Target-Oriented Scheduling in Directional Sensor Networks

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Target-Oriented Scheduling in Directional Sensor
Networks

• Yanli Cai, Wei Lou, Minglu Li ,and Xiang-Yang Li
• The Hong Kong Polytechnic University, Hong Kong
• Illinois Institute of Technology
• INFOCOM 2007

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Outlines

• Introductions
• Multiple Directional Cover Sets Problem (MDCS)
• Solutions to the MDCS problem
• Progressive algorithm
• Prog-Resd algorithm
• Feedback algorithm
• Simulation Results
• Conclusions

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Introductions

• omni-directional sensor
• Have an omni-angle of sensing range.
• 10 M. Cardei, M. T. Thai, Y. Li, and W. Wu,
  Energy-efficient target coverage in wireless
  sensor networks, in IEEE INFOCOM, 2005.
• directional sensor
• Video sensors, ultrasonic sensors, and infrared
  sensors.
• The sensing region of each direction of a
  directional sensor is a sector of the sensing
  disk centered at the sensor with a sensing
  radius.
• Each sensor has a uniform sensing region and the
  sensing regions of different directions of a
  sensor do not overlap.
• The objective of this paper
• To maximize the network lifetime of a directional
  sensor network
• network lifetime the time duration when each
  target is covered by the work direction of at
  least one active sensor.

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Introductions

• cover set
• A subset of directions of the sensors, in which
  the directions cover all the targets.
• No more than one direction of a sensor can be in
  a cover set.
• directional cover set problem (DCS)
• Finding a cover set and it is NP-complete.
• non-disjoint cover sets
• Organize the directions of sensors into
  non-disjoint subsets, each of which is a cover
  set, and allocate the work time for each cover
  set.
• Allow a direction or a sensor to participate in
  multiple cover sets.
• multiple directional cover sets problem (MDCS)
• Finding non-disjoint cover sets and allocating
  the work time for each of them to maximize the
  network lifetime.

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Multiple Directional Cover Sets Problem (MDCS)

• Notations
• M the number of targets.
• N the number of sensors.
• W the number of directions per sensor.
• am the mth target, 1 ? m ? M.
• si the ith sensor, 1 ? i ? N.
• di,j the jth direction of the ith sensor, 1 ? i
  ? N, 1 ? j ? W.
• di,j am am is covered by di,j , am? A
  and si di,j j 1W .
• A the set of targets. A a1, a2, , aM
• S the set of sensors. S s1, s2, , sN
• D the set of the directions of all the sensors.
  
• D di,j i 1N, j 1W
• Dk di,j ti,j,k gt 0, di,j ? D the kth
  cover set of work directions.
• tk the work time of the kth cover set of
  directions,
• ti,j,k the work time of the direction di,j in
  the kth cover set of directions
• Li the lifetime of a sensor si

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• Each sensor has an initial lifetime of 1 (time
  unit).
• Fig. 1(a), D1 d1,3, d3,1 with 0.5, D2 d1,3,
  d2,2 with 0.5, and D3 d2,2, d3,1 with 0.5.
  This results in a network lifetime of 1.5.
• Fig. 1(b), D1 d1,3, d2,2 with its available
  work time 1. This results in a network lifetime
  of 1.

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Multiple Directional Cover Sets Problem (MDCS)

• Model the MDCS as a Mixed Integer Programming
  (MIP) problem.
• A directional sensor network with
• a set A of M targets
• a set S of N sensors
• a set D of directions
• Each sensor si ? S has W directions and an
  initial lifetime of Li
• Organize the directions in D into K cover sets.
• The kth cover set is denoted as Dk, with the work
  time tk.
• A direction di,j is allowed to participate into
  multiple cover sets.

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Multiple Directional Cover Sets Problem (MDCS)
a boolean variable
The objective
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Multiple Directional Cover Sets Problem (MDCS)

• Let ti,j,k xi,j,k tk
• ti,j,k the work time of di,j in the cover set
  Dk
• Get the following Linear Mixed Integer
  Programming (LMIP) problem.

relax
0 ? ti,j,k ? tk
The objective
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Progressive Algorithm

• Compute several cover sets and their
  corresponding work time which is accumulated to
  the total network lifetime in each iteration.
• Step 1 solve the LP problem and get the optimal
  solution of tk and ti,j,k
• conflicting directions
• More than one direction of a sensor is in Dk and
  these directions conflict with each other.
• non-conflicting direction
• Only one direction of the sensor is in Dk
• conflicting direction elimination process
• The process of removing the conflicting
  directions in Dk to make it a cover set.
• Step 2 If the update cover set Dk ? 0, then call
  the direction selection process.
• Step 3 update the residual lifetime of any
  selected sensor si using the work time tk of the
  cover set Dk
• Repeat Step 1 Step 3 until the lifetime
  computed in the current iteration is less than a
  small positive value of ?.

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D d1,1, d1,2, d1,3, , d5,1, d5,2, d5,3.
Assume Dk d1,3, d2,1, d2,3, d3,1, d3,3, d4,1,
d4,3, d5,1 and the work time of the
corresponding directions in Dk is 0.8, 0.2, 0.8,
0.2, 0.8, 0.2, 0.8, 0.2. Two non-conflicting
directions d1,3 with longer work time 0.8 and
d5,1 with work time 0.2, so d1,3 is selected. Get
U a1 and then remove a1 from A . Get V
d1,3, d2,1, where d1,3 is a non-conflicting
direction and d2,1 conflicts with d2,3. Add d1,3
to Dk and remove both d1,3 and d2,1 from Dk.
Finally, we get Dk d1,3, d2,3, d3,3, d4,3
with 0.8, 1.0, 1.0, 1.0.
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Dk d1,1, d1,3, d2,1, d2,3, d3,1, d3,3, d4,1,
d4,3, d5,1, d5,3, d6,1, d6,3 and the work time
of each direction in Dk is 0.2, 0.8, 0.2, 0.8,
0.2, 0.8, 0.2, 0.8, 0.2, 0.8, 0.2, 0.8. There
is no non-conflicting direction in Dk, and we
select d1,3 with its work time 0.8, d1,1
conflicts with d1,3, so d1,1 is removed from Dk.
The direction d1,3 is a non-conflicting direction
in Dk after d1,1 is removed. Finally, we get Dk
d1,3, d2,3, d3,3, d4,3, d5,3, d6,3 with
1.0, 1,0, 1.0, 1.0, 1.0, 1.0.
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Direction Selection Process

• To save energy, only a subset of Dk can be
  selected.
• Select the direction di,j ? Dk that satisfies
  ti,j,k gt tk and has the longest work time, to
  cover some uncovered targets each time.
• Repeat selecting another direction from Dk to Dk
  until all the targets are covered by the selected
  directions.
• Then, remove redundant directions in Dk
• Because the targets covered by some directions
  formerly selected into Dk may be totally covered
  by the ones selected into Dk later, which causes
  redundancy.

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Prog-Resd Algorithm

• Direction selection process of Progressive
  algorithm
• The direction with the longest work time is
  selected each time.
• Prog-Resd algorithm takes into consideration the
  residual lifetime of sensors.
• This algorithm differentiates from the
  Progressive algorithm only in the direction
  selection process.
• Select a cover set that has the longest residual
  lifetime Li to cover some uncovered targets each
  time.

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Feedback Algorithm

• Too many cover sets may be inefficient or
  impractical.
• Frequently switching sensors from one direction
  to another may not be easy for physical reasons.
• Too many cover sets mean too many state
  transition periods
• Lead to the occurrence of some targets may not
  be covered during the state transition period.
• Feedback that utilizes the results obtained from
  the previous iterations and finds a group of
  cover sets in the last iteration. Then use the
  results obtained in previous iterations as a
  feedback to the next iteration.
• This algorithm is more useful and practical
  because it generates no more than K cover sets
  totally. (fewer cover sets)
• The LP problem, the conflicting direction
  elimination process, and the direction selection
  process are also used.
• In each iteration of the Feedback algorithm, we
  only determine one cover set from the solution to
  the LP problem, and add the constraints to the LP
  problem in the next iteration.
• Then we solve the updated LP problem again to get
  the next cover set.

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Simulation Results

• Simulations running on a computer with 3 GHz CPU
  and 1 GB memory.
• The optimization toolbox in Matlab is used to
  solve the LP problem.
• N sensors with sensing radius r and M targets are
  deployed uniformly in a region of 400m ? 400m.
• Each sensor has W directions.
• Each algorithm runs 10 times through random
  placement of sensors and targets.
• The Progressive algorithm and the Prog-Resd
  algorithm, set ? 0.001.
• The Feedback algorithm, set d 0.0001.

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The network lifetime increases almost linearly
when the number of sensors increases. The
Feedback algorithm has te best performance.
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The network lifetime increases almost linearly
when the sensing radius increases.
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The network lifetime drops quickly when M varies
from 1 to 2, and then drops relatively slowly
when M varies from5 up to 20.
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The network lifetime is almost linear to W.
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The runtime of the Feedback algorithm is longer
than the other two algorithms.
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• Both the Progressive algorithm and the Prog-Resd
  algorithm generate much more cover sets than the
  Feedback algorithm.
• Fewer cover sets with longer work time aremore
  efficient and practical.

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Conclusions

• Study the problem of the multiple directional
  cover sets (MDCS).
• Present the Progressive, Prog-Resd, and Feedback
  algorithm to solve the multiple directional cover
  sets (MDCS) problem.
• Future work
• Design distributed algorithms to prolong the
  network lifetime of a directional sensor network.

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References

• 10 M. Cardei, M. T. Thai, Y. Li, and W. Wu,
  Energy-efficient target coverage in wireless
  sensor networks, in IEEE INFOCOM, 2005.
• 11 H. Liu, P. Wan, C. Yi, X. Jia, S. Makki, and
  P. Niki, Maximal lifetime scheduling in sensor
  surveillance networks, in IEEE INFOCOM, 2005.
• 12 M. X. Cheng, L. Ruan, and W. Wu, Achieving
  minimum coverage breach under bandwidth
  constraints in wireless sensor networks, in IEEE
  INFOCOM, 2005.
• 13 H. Ma and Y. Liu, On coverage problems of
  directional sensor networks, in MSN, 2005.
• 14 J. Ai and A. A. Abouzeid, Coverage by
  directional sensors in randomly deployed wireless
  sensor networks, Journal of Combinatorial
  Optimization, vol. 11, no. 1, pp. 2141, Feb.
  2006.

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Target Coverage Problem (1/5)

• DefinitionTarget Coverage Problem(TCP)
• m targets with known location
• n sensors randomly deployed in the closed
  proximity of the targets
• schedule the sensor nodes activity
• all the targets are continuously observed and
  network lifetime is maximized.
• Scheduling mechanism
• Step1?Sensors send their location information to
  the BS
• Step2?BS executes the sensor scheduling algorithm
  and broadcasts the schedule when each
  node is active
• Step3?Every sensor schedules itself for
  active/sleep intervals

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Maximum Set Covers (2/5)

• DefinitionMSC Problem
• C set of sensors(n sensors)
• every sensor can be part of more than one set
• assume each sensors lifetime is 1
• R set of targets(m targets)
• Find a family of set covers S1, , Sp with time
  weight t1,, tp in 0,1
• Goalto maximize t1 tp

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Disjoint set (3/5)
R r1, r2, r3 C s1, s2, s3, s4

• S1 s1, s2 t11
• S2 s3, s4 t21 Lifetime G 2

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Maximum Set Covers (4/5)
S1 s1, s2 t1 0.5 S2 s2, s3 t2
0.5 S3 s1, s3 t3 0.5 S4 s4 t4
1 Lifetime G 2.5
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Solutions To Compute Maximum Set Covers (5/5)

• LP-MSC Heuristic
• Greedy-MSC Heuristic