets, computational costs

Memory requirements Fault tolerance:

what happens when nodes die?

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Fundamental Building Blocks of Time Synchronization Algorithms Resynchronization event detection block:

when to trigger a time synchronization round? 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

remote clock estimation Synchronization mesh setup block:

figure out which node synchronizes with each other in a multihop network

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Constraints for Time Synchronization in WSNs Scale to large networks of unreliable nodes Quite diverse precision requirements,

from ms to tens of seconds Use of extra hardware is mostly not an option Low mobility Often there are no fixed upper bounds on packet

delivery delay Negligible propagation delay between neighboring

nodes is negligible Manual node configuration is not an option

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6.2 Protocols Based on Sender/Receiver Synchronization In this kind of protocols, a receiver synchronizes to the

clock of a sender The classical Network Time Protocol (NTP) belongs

to this class We have to consider two steps: Pair-wise

synchronization How does a single receiver synchronize to a single

sender? Network wide synchronization

How to figure out who synchronizes with whom to keep the whole network / parts of it synchronized?

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Network Time Protocol (NTP) Synchronizing Physical Clocks

Computer Clocks in distributed system not in consistent Need to synchronize clocks

External synchronization (ES) Synchronized with an external reliable time source S |S - C| < D, where C is computer’s clock

Internal synchronization (IS) Synchronized with other computer in the distributed system | Ci - Cj| < D

IS does not imply ES Clock Ci and Cj may drift together

ES implies IS Within bound 2D

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Network Time Protocol (NTP) Distributed System Type

Synchronous distributed system Known upper bound on transmission delay Simplifies synchronization One process p1 sends its local time t to process p2 in a

message m p2 could set its clock to t + Ttrans , where Ttrans is

transmission delay from p1 to p2 Ttrans is unknown but min ≤ Ttrans ≤ max Set clock to t + (max - min)/2 then skew ≤ (max - min)/2

Asynchronous distributed system Internet is asynchronous system Ttrans = min + x where x ≥ 0

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Network Time Protocol (NTP) Cristian’s method (1989) for an asynchronous system A time server S receives signals from a Coordinated Universal

Time (UTC) source Process p requests time in mr and receives t in mt from S p sets its clock to t - Tround/2 Accuracy ± (Tround/2 - min) :

because the earliest time S puts t in message mt is min after p sent mr. the latest time was min before mt arrived at p the time by S’s clock when mt arrives is in the range [t + min, t + Tround

- min] Tround is observed round-trip time min is minimum delay between p and S mr

mtp Time server S 112/04/2413

Network Time Protocol (NTP) Issues with Christian’s Algorithms

A single time server might fail, so they suggest the use of a group of synchronized servers

It does not deal with faulty servers No authentication mechanism

Inaccuracy increases if the delay between messages is non-negligible

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Network Time Protocol (NTP) A time service for the Internet - synchronizes clients

to UTC (Coordinated Universal Time)

1

2

3

2

3 3

Reliability from redundant paths, scalable, authenticates time sources

Primary servers are connected to UTC sourcesSecondary servers are synchronized to primary servers

Synchronization subnet - lowest level servers in users’ computers

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Network Time Protocol (NTP) Synchronisation of servers

The synchronization subnet can reconfigure if failures occur, e.g. a primary that loses its UTC source can become a secondary a secondary that loses its primary can use another primary

Modes of synchronization: Multicast

A server within a high speed LAN multicasts time to others which set clocks assuming some delay (not very accurate)

Procedure call A server accepts requests from other computers (like Cristiain’s algorithm).

Higher accuracy. Useful if no hardware multicast. Symmetric

Pairs of servers exchange messages containing time information Used where very high accuracies are needed (e.g. for higher levels) 112/04/2416

Network Time Protocol (NTP) Messages exchanged between a pair of NTP peers

All modes use UDP Each message bears timestamps of recent events:

Local times of Send and Receive of previous message Local times of Send of current message

Recipient notes the time of receipt ( we have Ti-3, Ti-2, Ti-1, Ti) In symmetric mode there can be a non-negligible delay between messages

Ti

Ti-1Ti-2

Ti-3

Server B

Server A

Time

m m'

Time112/04/2417

Network Time Protocol (NTP) Accuracy of NTP

For each pair of messages between two servers, NTP estimates an offset oi between the two clocks and a

delay di (total time for the two messages, which take t and t’)

Ti-2 = Ti-3 + t + o and Ti = Ti-1 + t’ - o This gives us (by adding the equations) :

di = t + t’ = Ti-2 - Ti-3 + Ti - Ti-1 Also (by subtracting the equations)

o = oi + (t’ - t )/2 where oi = (Ti-2 - Ti-3 + Ti-1 - Ti)/2 Using the fact that t, t’ >0 it can be shown that

oi - di /2 ≤ o ≤ oi + di /2 . Thus oi is an estimate of the offset and di is a measure of the

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Network Time Protocol (NTP) Techniques to Improve Accuracy

NTP servers filter pairs <oi, di>, estimating reliability from variation, allowing them to select peers High variability in successive pairs implies unreliable data

Accuracy depends on the delay between the NTP servers Accuracy of 10s of millisecs over Internet paths (1 on

LANs) Peer selection

Lower layer peer favoured over higher layer server Peer with lower synchronization imprecision is preferred Synchronization imprecision is the sum of variability in

data from the server to the root

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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)

Considers only phase shifts Does not try to correct different drift rates

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LTS – Lightweight Time Synchronization

Two components: Pair-wise synchronization:

based on sender/receiver technique Network wide synchronization:

Minimum-height spanning tree construction with reference node as root

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i j

Trigger resynchronization

Format synch packet

Timestamp packet with

Hand over packet for transmission

Start packet transmission

Operating system, channel access

Propagation delay

Packet transmission time

Packet reception interrupt

Timestamp with

Timestamp with

Format synch answer packet




Timestamp with

OS, Channel access

22

LTS – Pairwise Synchronization

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LTS – Pair-wise Synchronization

Assumptions: Node i’s original aim is to estimate the true offset

O = Δ(t1) = Li(t1) – Lj(t1), where Li(tj) is the local software clock of node i at time tj

During the whole process the drift is negligible the algorithm in fact estimates Δ(t5) and assumes

Δ(t5) = Δ(t1)

There is one propagation delay τ and one packet transmission delay tp between nodes i and j

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i j


Format synch packet





Propagation delay



Timestamp with

Timestamp with





Timestamp with

OS, Channel access

24

Li(t5)

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i j


Format synch packet





Propagation delay



Timestamp with

Timestamp with





Timestamp with

OS, Channel access

25

t5 >= t1+ τ +tp

where τ :propagation delay

tp :packet transmission time

Li(t5)

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i j


Format synch packet





Propagation delay



Timestamp with

Timestamp with





Timestamp with

OS, Channel access

26

t5 <= t8- τ- tp

where τ :propagation delay

tp :packet transmission time

Li(t5)

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i j


Format synch packet





Propagation delay



Timestamp with

Timestamp with





Timestamp with

OS, Channel access

27

The uncertainty is in the interval [Li(t1) + τ + tp, Li(t8) - τ – tp – (Lj(t6) – Lj(t5)]

Li(t5)

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Under the assumption that the remaining uncertainty is allocated equally to both i and j, node i can estimate Li(t5) as

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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


Sources of inaccuracies: Medium access delay Interrupt latencies upon receiving packets Delays between packet interrupts and time-stamping

operation Delay in operating system and protocol stack

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i j


Format synch packet





Propagation delay



Timestamp with

Timestamp with





Timestamp with

OS, Channel access

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LTS – Pair-wise Synchronization Improvements:

Let node 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 node j timestamp receive packets as early as possible,

e.g. in the interrupt routine This removes the delay between packet interrupts and

time-stamping from the uncertainty, and leaves only interrupt latencies

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LTS – Pairwise Synchronization – Error Analysis

32

Pair-wise difference in packet reception time (μsec)

Num

ber of trials

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LTS – Networkwide Synchronization

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 Hence, a minimum spanning tree minimizes

synchronization errors

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Timing-sync Protocol for Sensor Networks (TPSN) Introduction

We present a Timing-sync Protocol for Sensor Networks (TPSN) that works on the conventional approach of sender-receiver synchronization

Pair-wise-protocol: time-stamping at node i happens immediately before first bit appears on the medium, and time-stamping at node j happens in interrupt routine

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Timing-sync Protocol for Sensor Networks (TPSN) Network Model

The network is “always-on” Every node maintains 16-bit register as clock Sensor has unique ID Build hierarchical topology for the network Node at level i can connect with at least one node at level i-1

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Timing-sync Protocol for Sensor Networks (TPSN) Level discovery Phase

Trivial Synchronization Phase

Pair-wise sync is performed along the edge of hierarchical structure

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Timing-sync Protocol for Sensor Networks (TPSN) Level discovery Phase

The root node is assigned a level 0 and it initiates this phase by broadcasting a level_discovery packet

level_discovery packet contains the identity and the level of the sender

The immediate neighbors of the root node receive this packet and assign themselves a level (level = level +1)

This process is continued and eventually every node in the network is assigned a level. On being assigned a level, a node neglects any such future packets. This makes sure that no flooding congestion takes place in this phase

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Timing-sync Protocol for Sensor Networks (TPSN) Synchronization Phase

T1: A is sender, starting sync by sending synchronization_pulse packet to B

T2 = T1 + Δ + d, where Δ is the clock offset d is propagation delay

T3: B replies acknowledgement containing T1, T2, T3

T4: A receive ack. and T4 = T3 – Δ + d. So:

Δ = [(T2 － T1) － (T4 － T3)] / 2 d = [(T2 － T1) ＋ (T4 － T3)] / 2

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Timing-sync Protocol for Sensor Networks (TPSN) Synchronization Phase

A

B

T1

T2 T1,T2,T3

T4

T1: A is sender, starting sync by sending synchronization_pulse packet to B with timestamp T1 T B receive the synchronization _pulse packet and ti2:mestamping immediately B replies acknowledgement containing T1,T2,T3

A receive an Ack and get timestamp T4

At time t1At time t4At time t2At time t3 112/04/2439

Timing-sync Protocol for Sensor Networks (TPSN) Simulation and Comparison

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Timing-sync Protocol for Sensor Networks (TPSN) Simulation and Comparison

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Flooding Time Synchronization Protocol (FTSP)

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Flooding Time Synchronization Protocol (FTSP) Introduction

The FTSP synchronizes the time to possibly multiple receivers utilizing a single radio message

Linear regression is used in FTSP to compensate for clock drift

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Flooding Time Synchronization Protocol (FTSP) Network Model

Every node in the network has a unique ID Each synchronization message contains three fields:

TimeStamp RootID SeqNum

The node with the smallest ID will be only one root in the whole network

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The root election phase FTSP utilizes a simple election process based on unique

node IDs

Synchronization phase

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Flooding Time Synchronization Protocol (FTSP) The root election phase

When a node does not receive new time synchronization messages for a number of message broadcast periods The node declares itself to be the root

Whenever a node receives a message, the node with higher IDs give up being root

Eventually there will be only one root

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Flooding Time Synchronization Protocol (FTSP) Synchronization phase

Root and synchronized node broadcast synchronization message

Nodes receive synchronization message from root or synchronized node

When a node collects enough synchronization message, it estimates the offset and becomes synchronized node

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B

C


Root

A

SynchronizedNodeUnsynchronizednode

Timestamp rootID seqNum



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Flooding Time Synchronization Protocol (FTSP) Simulation and Conclusion

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Ratio-based Time Synchronization Protocol (RSP)

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Ratio-based Time Synchronization Protocol (RSP) The RSP use two synchronization messages to

synchronize the clock of the receiver with that of sender

The RSP also can extend to multi-hop synchronization The nodes in the wireless sensor network construct a

tree structure and the root of this tree is the synchronization root

The global time of the root is flooding out to the nodes through the tree structure

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Ratio-based Time Synchronization Protocol (RSP) The local clock time of a sensor device is provided by the quartz oscillator

inside itself Transformation formula between t and Ci (t):

By (1), the local clock times of two sensor nodes i and j have the following relationship:

: the local clock time of a sensor node i.t : the Coordinated Universal Time (UTC).

: the drift ratio: the offset of node i’s clock at time t .

(2)

: relative drift ratio between nodes i and j: offset between the clocks of nodes i and j

(1)

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calculate the clock drift ratio

θ = (T3 − T1)/(T4 −T2).

Reference node

Sensor node

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Each node can estimate the local time of reference node in the following way:

Reference node

Sensor node

: the local time of sensor node:the corresponding local time of the reference node.: the initial offset between reference node and sensor node.

(3)


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It can be calculated using linear interpolation with the four time-stamps

the can be derived as follows

(4)


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Therefore, we can derive (5) from (3) and (4): Each sensor node can estimate the local time of

reference node, that is, the global time of the network

(5)


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R S

(T1)

Reference node

Sensor node

(T3)


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6.3. Protocols Based on Receiver/Receiver Synchronization

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Protocols Based on Receiver/Receiver Synchronization In this class of schemes

The receivers of packets synchronize among each other, not with the transmitter of the packet

Reference Broadcast Synchronization (RBS) Synchronize receivers within a single broadcast domain RBS does not modify the local clocks of nodes, but

computes a table of conversion parameters for each peer in a broadcast domain

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Reference Broadcast Synchronization (RBS)

Introduction Reference broadcasts do not have an explicit timestamp Receivers use reference broadcast’s arrival time as a point of

reference for comparing nodes’ clocks Receivers synchronizes with one another using the

message’s timestamp (which is different from one receiver to another)

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Reference Broadcast Synchronization (RBS) Types of errors in traditional synchronization protocol

Send time latency time spent at the sender to construct the message

Access time latency time spent at the sender to wait for access to transmit the

message Prorogation time latency

time spent by the message in traveling from the sender to the receiver

Receive time latency time spent at the receiver to receive the message from the

channel and to notify the host

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Reference Broadcast Synchronization (RBS) Types of errors in RBS

Phase error due to nodes’ clock that contains different times

Clock skew due to nodes’ clock that run at different rates

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Reference Broadcast Synchronization (RBS) Difference between RBS & Traditional

synchronization protocol RBS

Synchronizes a set of receivers with one another Supports both single hop and multi-hop networks

Traditional Senders synchronizes with receivers mostly supports only single hop networks

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Reference Broadcast Synchronization (RBS) The phase offset with the clock skew is estimated by:

Least-squares linear regression graph From the best-fit line of the graph, following can be inferred:

Slope of the line : Clock skew of the nodes’ clock Intercept of the line : Phase of the nodes’ clock

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Reference Broadcast Synchronization (RBS) Basic idea to estimate phase offset and clock skew for

non-deterministic receivers: Transmitter broadcasts m reference packets Each of the n receivers records the time that the reference

was received, according to its local clock The receivers exchange their observation Each receiver i can compute its phase offset to any other

receiver j Drift can be neglected when observations are exchanged

quickly after reference packets Drift can be estimated jointly with offset O when a number

of periodic observations of Oi,j have been collected

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i R j


Timestamp withPacket reception

interruptReceiver uncertainty

Timestamp with

Send

Send

66

Reference Broadcast Synchronization (RBS) Formula for calculating the phase offset and clock

skew of receiver r1 with another receiver r2: Let tr,b be r’s clock when it received broadcast b

for each pulse k that was received by receivers r1 and r2 , we plot a graph :

x = tr1, k

y = tr2,k – tr1,k

Diagonal line drawn through the points represents the best linear fit to the data

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Reference Broadcast Synchronization (RBS) Diagonal line minimizes the residual error (RMS) Therefore, we go for calculating the slope and

intercept of the diagonal line Time value of r1 is converted to time value of r2 by

combining the slope and intercept data obtained

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Step1: Transmitter broadcasts Step2: Receiver records its

local clock, and exchange observation

Step3:Use Least-squares linear regression to

estimate phase offset

BA

Transmitter

Receiver

Reference Packet

Reference Packet

A:Local time

B:Local time

Finish RBS

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Communication costs: Be m the number of nodes in the broadcast domain First scheme:

reference node collects the observations of the nodes, computes the offsets and sends them back 2 m packets

Second scheme: reference node collects the observations of the nodes, computes the offsets and keeps them, but has responsibility for timestamp conversions and forwarder selection m packets

70 112/04/24


Communication costs: Be m the number of nodes in the broadcast domain Third scheme: each node transmits its observation individually to the other

members of the broadcast domain m (m-1) packets Fourth scheme: each node broadcasts its observation m packets, but

unreliable delivery

71 112/04/24


Conclusion Collisions are a problem: the reference packets trigger all

nodes simultaneously to tell the world about their observations

Computational costs: least-squares approximation is not cheap!

Can be used without external timescales Does not require tight coupling between sender and its

network interface

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Hierarchy Referencing Time Synchronization (HRTS)

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Hierarchy Referencing Time Synchronization (HRTS) Goal :

Synchronize the vast majority of a WSN in a lightweight manner

Idea Combine the benefits of LTS and RBS

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Hierarchy Referencing Time Synchronization (HRTS) LTS : Lightweight Time Synchronization

Goal Synchronize the clocks of all sensor nodes of a

subset of nodes to one reference clock It considers only phase shifts and does not try to

correct different drift rates

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Hierarchy Referencing Time Synchronization (HRTS) LTS : Pairwise Synchronization

n1

Sync packet

n2

Record t2

Reply packet

Record t1Record t4 Record t3

In this packet contains t2 and t3

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LTS : Pairwise Synchronization Offset : O = Δ(t5 )=Li(t5) - Lj(t5)= [Li(t8)+ Li(t1)- Lj(t6)- Lj(t5)] / 2 Benefit : only two packet transmissions with each pair

Benefit of RBS Idea : ignore transmission delay By this idea, one packet can synchronize every node in one hop

Combining the two protocol’s benefit, the HRTS finds good solution to synchronize nodes in hierarchical way

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Timeline: Root node triggers time synchronization at t1 with timestamp LR(t1) Node i timestamps packet at time t2 with Li(t2) and node j

timestamps it at t2’ with Lj(t2’) Node i formats a packet and timestamps it at time t3 with Li(t3) –

the packet includes the values Li(t2) and Li(t3) Root node R timestamps the answer packet at time t4 with LR(t4)

and computes its offset OR,i with node i’s clock OR,i

=Li(t2) - LR(t2) = Li(t2) – (LR(t1) + LR(t4) – (Li(t3)- Li(t2))/2 =[ (Li(t2) - LR(t1)) – (LR(t4)- Li(t3))]/2

Root node R broadcasts the values OR,i and Li(t2)

80 112/04/24


The root node R can estimate the offset OR,i between its own clock and the local clock i in a similar fashion as the protocol LTS

Root R broadcast the values O and Li(t2) to all nodes Node i simply subtract the offset OR,i from its local clock Node j can compute Oj,i directly as Oj,i = Li(t2) – Lj(t’2)

and OR,j = OR,i – Oj,i

81

2))()(())()(( 3412

,tLtLtLtLO iRRi

iR

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Hierarchy Referencing Time Synchronization (HRTS)- Discussion Node j is not involved in any packet exchange by this scheme is possible to synchronize an arbitrary

number of nodes to R’s clock with only three packets!! The synchronization uncertainty comes from:

The error introduced by R when estimating OR,i

The error introduced by setting t2 = t2’ This makes HRTS only feasible for geographically small

broadcast domains

82 112/04/24

Hierarchy Referencing Time Synchronization (HRTS)- Discussion Both kinds of uncertainty can again be reduced by:

timestamping outgoing packets as lately as possible (relevant for t1 and t3)

timestamping incoming packets as early as possible (relevant for t2, t2’, t4 )

The authors propose to use extra channels for synchronization traffic when late timestamping of outgoing packets is not an option Rationale: keep MAC delay small

83 112/04/24


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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

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Summary Some of the presented protocols take significant

advantage of WSN peculiarity like: small propagation delays the ability to influence the node firmware to

timestamp outgoing packets late, incoming packets early

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References[1] Ed. Ivan Stojmenovic, Handbook of Sensor Networks Algorithms and

Architectures, 2005.[2] F. Sivrikaya,and B.Yener, Time Synchronization in Sensor Networks: A

Survey,2004. (www.cs.rpi.edu/~yener/PAPERS/WINET/timesync04.pdf)[2] J. Elson, L. Girod, and D. Estrin ,Fine-Grained Network Time Synchronization

using Reference Broadcasts. (In Proceedings of the Fifth Symposium on OSDI 2002)

[3] S. Ganeriwal, R. Kumar, and M. Srivastava, Timing-Sync Protocol for Sensor Networks. (SenSys ’03)

[5] D. L. Mills. Network Time Protocol (Version 3) Specification, Implementation and Analysis. RFC 1305, 1992.

[6] D. L. Mills. Improved Algorithms for Synchronizing Computer Network Clocks. IEEE/ACM Transactions on Networking, 3(3): 245–254, 1995.

[7] D. L. Mills. Adaptive Hybrid Clock Discipline Algorithm for the Network Time Protocol. IEEE/ACM Transactions on Networking, 6(5): 505–514, 1998.

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References[8] S. Ganeriwal, R. Kumar, S. Adlakha, and M. Srivastava. Network-Wide Time

Synchronization in Sensor Networks. Technical Report NESL 01-01-2003, Networked and Embedded Systems Lab (NESL), University of California, Los Angeles (UCLA), 2003.

[9] S. Ganeriwal, R. Kumar, and M. B. Srivastava. Timing-Sync Protocol for Sensor Networks. In Proceedings of the 1st ACM International Conference on Embedded Networked Sensor Systems (SenSys), pages 138–149, Los Angeles, CA, November 2003.

[10] Miklós Maróti , Branislav Kusy , Gyula Simon , Ákos Lédeczi, The Flooding Time Synchronization Protocol, In Proceedings of the 2ed ACM International Conference on Embedded Networked Sensor Systems (SenSys), pages 39 – 49, Baltimore, MD, USA, 2004 .

[11] J.-P. Sheu, W.-K. Hu, and J.-C. Lin, Ratio-Based Time Synchronization Protocol in Wireless Sensor Networks, Telecommunication Systems, Vol. 39, No. 1, pp. 25-35, Sep. 2008.

[12] J. Elson, L. Girod, and D. Estrin. Fine-Grained Network Time Synchronization using Reference Broadcasts. In Proceedings of the Fifth Symposium on Operating Systems Design and Implementation (OSDI 2002), Boston, MA, December 2002.

[13] H. Dai and R. Han. TSync: A Lightweight Bidirectional Time Synchronization Service for Wireless Sensor Networks. ACM SIGMOBILE Mobile Computing and Communications Review, 8(1): 125–139, 2004. 112/04/2488

Recommend Reading Particular Challenges and Constraints for Time Synchronization

Algorithms in WSN J. Elson and K. R¨omer. Wireless Sensor Networks: A New

Regime for Time Synchronization. In Proceedings of the First Workshop on Hot Topics In Networks (HotNets-I), Princeton, NJ, October 2002.

J. E. Elson. Time Synchronization in Wireless Sensor Networks. PhD dissertation, University of California, Los Angeles, CA, Department of Computer Science, 2003.

Other Time Synchronization Protocol Lightweight time synchronization protocol (LTS)

J. V. Greunen and J. Rabaey. Lightweight Time Synchronization for Sensor Networks. In Proceedings of the 2nd ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), San Diego, CA, September 2003.

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Chapter 6 Time Synchronization

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