Optimal QoS-aware Sleep/Wake Optimal QoS-aware Sleep/Wake Scheduling for Time Synchronized Scheduling for Time Synchronized

Sensor NetworksSensor Networks

CISS 06

Yan Wu, Sonia Fahmy, Ness B. ShroffCenter for Wireless Systems and

Applications(CWSA)Purdue University

Wireless Sensor Networks Application specific networks

– Habitat monitoring, military surveillance etc

– Sensor Nodes• Unattended during their life cycle• Limited in processing/communication

capabilities• Constrained in battery life time

One large application class: Continuous Monitoring– Examples: habitat monitoring, civil

structure maintenance– Nodes monitor the environment and

periodically upload sensing data to a Base Station

– Duty cycle is usually low– Clustering is often used [1]

• Nodes in the same neighbourhood elect a cluster head (CH)• 2-step communication: intra-cluster and inter-cluster

Cluster Head (CH) is heavily utilized– To extend the lifetime of the CH

• Re-clustering – extensively investigated• Sleep/wake scheduling – our interest

– Idle energy is significant for low duty cycle networks– Turn off the CH radio when no transmissions– Wake it up right before transmissions occur– Good match with periodic traffic pattern

[1] S. Tilak, N. B. Abu-Ghazaleh, and W. Heinzelman. A taxonomy of wireless micro-sensor network models. ACM Mobile Computing and Communication Review, April 2002.

Continuous Monitoring Applications

Under periodic traffic pattern – If time synchronization is perfect Sleep/wake scheduling of CH will

be trivial – Most previous sleep/wake scheduling work assumes perfect

synchronization--This assumption is not always true!– Existing synchronization protocols[2] achieve precise (µs)

synchronization immediately after exchange of synchronization messages

– But clock drifts away as time progresses• E.g., two nodes exchange a message every 5 minutes• Motes datasheet: max clock skew = 100ppm• After 5 minutes, clock disagreement = 30ms• Larger than message transmission time in sensor networksSynchronization error is non-trivial!

[2] J. Elson, L. Girod, and D. Estrin. Fine-Grained Network Time synchronization Using Reference Broadcasts. In Proceedings of OSDI, 2002.

Motivation

Environment– Continuous monitoring applications with periodic

transmissions– Network has already been clustered using some

existing clustering algorithm.

Problem– Cluster Head (CH) is heavily utilized– Goal: save energy for CH via sleep/wake scheduling

Difficulty– Trivial if synchronization is perfect– But in practice synchronization is imperfect and

synchronization error is non-negligible

Motivation (summary)

Sleep/wake scheduling with consideration of synchronization error

Outline

Motivation Review Time Synchronization System model Problem definition Solution Conclusions and future work

Why are clocks different from each other? – Phase offset: clock disagreement at a given time instant– Clock skew: clocks run with different speed

– May slowly change over timeSynchronization is to estimate phase offset and clock

skew– Mechanism -- exchange messages to synchronize

Example: one node sends a message to another Uncertainty: sender (random backoff), receiver

(PHY/MAC layer) Random Estimation Error Many synchronization protocols try to reduce the

uncertainty RBS[2]/TPSN[3]

[2] J. Elson, L. Girod, and D. Estrin. Fine-Grained Network Time synchronization Using Reference Broadcasts. In Proceedings of OSDI, 2002.

[3] S. Ganeriwal, R. Kumar, and M. Srivastava. Timing-sync Protocol for Sensor Networks. In Proceedings of ACM SenSys, November 2003.

Time Synchronization

System Model

Time is divided into epochs– Epoch = Synchronization interval + Transmission interval

. . .

CH

Ts

n1

Ts+T/M Ts+2*T/M

n2 . . .

Ts+T

nM

Ts+T+T/M

n1 . . .

Te

A single cluster with a CH and M members: n1, …nM

Each member uploads to the CH every T seconds

System Model

Assumptions– Neighbouring clusters use orthogonal frequency

channels– Focus on intra-cluster communications– Clock skew and phase offset are constant over each

epoch– Only account for communication energy

Synchronization Scheme in This Work– Adopt the widely used RBS[2] synchronization scheme– RBS Procedure

• Exchange sync. messages to obtain multiple corresponding time pairs

• Use linear regression to estimate clock skew and phase offset

RBS Synchronization Scheme

– C: time of CH, tx : time of member x– a/b: clock skew/phase offset– a’/b’: estimation of a/b

• Recall that clock skew and phase offset are constant over an epoch– For a given epoch, tx = a×C + b

• RBS– Obtain Ns corresponding time pairs (txi, Ci) i=1…Ns

txi = a×Ci + b + ei, ei: random error» System measurements show that ei is normally

distributed » Chi-square test, 99.8% confidence level

– Use linear regression to estimate a and b• The existence of ei causes estimation error: (a’, b’) ≠(a, b)

Outline

Motivation

Review Time Synchronization

System model

Problem definition

Solution

Conclusions and future work

Problem Definition• CH and the member x agree upon a message send time t (CH

clock)• x should transmit at t by CH clock (scheduled send time)

• x coverts t into its own clock: tx = a’× t + b’ and transmits at tx• The actual send time is tx (x’s clock), express it using CH clock

τ = (tx – b)/a = a’/a × t + (b-b’)/aIf there is no estimation error, (a’, b’)=(a, b), then τ =tBut there exists random estimation error, so τ ≠ t Because of estimation error, message may not be sent at scheduled

time.

– How does the CH combat the estimation error?• Uses a wake up interval to “capture” the message

t

Scheduled Msg Arrival

Actual Msg Arrival

( )Wake Sleep

Question: how early should the CH wake up and how long should it stay active? – wakes up early and stays up long -- wastes energy– wakes up late and stays up short -- miss msg.

Trade-off between energy consumption and message capture probability!

– Guarantee a minimum message capture probability th

– Minimize the expected energy consumption

Problem Definition

Sleep/wake scheduling – considering sync. error– Minimize the expected energy consumption under

constraint on capture probability

Minimize:

such thatwhere:w: wake up times: sleep timeτ: actual message arrival timel: message lengthR: data rate : idle/receiving power : Probability Density Function of τth: QoS parameter

,)(}){()},({)( dxxfRlwxswPws rI

s

wI ,)},({ thswP

rI /)(xf

Problem Definition

Outline

Motivation

Review Time Synchronization

System model

Problem definition

Solution

Conclusions and future work

Solution Sketch)(xf Computing PDF

τ = a’/a × t + (b-b’)/a– a’/b’ are computed from standard Linear Regression– sync. error is Normal τ is also Normal

E(τ) = t, VAR(τ) ])(

)(1[ 2

2

2

2

CC

CtNa is

e

Solution Sketch

rI

yx

II RlyQxQeexyQxQxyyQxQyxF

)]()([][

21)]()([))](()(1[),( 22

22

thyQxQ )()(

Put the PDF into the formulation– Change of variable: x=[w-E(τ)]/στ, y =[s-E(τ)]/στ – Minimize:

such that

Non-convex optimization problem– Compute the Hessian Matrix– Cannot directly solve it using conventional

techniques

Solution Sketch

Proposition: optimal solution satisfies Q(x)-Q(y) = th– Meaning: optimum is achieved when

capture_probability=th

Put this result into F(x,y)rI

yx

II RlyQxQeexyQxQxyyQxQyxF

)]()([][

21)]()([))](()(1[),( 22

22

rI

yx

II Rltheexthxyth

][

21))(1( 22

22

Simplified Formulation

Minimize

such that

Solve the simplified formulation– Proposition: G”(x) >0

Proof: Implicit Differentiation and Mean Value Theorem

– The simplified formulation is convex

)(21)()1()( 2

)(2

22 xyx

eexxythxG

))(()(),( 11 thxQQxythQx

Performance Evaluation

A previous scheme to combat sync. error– Assume an upper bound on the clock

disagreement and use it as a guard time

Simulation results– In order to guarantee the same capture

performance, the energy consumption of our scheme is 20-40% less than the previous scheme

So far– Assumed capture probability threshold th is already given– Extension -- How to assign th for different nodes n1, … nM?•Uniform assignment: assign same value to all nodes

– Problem: heterogeneity among nodes» Some nodes: expensive high-precision

thermometer» Others: cheap low-precision thermometer

Differentiated Assignment

Conclusions This work

– Studied sleep/wake scheduling in clustered networks– Identified the impact of sync. error on sleep/wake

scheduling– Proposed an optimal sleep/wake scheduling scheme

with consideration for sync. error– Simulations validate the effectiveness of our scheme

Future work– This work

• Focus on intra-cluster communications (memberCH)

• CH Base Station?– Future work

• Inter-cluster communications -- Multi-hop

RBS Receiver-receiver synchronization Nodes A and B want to synchronize with each other Requires an additional beacon node C

Procedure– Beacon Node send reference beacons to A and B– A and B record the arrival time of the beacon, tA and tB– A and B compare the arrival times

Properties– Removes completely randomness caused by the

sender– Leaves only one source of error – receiver

Clock skew

crystal oscillator– expected frequency: the frequency that it should

work. – actual frequency: might differ from expected

frequency. • Accuracy: <100 ppm

Decided by manufacturing imprecision and aging effect Affected by environment factors like variations in

temperature, humidity etc. – Slow changing– For off-the-shelf oscillator, clock skew < 100pm

Transmission Error

Not considered in the current formulation– During cluster construction, nodes will select nearby

CH• Error probability should not be very large

– In case of transmission error, our scheme is still robust• Prob(receive) = Prob(capture) * (1-Pe)

Adaptive adjustment of the wake up interval

Idea: a message not received synchronization is wrong adjust the wake up interval for next message– Implicit assumption: message not received is only

caused by wrong synchronization– Not necessarily true: message not received might

also be caused by transmission error

Retransmission

No retransmissions– Retransmissions need acknowledge mechanism, cost

energy– Sensor networks usually deployed with redundancy

CH and member x– The difference between them is 10 minutes.– They estimate the difference to be 10 minutes – CH tells x: “Send the message to me at 6pm.”– x will compute: ”CH’s 6pm is my 6:10” and send at

6:10pm (by its own clock)

– Now suppose their difference is 10 minutes, but they estimate the difference to be 9 minutes.

– X will compute: “CH 6pm is my 6:09”transmit at 6:09 by its own clock 6:09 in x is 5:59pm in CH, not 6pm in CH!

Problem definition