1 rendezvous design algorithms for wireless sensor networks with a mobile station guoliang xing;...
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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@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
• Mobile nodes collect data via short-range communications
• Mobile nodes are less power-constrained– Can move to wired power sources
Base Station
500K bytes
100K bytes 100K bytes
150K bytes5 m
ins
10 mins5 mins
5
Mobile Sensor Platforms
• Low movement speed (0.1~2 m/s)– Increased latency of data collection– Reduced network capacity
Networked Infomechanical Systems (NIMS) @ CENS, UCLA
Robomote @ USC [Dantu05robomote]
XYZ @ Yale http://www.eng.yale.edu/
enalab/XYZ/
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Static vs. Mobile
All-static networks
Mobility-assisted Networks
Delay Low High
Energy Consumption
High nonreplenishable
High
replenishable
Bandwidth Medium Medium to high
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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
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mobile node
rendezvous point
Rendezvous-based Data Collection
source node
• 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
9
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
source nodes
Source nodes
approximated data route
real data route
Non-source nodes
Rendezvous points
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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
R1s1
s5
s4
B
s2s3
R2
R3
R4
s6
Hardness• General case is NP-Hard •When L=0, the opt solution is Steiner Min Tree that connects {B} U { si }
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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. Y=L/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) > δ Y=Y+X/2; goto 3;
else exit;
TSP(I) – the length of tour visiting points in set I, computed by a Traveling Salesman Problem solver
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Illustration1. Find T - an approx. Steiner min
tree of {B}U{si}
2. Y=L/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) > δ Y=Y+X/2; goto 3;
else exit;
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Approx. Ratio
• The approximation ratio of the algorithm is α+β(2α-1)/2(1-β)
– α is the best approximation ratio of the Steiner Minimum Tree problem
– β = L / SMT(BS + Sources)
– Assume L << SMT(BS + Sources)
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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
Track of Mobile
XYZ node @ Yale
source node
rendezvous point
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Theoretical Results
• An MST-based approximation algorithm
• Approximation ratio is 2(1+3 β)/sqrt(3)– β = ∆L/c(MSTopt) – ∆L is a user-specified constant– c(MSTopt) is cost of the optimal Min Spanning
Tree connecting sources to the track
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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
23
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
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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
Source nodes
Source nodes
approximated data route
real data route
Non-source nodes
Branch nodes
Rendezvous points
a branch node lies on two or more source-to-root routes
25
Problem Formulation
• Given a tree T(V,E) rooted at B and sources {si}, find RPs, {Ri}, and a tour no longer than L=vD that visits {B}U{Ri}, and
• The problem is NP-hard (reduction from the Traveling Salesman Problem)
minimized is ),( isS
iiT Rsd
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
Rendezvous points data route
branch nodes
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Proof Sketch I• A* is opt solution
• R={B} U {Ri}
• S={B} 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
R2
R3
B
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