Maximizing Sensor Lifetime in A Rechargeable Sensor Network via Partial Energy Charging on Sensors

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Maximizing Sensor Lifetime in A Rechargeable
Sensor Network via Partial Energy Charging on
Sensors

• Wenzheng Xu, Weifa Liang, Xiaohua Jia, Zichuan Xu
• Sichuan University, P.R. China
• Australian National University, Australia
• City University of Hong Kong, Hong Kong

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Outline

• Introduction
• Preliminaries
• Algorithm for the sensor lifetime maximization
  problem
• Algorithm for the service cost minimization
  problem with the maximum sensor lifetime
• Performance Evaluation
• Conclusion

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Wireless Sensor Networks

• Environmental and Habitat Monitoring
• Structural Health Monitoring
• Precision Agriculture
• Military Surveillance

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Wireless Energy Transfer

• Energy issue sensors will run out of their
  energy
• Wireless energy transfer is very promising for
  charging sensors
• High energy transfer efficiency
• 40 within two meters
• Deploy mobile chargers to charge sensors
• high and reliable charging rate

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Problem of existing studies

• Existing studies adopt the full-charging model
• A mobile charger must charge a sensor to its full
  energy capacity before moving to charge the next
  one
• It takes a while to fully charge a sensor, e.g.,
  30-80 minutes
• Problem an energy-criticial sensor may run out
  of its energy for a long time before its
  charging, especially when there are a lot of
  to-be-charged sensors

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Example the full-charging model

• Assume that there are two energy-critical sensors
• The 1st sensor is charged before its energy
  depletion
• The 2nd sensor has run out of its energy for a
  while when the charger has fully charged the 1st
  sensor

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A novel charging modelthe partial-charging model

• First, the 1st sensor is partially charged
• Then, the 2nd sensor is fully charged
• Finally, the 1st sensor is also charged to its
  full energy capacity
• Both of the two sensors are charged before their
  energy depletions

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Side effect of the partial charging model

• The travel distance of the mobile charger will be
  longer than that under the full-charging model
• Higher service cost

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Contributions of this paper

• How to find a charging tour for the mobile
  charger, so that the sensor lifetime is
  maximized without increasing the chargers travel
  distance too much, under the partial-charging
  model?
• Propose a novel algorithm for the problem
• Experimental results
• Avg energy expiration time per sensor is only 10
  of that by the state-of-the-art
• Travel distance is only 718 longer than that
  by the state-of-the-art

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Outline

• Introduction
• Preliminaries
• Algorithm for the sensor lifetime maximization
  problem
• Algorithm for the service cost minimization
  problem with the maximum sensor lifetime
• Performance Evaluation
• Conclusion

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Network Model

• A set V of energy-critical sensors at some time t
• n sensors v1, v2, ..., vn
• Battery capacities B1, B2, ..., Bn
• Amounts of residual energy RE1, RE2, ..., REn
• Energy demands B1-RE1, B2-RE2, ..., Bn-REn
• Energy consumption rates ?1, ?2, ..., ?n
• Residual lifetimes l1, l2, ..., ln, li REi / ?i
• A mobile charger located at depot r
• Fixed charging rate µ to every sensor
• Travel speed s

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A Novel Partial-charging Model

• Energy demand of sensor vi Bi-REi
• A unit amount ? of charging energy
• The amount of energy charged to sensor vi
• ?, 2?, ..., ki?, Bi-REi, where
• ? should not be too small, so that the travel
  distance of the charger will not be increased too
  much, e.g., ? Bi/5
• A charging tour C of the charger
• (r,0)?(v1, e1) ?(v2, e2) ?... ?(vn, en)
  ?(r,0)
• ej the amount of energy charged to sensor vj
• Each sensor vi may be charged multiple times in
  tour C

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Charging time vs. travel time

• Travel time ttravel from one sensor to the next
  sensor in a charging tour usually is much shorter
  than the charging time on a sensor
• e.g., 1 minute vs 10 miminutes (for an amount ?
  of energy)
• The travel time ttravel is considered as a small
  constant
• Divide time into equal time slots
• Each time slot lasts time
  units

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Normalized lifetime of a sensor

• Assume each sensor vi is charged ci times in a
  charging tour C
• An amount Bi-REi of energy is required to be
  charged to the sensor in the ci chargings
• dead time if no charging is performed
• dead time after the ci
  chargings
• and live and dead durations of
  sensor vi from time to time
• Normalized sensor lifetime

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Sum of normalized sensor lifetimes

• Sum of normalized lifetimes
• can be considered as the live
  probability of sensor vi at any time
• thus is the expected number of live
  sensors maintained in the network by the charging
  tour C

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Problem definitions

• Sensor lifetime maximization problem
• Find a charging tour C so that the sum
  of normalized lifetimes is maximized
• the maximum sum of normalized
  lifetimes
• The service cost mimimization problem with the
  maximum sensor lifetime
• Find a charging tour C so that the length of the
  tour is minimized, subject to that the maximum
  sum of normalized lifetime is acheived

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Outline

• Introduction
• Preliminaries
• Algorithm for the sensor lifetime maximization
  problem
• Algorithm for the service cost minimization
  problem with the maximum sensor lifetime
• Performance Evaluation
• Conclusion

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Basic idea of the algorithm

• Observation an amount ? of energy is charged to
  a sensor at every time slot
• A feasible solution to the problem can be
  considered as a matching between sensors and time
  slots
• Reduce the problem to the maximum weighted
  matching problem

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Algorithm for the sensor lifetime maximization
problem

• For each sensor vi in V, create ki virtual
  sensors vi,1, vi,2, ..., vi,ki, where ki
• Vj the set of the jth virtual sensors for
  sensors in V
• Iteratively create kmax bipartite graphs,
  kmaxmaxki
• ,
• S the set of time slots
• weight wj(vi,j, sq) the normalized lifetime of
  sensor vi if the charger performs the jth
  charging to it at time slot sq
• Find a maximum weighted matching Mj in graph Gj
• Construct a charging tour from the last matching

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Algorithm for the sensor lifetime maximization
problem

• Theorem there is a heurisitc algorithm for the
  sensor lifetime maximization problem, which takes
  O(n3) time. Also, the algorithm finds an optimal
  solution if .
• indicates that the lifetime of
  any sensor for consuming an amount ? of energy is
  no less that the total time of charging every
  sensor with an amount ? of energy, i.e.,
• ?max the maximum energy consumption rate

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Outline

• Introduction
• Preliminaries
• Algorithm for the sensor lifetime maximization
  problem
• Algorithm for the service cost minimization
  problem with the maximum sensor lifetime
• Performance Evaluation
• Conclusion

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Motivation for the problem

• The charging tour found by the matchings in the
  previous section may not be cheap, since the
  factor of sensor locations is not taken into
  consideration
• There may be multiple charging tours with the
  maximum sensor lifetime
• How to find the shortest one?

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Algorithm overview

• A virtual sensor vi,j is expired if it is matched
  to a time slot q after its energy expiration time
  li,j1 in matching MKmax, i.e., q gt li,j1
• Virtual sensor vi,j must be charged at time slot
  q in any charging tour with the maximum sensor
  lifetime
• Otherwise, virutal sensor vi,j is unexpired,
  i.e., q li,j1
• Sensor vi,j is still unexpired if it is charged
  at any time slot no later than li,j1
• Find a shortest charging tour subject to the
  constraint of the energy expiration times of
  unexpired virtual sensors

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Algorithm overview

• Create two virtual nodes rs and rf for depot r
• Have the same locations as depot r
• Find a minimum weighted rf-rooted treeT spanning
  all virtual sensors and nodes rs and rf, so that
• the number of virtual sensors in the subtree
  rooted at each unexpired sensor vi,j is no more
  than its energy deadline li,j1
• the number for each expired sensor vi,j is equal
  to q
• Transform tree T into a path P starting from rs
  and ending at rf
• Path P actually is a closed tour, by noting that
  nodes rs and rf have the same location as depot r

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Construct tree T

• Partition the set V of virtual sensors into
  nV sets
• An expired sensor is contained in Vq (q is the
  matched time slot)
• An unexpired sensor vi,j is contained in Vj,
  jminli,j1, n
• V1, V2, ..., Vn , some sets may contain no
  virtual sensor
• due to the matching
  property
• Let V0 rs and Vn1 rf
• Add nodes in V0, V1, V2, ..., Vn , Vn1 to
  tree T one by one

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Construct tree T-cont.

• Initially, T constains only node rs
• Assume that V0, V1, V2, ..., Vj have been
  added
• Consider the next non-empty set Vk, kgtj
• For each residual node vi, find a minimum subtree
  Tik , by expanding from node vi to a subtree
  contains nodes in Vk and other
  nodes in a greedy way
• Let subtree
  , where w(Tik) is the tree weight, ei,j is the
  nearest edge between node vi and nodes in set Vj
• Add subtree Tk to tree T

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Transform tree T into a path P

• Find the path from node rs to rf in tree T
• Obtain a graph G by replicating the edges in tree
  T except the edges on the path
• There is a Eulerian path from rs to rf in graph G
• G is a connected graph
• The degrees of nodes rs and rf are odd
• The degrees of the other nodes are even
• Find a path P from rs to rf by shortcutting
  repeated nodes in the Eulearian path

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Outline

• Introduction
• Preliminaries
• Algorithm for the sensor lifetime maximization
  problem
• Algorithm for the service cost minimization
  problem with the maximum sensor lifetime
• Performance Evaluation
• Conclusion

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Simulation Environment
Parameters Values
Sensing Field 1,000m 1,000m
Network Size n 100-500 sensors
Battery capacity Bi Bi B 10.8kJ
Data rate bmin, bmax 1 kbps, 10 kbps
Monitoring Period T One year
Energy charging unit ? B/5 B
Algorithm TSP The shortest tour
Algorithm EDF Earliest deadline first
Algorithm NETWRAP 12 Charge the sensor with the minimum weighted sum of residual lifetime and travel time
Algorithm AA 13 Maximize the amount of energy charged to sensors minus the total traveling energy cost
Parameters Values
Network Size (Small Scale) 10,000 m
Sensing Field (Small Scale) 100 600
Given Time Period T (Small Scale) 200 m
Network Size (Large Scale) 1, 2, 4, 8, 16s
Sensing Field (Large Scale) 0.4, 0.9 mJ/s
Given Time Period T (Large Scale) 5, 10, 30 m/s
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Experimental Results--?B/2

• Avg energy expiration time per sensor is only 10
  of that by the state-of-the-art
• Travel distance is only 718 longer than that
  by the state-of-the-art

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Experimental Results--?B/2

• Each sensor is unnecessary to be charged twice,
  though it is allowed to be charged twice
• 60 of sensors are charged only once

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Experimental results-vary ? from B to B/5

• Sharp decrease of avg dead duration per sensor of
  algorithm heuristic when decreasing ? from B to
  B/2, slow decrease from B/2 to B/5
• Longer travel distance of the mobile charger for
  a smaller energy charging unit ?
• Alg. heuristic acheives the best trade-off when
  ?B/2

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Conclusions

• Unlike existing studies that adopt the
  full-charging model, we were the first to propose
  a partial-charging model-gtsignificantly shorten
  sensor dead durations
• Formulated a problem of finding a charging tour,
  so as to maximize sensor lifetime while
  minimizing the chargers travel distance
• Proposed a novel algorithm for the problem
• Experimental results showed that the proposed
  algorithm is very promising

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• Questions ?