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

Processor

Sensor Actuator NetworkInterface

Memory(Application)

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

Berkeley DOT Mote

Atmel AVR 8535– 4MHz– 8KB of Memory– 0.5KB of RAM

Low power radio Power consumption

– Active 5mA– Standby 5μA

Berkeley Smart Dust

bi-directional communications

sensor: acceleration and ambient light

11.7 mm3 total circumscribed volume

4.8 mm3 total displaced volume

Smart Clothing & Wearable Computing

Smart Underwear Smart Eyeglasses Smart Shoes …

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  

Sensor Networks

Nodes:– Limited in power, computational capacity,

memory, communication capacity– Prone to failures

Networks– Large scale– High density– Topology change

Sensor Deployment

How to deploy sensors over a field?– Planned deployment– Random deployment

What are desired properties of a “good” deployment?

Coverage, Connectivity, Density

Every point is covered by a sensor– K-covered

The network is connected– K-connected

Nodes are not too dense Others

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

Covered Connected

If the covered area is convex and Rt > 2Rs

Rs

Rt

Simple Coverage Problem

Given: an area and a sensor deployment Question: Is the entire area covered?

6

54

3

2

1

7

8 R

Is the perimeter covered?

0 360

K-covered

1-covered2-covered3-covered

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

Is the perimeter k-covered?

0 360

Density Control

Given: an area and a sensor deployment Problem: turn on/off sensors to maximize the

coverage time of the sensor network

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

PEAS: basic idea

Sleep Wake up Go to Work?

workyes

no

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?

How often to wake up?

Desired: the total wake-up rate around a node equals some given value

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

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)

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)

Go to work or return to sleep?

Depends on whether there is a working node nearby.

Go back to sleep go to work

Rp

Rp

Is the resulting network covered or connected?

If Rt ≥ (1 + √5) Rp and …

P(connected) → 1

OGDC: Optimal Geographical Density Control

“Maintaining Sensing Coverage and Connectivity in Large sensor networks”

Honghai Zhang and Jennifer Hou MobiCom’03

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

Minimum overlap

Optimal distance = √3 R

Minimum overlap

Near-optimal

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.

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

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

OGDC vs. PEAS

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

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?

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.

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

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

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.

Application 2

A = 1000m x 1000m R = 50 m 3-connected required N = ?

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

Conditions for Asymptotic Coverage and Connectivity

Necessary:

Sufficient:

Individually Adjusting Power

Homogeneous transmission range Node-based transmission range Problem: individually adjusts the

transmission range to guarantee connectivity.

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?

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

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