노상훈@pllab.kut
2009. 04. 27
PLLAB@KUT
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Introduction
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CGS Algorithm
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Fault Tolerance of The CGS Algorithm
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Result
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Summary
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Background
Assumption
QoS Metrics
Algorithm
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Purpose
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Random approach
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Coordinated approach
◦ Energy conservation -> Prolong network lifetime
◦ Assign probability
◦ Awake/sleep randomly on probability
◦ Cannot ensure k-coverage
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Use “drowsiness factor” for scheduling
Centralized approach
Distributed approach
Ensure k-coverage if physically possible
Cost: network overhead and energy consumption
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CGS:Controlled greedy sleep
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Graph: G(R∪S,E)
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k-Coverage problem
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Minimal k-Coverage problem
◦ R:Range
◦ S:Sensors
◦ E:Edges
◦ subgraph problem
◦ G’(R∪S’,E’)
where S’ ⊆ S
◦ Nonredundant with
G’’(R∪S’’,E’’)
where S’’ ⊆ S
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Centralized solution
◦ A Coordinated node knows whole graph G
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Distributed solution
◦ Each node q knows itself and it’s neighbors
and covers Rq
◦ Gq(Rq∪Sq,Eq)
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Assumption 1
◦ communication radius ≥
2*sensing radius
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Assumption 2
◦ Coverage of each sensor
modeled by a sensing disk
and the radius is B
◦ Approximation of the
sensing disk by a set of
squares
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Assumption 3
◦ The sensors know their own coordinates and the
observed area Σ
◦ Reflect Maximum location error Δl
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k-coverage ratio
◦ Ak: area of the k-coverage regions
◦ A: Area of the target space Σ
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Approximation of
◦ Nk: number of the k-covered regions
◦ N: total number of regions in the target space
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k-lifetime
of a network
◦ Maximum operation time of the network with
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Drowsiness factor
◦ Energy status
◦ importance in the network
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Coverage ratio of region r
◦ cr : degree of region r in Gs
◦ positive if overcovered
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Whole sensors awaken
Drowsiness Factor
Decision Time Delay
Awake Message
List of awake
neighbors
Delay List
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Kind of Messages
◦ Hello messages
◦ DTD messages
◦ AMs
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Messages can be lost
◦ Collision
◦ Fading
◦ External disturbances
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Assume
◦ Any messages can be lost (worst case whole message)
◦ but received message is correct (error detecting coding)
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Theorem: If physically possible, the algorithm will provide
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Lost Hello Messages
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Lost DTD messages
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Lost AMs
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Lost messages cause overcoverage
◦ Prevent inclusion of neighbors to in the alive neighbor set Ss →
drowsiness factor will be unnecessarily high
◦ The DTD is higher → harmful
◦ Sender is not considered as a potential participant in the coverage
◦ Potential overcoverage
◦ Cannot rely on the presence of the senders of them
◦ Unnecessarily high number of sensors staying awake
◦ Shortening of the network lifetime
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Effect of node failure can be divide by steps
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During an awake period
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During a sleep period: No effect
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During the Hello phase
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During the DTD phase (problem!)
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Node failure generally cause
◦ Some regions will undercovered until the end of the period
◦ Next election will provide sufficient coverage
◦ CGS behavior is equivalent to the loss of Hello messages
◦ Node with higher drowsiness factor may incorrectly rely on the presence of the failed
node
◦ Shortening of the lifetime of the network
◦ Possible coverage in certain regions
and total amount of energy in the network decrease
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A out of synchronized node
◦ Wakes up while the synchronization phase is running
 Synchronize again
◦ Cannot synchronize
 Provide extra coverage in its neighborhood
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To ensure proper operation,
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Small timing errors have no effect
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In general,
◦ The synchronization period must be long enough
◦ To enable all nodes to wake up and join the synchronization
◦ On Hello/DTD messages
◦ But AM’s timing error might change priority
◦ Large timing errors cause large message delays(ultimately loss)
◦ But the algorithm is very tolerant in this respect
◦ Do not affect the provided k-coverage, still shorten the network lifetime
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Distributed algorithm proposed
◦ Solve k-coverage problems
◦ Provide prolong network time
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Proposed algorithm broadcast few messages
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CGS algorithm is robust and fault tolerant
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CGS algorithm is better than random k-coverage
algorithm
◦ Guarantees required coverage if possible
◦ Degrading curve is much gentler
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
G. Simon, M. Molnar, L. Gonczy, B. Cousin, Robust k-Coverag
e Algorithms for Sensor Networks, IEEE Transactions on Instru
mentation and Measurement, Vol. 57, No. 8, pp. 1741-1748,
Aug. 2008.
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See Theorem 1
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