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Optimal QoS-aware Sleep/Wake Scheduling for Time Synchronized Sensor Networks. CISS 06. Yan Wu, Sonia Fahmy, Ness B. Shroff Center for Wireless Systems and Applications(CWSA) Purdue University. Application specific networks Habitat monitoring, military surveillance etc Sensor Nodes - PowerPoint PPT Presentation
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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
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