coverage and connectivity issues in sensor networks
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Coverage and Connectivity Issues in Sensor Networks. Ten-Hwang Lai Ohio State University. Outline. Introduction to Sensor Networks Coverage, Connectivity, Density Problems. A Sensor Node. Memory (Application). Processor. Network Interface. Actuator. Sensor. - PowerPoint PPT PresentationTRANSCRIPT
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Coverage and Connectivity Issues in Sensor Networks
Ten-Hwang Lai
Ohio State University
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Outline
Introduction to Sensor Networks Coverage, Connectivity, Density Problems
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A Sensor Node
Processor
Sensor Actuator NetworkInterface
Memory(Application)
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Berkeley Mote: a sensor device prototype
Atmel ATMEGA103 – 4 Mhz 8-bit CPU– 128KB Instruction
Memory– 4KB RAM
RFM TR1000 radio– 50 kb/s
Network programming
51-pin connector
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Berkeley DOT Mote
Atmel AVR 8535– 4MHz– 8KB of Memory– 0.5KB of RAM
Low power radio Power consumption
– Active 5mA– Standby 5μA
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Berkeley Smart Dust
bi-directional communications
sensor: acceleration and ambient light
11.7 mm3 total circumscribed volume
4.8 mm3 total displaced volume
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Smart Clothing & Wearable Computing
Smart Underwear Smart Eyeglasses Smart Shoes …
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Speckled Computing
愛丁堡大學( University of Edinburgh)科學家即將研發出大小跟灰塵差不多的超微型晶片 , 這些晶片可以分散或
噴灑到物體上彼此溝通、傳遞資訊。這種名為斑點運算( speckled computing)的技術可望在三年內成為事實。
將晶片噴到患者的衣物上 , 可監控其心跳、呼吸與體溫。
Source: Silicon Glen R&D Update, April, 2003
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Sensor Networks
Nodes:– Limited in power, computational capacity,
memory, communication capacity– Prone to failures
Networks– Large scale– High density– Topology change
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Sensor Deployment
How to deploy sensors over a field?– Planned deployment– Random deployment
What are desired properties of a “good” deployment?
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Coverage, Connectivity, Density
Every point is covered by a sensor– K-covered
The network is connected– K-connected
Nodes are not too dense Others
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Coverage, Connectivity, and Density Problems
Simple coverage, k-coverage Density control by turning on/off power
– PEAS– OGDC
Topology control by adjusting power– Homogeneous– Per-node
Asymptotic connectivity/coverage
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Covered Connected
If the covered area is convex and Rt > 2Rs
Rs
Rt
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Simple Coverage Problem
Given: an area and a sensor deployment Question: Is the entire area covered?
6
54
3
2
1
7
8 R
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Is the perimeter covered?
0 360
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K-covered
1-covered2-covered3-covered
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K-Coverage Problem
Given: an area, a sensor deployment, an integer k
Question: Is the entire area k-covered?
6
54
3
2
1
7
8 R
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Is the perimeter k-covered?
0 360
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Density Control
Given: an area and a sensor deployment Problem: turn on/off sensors to maximize the
coverage time of the sensor network
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PEAS
PEAS: A robust energy conserving protocol for long-lived sensor networks
Fan Ye, Gary Zhong, Jesse Cheng, Songwu Lu, Lixia Zhang
UCLA ICNP 2002
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PEAS: basic idea
Sleep Wake up Go to Work?
workyes
no
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Design Issues
How often to wake up? How to determine whether to work or not?
Sleep Wake up Go to Work?
workyes
no
Wake-up rate?
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How often to wake up?
Desired: the total wake-up rate around a node equals some given value
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How often to wake up?
f(t) = λ exp(- λt)
• exponential distribution• λ = # of times of wake-up per unit time• λ is dynamically adjusted
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Wake-up rates
f(t) = λ exp(- λt)
f(t) = λ’ exp(- λ’t)
A
B
A + B: f(t) = (λ + λ’) exp(- (λ + λ’) t)
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Adjust wake-up rates
Working node knows– Desired wake-up rate λd
– Measured wake-up rate λm
Probing node adjusts its λ byλ := λ (λd/ λm)
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Go to work or return to sleep?
Depends on whether there is a working node nearby.
Go back to sleep go to work
Rp
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Rp
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Is the resulting network covered or connected?
If Rt ≥ (1 + √5) Rp and …
P(connected) → 1
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OGDC: Optimal Geographical Density Control
“Maintaining Sensing Coverage and Connectivity in Large sensor networks”
Honghai Zhang and Jennifer Hou MobiCom’03
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Basic Idea of OGDC
Minimize T, the total amount of overlap– Equivalent to minimizing the number of working nodes
F(x) = the degree of overlap
T = ∫ F(x) dx
F( ) = 0F( ) = 1F( ) = 2
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Minimum overlap
Optimal distance = √3 R
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Minimum overlap
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Near-optimal
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OGDC: the Protocol
Time is divided into rounds. In each round, each node decides whether to be active or not.
1. Select a starting node. Turn it on and broadcast a power-on message.
2. Select a node closest to the optimal position. Turn it on and broadcast a power-on message. Repeat this.
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Selecting starting nodes
Each node volunteers with a probability p. Backs off for a random amount of time. If hears
nothing during the back-off time, then sends a power-on message carrying
Sender’s positionDesired direction
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Select the next working node
On receiving a power-on message from a starting node, each node sets a back-off timer inversely proportional to its deviation from the optimal position.
On receiving a power-on message from a non-starting node
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OGDC vs. PEAS
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Coverage, Connectivity, and Density Problems
Simple coverage, k-coverage Density control by turning on/off power
– PEAS– OGDC
Topology control by adjusting power– Homogeneous– Per-node
Asymptotic connectivity/coverage
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Power Control for Coverage and Connectivity
Randomly deploy n nodes over an area. n: a large number. How small can transmission power be in
order to ensure coverage/connectivity with high probability?
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Model
A: a unit area n: number of nodes randomly deployed over A R(n): transmission range An edge exists between two nodes if their
distance is less than R(n). G(n): the resulting graph. Problem: determine R(n) which guarantees
G(n)’s connectivity with high probability.
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On k- Connectivity for a Geometric Random Graph, M.D. Penrose, 1999
R(n) = the minimum transmission range required for G(n) to have k-connectivity
R’(n) = the minimum transmission range required for G(n) to have degree k.
lim Prob( R(n) = R’(n) ) = 1, as n → infinity
R(n) ≈ R’(n) for large n
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On the Minimum Node Degree and connectivity of a Wireless Multihop Network, C. Bettstetter, MobiHoc’02
Prob(G(n) is of degree k) can be calculated from k, n, R’(n), node density
To determine R(n), – Choose R’(n) so that Prob(G(n) is of degree k) ≈ 1– With this transmission range, G is of degree k with
high probability– So, G is k-connected with high probability
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Application 1
N = 500 nodes A = 1000m x 1000m 3-connected required R = ?
With R = 100 m, G has degree 3 with probability 0.99.
Thus, G is 3-connected with high probability.
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Application 2
A = 1000m x 1000m R = 50 m 3-connected required N = ?
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Unreliable Sensor Grid: Coverage and Connectivity, INFOCOM 2003
Active Dead Be active with a prob p(n) transmission and sense
range R(n) A necessary and sufficient
condition for the network to remain covered and connected
N nodes
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Conditions for Asymptotic Coverage and Connectivity
Necessary:
Sufficient:
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Individually Adjusting Power
Homogeneous transmission range Node-based transmission range Problem: individually adjusts the
transmission range to guarantee connectivity.
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The k-Neigh Protocol for Symmetric Topology Control in Ad Hoc Networks,MobiHoc’03
K- neighbor graph. Each node adjusts its transmission range so
it can communicate with its k nearest neighbors
Is it connected?
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The number of neighbors needed for connectivity of wireless networks, F. Xue and P.R. Kumar, UIUC
N nodes are uniformly placed in a unit square.
lim Prob(K-neighbor graph is connected) = 1 if K ≥ 5.1774* log N
lim Prob(K-neighbor graph is disconnected) = 1 if K ≤ 0.074* log N
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Summary
Coverage and connectivity problems Simple coverage, k-coverage Density control by turning on/off power
– PEAS– OGDC
Topology control by adjusting power– Homogeneous– Per-node
Asymptotic connectivity/coverage