Rendezvous Design Algorithms for Wireless Sensor Networks with a Mobile Station

1
Rendezvous Design Algorithms for Wireless Sensor
Networks with a Mobile Station

• Guoliang Xing Tian Wang Weijia Jia Minming Li
• Department of Computer Science City University
  of Hong Kong

2
Outline

• Motivation
• Problem formulation
• Rendezvous design algorithms
• Free mobility model
• Limited mobility model
• Simulations
• Conclusion

3
Challenges for Data-intensive Sensing Applications

• Many applications are data-intensive
• Structural health monitoring
• Accelerometer_at_100Hz, 30 min/day, 80Gb/year
• Micro-climate and habitat monitoring
• Acoustic video, 10 min/day, 1Gb/year
• Most sensor nodes are powered by batteries
• A tension exists between the sheer amount of data
  generated and the limited power supply

4
Mobility-assisted Data Collection
Base Station
5 mins
150K bytes
10 mins
500K bytes
5 mins
100K bytes
100K bytes

• Mobile nodes collect data via short-range
  communications
• Mobile nodes are less power-constrained
• Can move to wired power sources

5
Mobile Sensor Platforms
Robomote _at_ USC Dantu05robomote
XYZ _at_ Yale http//www.eng.yale.edu/enalab/XYZ/
Networked Infomechanical Systems (NIMS) _at_ CENS,
UCLA

• Low movement speed (0.12 m/s)
• Increased latency of data collection
• Reduced network capacity

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Static vs. Mobile
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Rendezvous-based Data Collection

• Some nodes serve as rendezvous points (RPs)
• Other nodes send their data to the closest RP
• Mobiles visit RPs and transport data to base
  station
• Advantages
• In-network caching controlled mobility
• Mobiles can collect a large volume of data at a
  time
• Minimize disruptions due to mobility
• Mobiles contact static nodes at RPs at scheduled
  time

8
Rendezvous-based Data Collection

• Some nodes serve as rendezvous points (RPs)
• Others nodes send data to the closest RP
• Mobiles visit RPs and carry data to base station
• Advantages
• In-network caching controlled mobility
• Minimize disruptions due to mobility

mobile node
rendezvous point
source node
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Outline

• Motivation
• Problem formulation
• Rendezvous design algorithms
• Free mobility model
• Limited mobility model
• Simulations
• Conclusion

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The Rendezvous Design Problem

• Choose RPs s.t. mobile nodes can visit all RPs
  within data collection deadline
• Total network energy of transmitting data from
  sources to RPs is minimized
• Joint optimization of positions of RPs, mobile
  motion paths, and data routes

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Assumptions

• Only one mobile, moves at speed v
• Mobile picks up data at locations of nodes
• Data from two sources can be aggregated
• Data collection deadline is D
• User requirement report every 10 minutes and
  the data is sampled every 10 seconds
• Recharging period e.g., Robomotes powered by 2
  AA batteries recharge every 30 minutes

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Geometric Network Model

• Transmission energy is proportional to distance
• Base station, source nodes and RPs are connected
  by straight lines

a multi-hop route is approximated by a straight
line
Rendezvous points
Non-source nodes
Source nodes
approximated data route
real data route
source nodes
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The Rendezvous Design Problem

• Given a base station B, and sources
• si , find trees Ti( Vi, Ei ), and a tour
• visiting the roots of Ti such that
• 1) the tour is no longer than L
• 2) the total edge length of Ti is minimized

B
s6
R4
s1
R1
s5
R3
R2
s4
s2

• Hardness
• General case is NP-Hard
• When L0, the opt solution is Steiner Min Tree
  that connects B U si

s3
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Outline

• Motivation
• Problem formulation
• Rendezvous design algorithms
• Free mobility model
• Limited mobility model
• Simulations
• Conclusion

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An Approx. Algorithm

• Find an approx. Steiner Min Tree for
• B U si
• Depth-first traverses the tree until covers L/2
  edge length

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An Improved Algorithm

• 1. Find T -- an approx. SMT for B U si
• 2. YL/2
• 3. Depth-first traverses T from B until cover Y
  length, denote I as the set of current RPs
• 4. if X L - TSP(I) gt d
• YYX/2 goto 3
• else exit
• TSP(I) the length of tour visiting points in
  set I, computed by a Traveling Salesman Problem
  solver

17
Illustration
1. Find T - an approx. Steiner min tree of
BUsi 2. YL/2 3. Depth-first traverse T
from B until cover Y length, denote I as the set
of border points 4. if X L - TSP(I) gt d
YYX/2 goto 3 else exit
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Approx. Ratio

• The approximation ratio of the algorithm is
  aß(2a-1)/2(1-ß)
• a is the best approximation ratio of the Steiner
  Minimum Tree problem
• ß L / SMT(BS Sources)
• Assume L ltlt SMT(BS Sources)

19
Outline

• Motivation
• Problem formulation
• Rendezvous design algorithms
• Free mobility model
• Limited mobility model
• Simulations
• Conclusion

20
Illustration

• The mobile only moves along a fixed track

source node
XYZ node _at_ Yale
rendezvous point
Track of Mobile
21
Theoretical Results

• An MST-based approximation algorithm
• Approximation ratio is 2(13 ß)/sqrt(3)
• ß ?L/c(MSTopt)
• ?L is a user-specified constant
• c(MSTopt) is cost of the optimal Min Spanning
  Tree connecting sources to the track

22
Simulation Results

• 100 sources are randomly distributed in a 300m X
  300m field, base station is on the left corner
• Each source generates 2 bytes/s, deadline is 20
  mins

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Conclusions

• Rendezvous-based data collection for WSNs w/ a
  mobile base station
• In-network caching controlled mobility
• Problem formulations under both free/limited
  mobility models
• Two graph-theoretical rendezvous algos
• Provable performance bounds
• Simulation-based evaluation

24
Geometric Network Model

• Transmission energy is proportional to distance
• Base station, source nodes and branch nodes are
  connected with straight lines

a multi-hop route is approximated by a straight
line
Rendezvous points
Non-source nodes
a branch node lies on two or more source-to-root
routes
Source nodes
Branch nodes
approximated data route
real data route
Source nodes
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Problem Formulation

• Given a tree T(V,E) rooted at B and sources si,
  find RPs, Ri, and a tour no longer than LvD
  that visits BURi, and
• The problem is NP-hard (reduction from the
  Traveling Salesman Problem)

dT(si,Ri) the on-tree distance between si and Ri
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Illustration of Problem Formulation

• Objective
• Minimize edge length of routing tree
• Constraint
• Tour length L

Source nodes
branch nodes
Rendezvous points
data route
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Proof Sketch I
B

• A is opt solution
• RB U Ri
• SB U Si
• T is the tree used in input
• SMT(X) - SMT connecting points in set X
• TSP(X) - length of the shortest tour visiting
  points in R

R1
R3
R2
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Proof Sketch II
B
A U SMT(R) is a Steiner tree connecting S c(A)
c(SMT(R)) c(SMT(S)) SMT is a lower bound
of TSP problem c(SMT(R)) lt c(TSP(R)) L ?
c(A) gt c(SMT(S)) L gt c(T)/ a - L
S1
R1
R3
S4
R2
S5
S3
Our solution c(T)-L/2
S2