Neeraj Jaggi - Witchita State University - Wichita State University

Rechargeable Sensor Activation under
Temporally Correlated Events
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Neeraj Jaggi
Joint work with
Koushik Kar (Rensselaer Polytechnic Institute) and
Ananth Krishnamurthy (Univ. of Wisconsin Madison)
WICHITA STATE UNIVERSITY
Wichita, KS

Outline
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• Sensor Networks
• Rechargeable Sensor System
◦ Design of energy-efficient algorithms
◦ Activation question – Single sensor scenario
• Temporally correlated event occurrence
◦ Perfect state information
Optimal policy
◦ Imperfect state information
Structure of optimal policy
Practical algorithm with performance guarantees
Neeraj Jaggi Dept of EECS Wichita State University

• Sensor Nodes
◦ Tiny, low cost devices
◦ Prone to Failures
◦ Redundant Deployment
◦ Rechargeable Sensor Nodes
• Range of Applications
• Important Issues
◦ Energy Management
◦ Quality of Coverage
Sensor Networks
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Neeraj Jaggi Dept of EECS Wichita State University

Rechargeable Sensor System
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Event Phenomena
Renewable Energy
Randomness
Spatio-temporal Correlations
Control
Rechargeable Sensors
Discharge
Recharge
Activation Policy
Quality of Coverage
Neeraj Jaggi Dept of EECS Wichita State University

Dynamic Sleep Scheduling
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• How should a sensor be activated (“switched on”)
dynamically so that the quality of coverage is
maximized over time ?
• A sensor became ready. What should it do ?
◦ Activate itself now :
Gain some utility in the short-term
◦ Activate itself later :
No utility in the short term
Activate when the system “needs it more”
Neeraj Jaggi Dept of EECS Wichita State University

Temporal Correlations
• Goal – Try to detect certain interesting events
• Correlated Event Process (e.g. Forest fire)
◦ On period (events occurring)
Region is HOT
◦ Off period (events not occurring)
Region is COLD
◦ Correlation probabilities
on off
p c
p c
0.5 < ( , ) < 1
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( = = 0.8)
• Performance Criteria – Single Sensor Node
◦ Fraction of Events Detected over time
on
p c
off
p c
Neeraj Jaggi Dept of EECS Wichita State University

Sensor Energy Consumption Model
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• Discrete Time Energy Model
◦ Operational Cost (δ 1 )
◦ Detection Cost (δ 2 )
◦ Recharge Rate (qc)
sensor activated
K
δ 1 +δ 2
discharge - On period
• System Parameters
◦ Recharge – Bernoulli
c w.p. q
0 otherwise
qc
recharge
◦ Discharge – Depends upon
Event occurrence (Random)
discharge - Off period
activation policy
sensor not activated
(no discharge)
Activation decisions (Policy)
Neeraj Jaggi Dept of EECS Wichita State University
δ 1

System Observability
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• Perfect State Information (Completely Observable)
◦ Sensor can always observe state of event process (even
while inactive)
• Imperfect State Information (Partially Observable)
◦ Inactive sensor can not observe current state of event
process
Neeraj Jaggi Dept of EECS Wichita State University

Approach/Methodology
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• Perfect State Information
◦ Formulate Markov Decision Problem (MDP)
◦ Upper Bound on Performance
◦ Optimal Policy
• Imperfect State Information
◦ Formulate Partially Observable MDP (POMDP)
◦ Transform POMDP to equivalent MDP (Known techniques)
◦ Structure of Optimal Policy
◦ Near-optimal practical Algorithms
Neeraj Jaggi Dept of EECS Wichita State University

Perfect State Information
• Markov Decision Process (Finite K)
◦ State Space = {(L, E); 0 ≤ L ≤ K, E є [0, 1]}
L – Current Energy Level, E – On/Off period
Reward r– one if event detected; zero otherwise
Action u є [0, 1]; Transition probabilities p
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• Optimality equations (average reward criteria)
◦ h* – state variables
◦ λ* – optimal reward
Neeraj Jaggi Dept of EECS Wichita State University

Perfect State Information (contd.)
• Approximate Solution
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◦ Closed form solution for h* does not seem to exist
• Value Iteration
◦ Activation Algorithm
When L

Performance Bound
• Upper Bound on achievable performance for any
stationary policy (Infinite K)
◦ Have to consider “low recharge rate” and “high recharge
rate” cases separately
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◦ Useful observation to derive the bounds
Success probability for event detection is upper bounded by
on
p c
OR (Event predictability is upper bounded by )
on
p c
Neeraj Jaggi Dept of EECS Wichita State University

Optimal Activation Policy
• Optimal policy structure
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◦ Activate when events are occurring
◦ Activate with a probability when events are not occurring
P* is directly proportional to the recharge rate
Attains Energy Balance
Average recharge rate equals average discharge rate in steady state
Neeraj Jaggi Dept of EECS Wichita State University

• Difficulty
Imperfect State Information
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◦ State partially observable when sensor is inactive – (L , E )
• Partially Observable Markov Decision Process
◦ Is converted to a completely observable MDP
With a transformed state space of the form (L, E, t)
◦ Information available while decision making
L – Current Energy Level
E – State of event process last observed (while in active state)
t – Number of time slots spent in inactive state
◦ Optimal policy
Can now be computed numerically using value iteration
Optimal actions do not seem to have a closed form expression
Neeraj Jaggi Dept of EECS Wichita State University

Structure of Optimal Policy
• Optimal actions computed using value iteration algorithm
◦ Threshold energy wakeup functions
f 0 – (L, 0, t), f 1 – (L, 1, t)
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◦ Properties
Last observed state ON
Aggressive Wakeup
Last observed state OFF
Reluctant Wakeup
◦ Sensitive to system parameters
◦ Convergence of f 0 and f 1
Effects of temporal correlations diminish over time
Neeraj Jaggi Dept of EECS Wichita State University

Near-Optimal Policies
• AW (Aggressive Wakeup) Policy
◦ Activate whenever sufficient energy available L ≥ δ 2 + δ 1
◦ Ignores temporal correlations
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◦ Optimal if no temporal correlations
• CW (Correlation dependent Wakeup) Policies
◦ Activate during On periods; Deactivate during Off
◦ Employ an appropriate sleep duration
Performance depends upon sleep duration
◦ Upper Bound U * CW =
◦ Best CW policy performance
ε-optimal (ε ~ O(1/β)); β = δ 2 /δ 1
Neeraj Jaggi Dept of EECS Wichita State University

EB-CW Policy
• Energy balancing CW policy
◦ Sleep Interval (SI*)
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Derived using energy balance during a renewal interval [t 1 t 2 ]
A A A A A A
Y Y Y Y Y N
I
SI
I
A A A A
Y Y Y N
I
A – Active
I – Inactive
Y – On, N – Off
SI – sleep duration
t 1 , t 2 – renewal
instances
• Coupled equations
◦ Fixed point exists
t 1
t 2
t
Neeraj Jaggi Dept of EECS Wichita State University

Simulation Results
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[δ 1 = c = 1, δ 1 = 6, q = 0.5, K = 2400]
on off
[ = 0.6, = 0.9, SI * on off
p = 7] [ = 0.7, = 0.8, SI * c
pc
= 18]
Energy balancing Sleep Interval SI*
Neeraj Jaggi Dept of EECS Wichita State University
p c
p c

Summary and Contributions
• We considered sensor node activation scheduling problem
in a stochastic optimization framework
• Finding optimal policy is difficult and closed form
expressions may not exist
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• Policies based upon the notion of energy balance perform –
◦ Optimally for Perfect State Information
◦ Near-optimally for Imperfect State Information
5 th International Symposium on Modeling and Optimization in Mobile
Ad hoc and Wireless Networks (WIOPT) April 2007
ACM/KLUWER Wireless Networks 2008 (Accepted )
Neeraj Jaggi Dept of EECS Wichita State University

Open Questions
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• EB CW Policy performance
◦ Is it optimal over all stationary policies ?
◦ Simulation results in test cases seem to suggest so.
• Extensibility to general network scenario
◦ Presence of multiple sensors
Neeraj Jaggi Dept of EECS Wichita State University

Q & A
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THANK YOU !!
Neeraj Jaggi Dept of EECS Wichita State University