1-1

CMPE 259 Sensor Networks

Katia Obraczka

Winter 2005

Topology Control II

1-2

Announcements

Homework due on 02.14. Projects? Gabriel Elkaim’s talk on GPS: 02.09. Venkatesh Rajendra’s talk on MAC:

02.16.

1-3

PEAS

1-4

PEAS

Probing Environment, Adaptive Sleeping.

“Extra” nodes are turned off. Nodes keep minimum state.

No need for neighborhood-related state. PEAS consiers very high node density

and failures are likely to happen.

1-5

Bi-modal operation

Probing environment. Adaptive sleeping.

1-6

PEAS state diagram

Working

Sleeping Probing

No reply for probe

Wakes up

Hears probe reply.

1-7

Probing

When node wakes up, enters probing mode.

Is there working node in range? Broadcasts PROBE to range Rp. Working nodes send REPLY (randomly

scheduled). Upon receiving REPLY, node goes back to

sleep.• Adjusts sleeping interval accordingly.

Else, switches to working state.

1-8

Considerations

Probing range is application-specific. Robustness (sensing and communication)

versus energy-efficiency. Location-based probing as a way to

achieve balance between redundancy and energy efficiency.

Randomized sleeping time. Better resilience to failure. Less contention. Adaptive based on “desired probing rate”.

1-9

More considerations…

Multiple PROBEs (and multiple REPLIES) to compensate for losses. Multiple PROBEs randomly spread over

time. Multiple working nodes in the

neighborhood. Favor “oldest” one.

Nodes with fixed transmit power. Deployment density.

1-10

Evaluation

Simulations. Simulated failures: failure rate and

failure percentage. Metrics:

Coverage lifetime. Delivery lifetime.

1-11

Results

With and without failures. From the paper…

1-12

“Exposure In Wireless Ad-Hoc Sensor Networks”

1-13

Sensor Coverage

Given: Field A N sensors

How well can the field be observed ? Closest Sensor (minimum distance) only

Worst Case Coverage: Maximal Breach Path Best Case Coverage: Maximal Support Path

Multiple Sensors: speed and path considered

Minimal Exposure Path

1-14

Exposure - Semantics Likelihood of detection by sensors function

of time interval and distance from sensors. Minimal exposure paths indicate the worst

case scenarios in a field: Can be used as a metric for coverage

• Sensor detection coverage• Wireless (RF) transmission coverage

For RF transmission, exposure is a potential measure of quality of service along a specific path.

1-15

Preliminaries: Sensing Model

KpsdpsS

),(),(

Sensing model Sensing model SS at an arbitrary point at an arbitrary point p p for for a sensor a sensor s s ::

where where d(s,p)d(s,p) is the Euclidean distance between is the Euclidean distance between the sensor the sensor ss and the point and the point pp, and positive , and positive constants constants and and K K are technology- and are technology- and environment-dependent parameters.environment-dependent parameters.

1-16

Preliminaries: Intensity Model(s)

Effective sensing intensity at point Effective sensing intensity at point pp in field in field F F ::

n

iA psSpFI1

),(),(

),(),(

),(),(

min

min

psSpFI

SspsdpsdSss

C

mm

All All SensorsSensors

Closest Closest SensorSensor

KK Closest Sensors Closest SensorsK=3K=3 for Trilateration for Trilateration

1-17

Definition: Exposure

The The ExposureExposure for an object for an object OO in the in the sensor field during the interval [sensor field during the interval [tt11,t,t22]] along along

the path the path p(t)p(t) is: is:

2

1

)()(, ,),( 21

t

t

dtdt

tdptpFItttpE

1-18

Exposure – Coverage Problem Formulation

Given: Field A N sensors Initial and final points I and F

Problem: Find the Minimal Exposure Path PminE in

A, starting in I and ending in F.

PminE is the path in A, along which the exposure is the smallest among all paths from I to F.

1-19

Special case – one sensor

pS =(1,-1)

s = (0,0) x

y

pD =(-1,1)

Minimal exposure path for one sensor in a Minimal exposure path for one sensor in a square field:square field:

1-20

General Exposure Computations

Analytically intractable. Need efficient and scalable methods to

approximate exposure integrals and search for Minimal Exposure Paths.

Use a grid-based approach and Use a grid-based approach and numerical methods to approximate numerical methods to approximate Exposure integrals.Exposure integrals.

Use existing efficient graph search Use existing efficient graph search algorithms to find Minimal Exposure algorithms to find Minimal Exposure Paths.Paths.

1-21

Minimal Exposure Path Algorithm

Use a grid to approximate path exposures. The exposure (weight) along each edge of the

grid approximated using numerical techniques. Use Dijkstra’s Single-Source Shortest Path

Algorithm on the weighted graph (grid) to find the Minimal Exposure Path.

Can also use Floyd-Warshall All-Pairs Shortest Paths Algorithm to find PminE between arbitrary start and end points.

1-22

Generalized Grid

(a) n=2, m=1 (b) n=2, m=2 (c) n=2, m=3

Generalized Grid – 1Generalized Grid – 1stst order, 2 order, 2ndnd order, 3 order, 3rdrd order …order …More movement freedom More movement freedom more accurate more accurate resultsresults

Approximation quality improves by increasing grid divisionsApproximation quality improves by increasing grid divisionswith higher costs of storage and run-time. with higher costs of storage and run-time.

1-23

Minimal Exposure Path Algorithm Complexity

Single Source Shortest Path (Dijkstra) Each point is visited once in the worst case. For an nxn grid with m divisions per edge:

n2(2m-1)+2nm+1 total grid points. Worst case search: O(n2m) Dominated by grid construction. 1GHz workstation with 256MB RAM requires less than

1 minute for n=32, m=8 grids.

All-Pairs Shortest Paths (Floyd-Warshall) Has a average case complexity of O(p3). Dominated by the search: O((n2m)3) Requires large data structures to store paths.

1-24

Uniform Random Deployment

Minimal exposure path for 50 randomly deployed sensors Minimal exposure path for 50 randomly deployed sensors using the All-Sensor intensity model (using the All-Sensor intensity model (IIAA).).

8x8 m=18x8 m=1Exposure:Exposure: 0.70790.7079Length:Length: 1633.91633.9

16x16 m=216x16 m=2Exposure:Exposure: 0.69760.6976Length:Length: 1607.71607.7

32x32 m=832x32 m=8Exposure:Exposure: 0.69450.6945Length:Length: 1581.01581.0

1-25

Exposure – Statistical Behavior

20 52 84 116 1480.05

0.1

0.15

0.2

0.25

0.3

Number of SensorsR

elat

ive

Std

. Dev

.

Exposure(d-2 Sensor Model)

Closest

All

20 52 84 116 1480.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2Exposure

(d-4 Sensor Model)

Number of Sensors

Rel

ativ

e S

td. D

ev.

All

Closest

Diminishing relative standard deviation in exposure for 1/d2 and 1/d4 sensor models.

1-26

Deterministic Deployments

Minimal exposure path under the All-Sensor intensity model Minimal exposure path under the All-Sensor intensity model ((IIAA) and deterministic sensor deployment schemes. ) and deterministic sensor deployment schemes.

CrossCross SquareSquare TriangleTriangle HexagonHexagon

Exposure LevelExposure Level(compared to Square)(compared to Square) 1.5x1.5x30x~120

1.5x3x6x~20

HexagonTriangleCrossSensors

1-27

Exposure – Research Directions

Localized implementations Performance and cost studies subject to

Wireless Protocols (MAC, routing, etc) Errors in measurements

• Locationing• Sensing• Numerical errors

Computation based on incomplete information

• Not every node will know the exact position and information about all other nodes

1-28

Parametric probabilistic routing

1-29

Approaches to routing Ad hoc network “on-demand” routing:

Compute path then send data. If data is small, overkill?

Flooding is expensive. Wanderer approach: pick neighbor with

some probability to forward data to. Problems?

Pure gossip: flooding+wanderer. At each node, picks one or the other with

some probability. Either almost all nodes receive packet or

almost no nodes receive it.

1-30

Proposed approach

Parametric probability routing: Controlled flooding. Every node decides to forward packet to

neighbors using a probability function. Probability function based on: distance to

destination, distance from original source to destination, number of copies already received, etc.

2 variants:• Destination attractor.

– S-D distance and CS-D distance.• Directed transmission.

– Also uses number of hops already traversed by packet.

1-31

Destination attractor

PRi, or retransmission probability, given by: (1+k) PRi-1 if packet is getting closer to D.

(1-k) PRi-1 if packet is getting farther from D.

PRi-1 if same or undefined.

k can be adjusted to compensate for “noise” due to losses, mobility, etc.

1-32

Directed transmission

Nodes on shortest path from S-D should forward with high probability.

PRi = exp{k[d(S,D) – d(Ri,D) – I]}, where d(S,D) is distance between source and

destination. d(Ri,D) is distance between current node

and destination, and i is number of hops traveled so far.

1-33

Estimating global information

Number of hops traveled so far, i, is easy. Estimating distance to D:

Each sensor includes its current estimate of distance to D.

When receiving that information from neighbor, sensor updates its information by adding 1.

Sensor chooses its d(S,D) to be the minimum of the currently received information from neighbors.

1-34

Evaluation

Simulations. Noise is used to simulate inaccuracies. Metrics:

Load Lag. Fraction delivered. Overhead?

1-35

Results

From paper…