Lightweight Neighborhood Cardinality Estimation in Dynamic Wireless Networks (IPSN 2014)

1 Challenge the future

Neighborhood Cardinality Estimation in Dynamic Wireless Networks

Marco Cattani, M. Zuniga, A. Loukas, K. Langendoen Embedded Software Group, Delft University of Technology


Motivations

Improve safety of people during an outdoor festival

© Alex Prager


Motivations

Helping people to avoid areas where density crosses dangerous thresholds

© Alex Prager


Requirements

•  Providing each participant with a compact, battery powered device

• Concurrently estimate and communicate the density of the crowd



Requirements

•  Providing each participant with a compact, battery powered device

• Concurrently estimate and communicate the density of the crowd neighborhood cardinality



Existing solutions

Error Scale Energy Concur. Speed

Existing works on cardinality estimation do not fit our requirements


Existing solutions


RFID Low 1000 Low No Fast



Existing solutions



Group testing Low 10 - No V. Fast



Existing solutions




Neigh. Discovery Low 10 Low Yes Slow



Existing solutions





Mobile phones High 10 High Yes Fast



Existing solutions





Mobile phones High 10 High Yes Fast

Estreme Low 100s Low Yes Fast



Estreme’s mechanism


The basic idea

When a room get crowded, the more persons the less is the personal space (in orange)

Person

Personalspace


The basic idea



The same idea applies in time.


The basic idea

The more devices (that periodically generate an event), the shorter is the inter-arrival time

12

7

Period

Inter-arrival time

Event


The basic idea


123

7


The basic idea


12

45

3

7


The basic idea


12

45

3

67


Model

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45

3

67

E(n) = ( period / cardinality )

Given N devices (that periodically generate an event), the expected inter-arrival length (n) is


Model

12

45

3

67


inverting

Cardinality = ( period / n ) – 1



Model

12

45

3

67


inverting

Cardinality = ( period / n ) – 1


ESTREME


Implementation


Implementation

• Duty cycling

Apply Estreme • Periodic event: wakeup

We implemented Estreme in Contiki OS, on top of an asynchronous low-power listening MAC

1

2

rendezvous

B1 BB

4 A1

3

inter-arrival


Implementation

• Duty cycling •  Low-power listening •  First (next) awake neighbor

Apply Estreme • Periodic event: wakeup •  Inter-arrival: rendezvous

We implemented Estreme in Contiki OS, on top of an asynchronous low-power listening MAC

1

2

rendezvous

B1 BB

4 A1

3

inter-arrival


Implementation

• Detect collision • Retransmit the last ACK with

a given probability

Nodes must rendezvous with the first awake neighbor

A1

B B1

2

rendezvous

B1 BB

4 A1

3

inter-arrival

A1

delay


Implementation


a given probability • Accurate timing

•  Measure delay

Still, due to delays, the rendezvous time is longer than the inter-arrival time

A1

B1

2

rendezvous

B1 BB

4 A1

3

inter-arrival

A1

delays


Implementation





A1

B1

2

rendezvous

B1 BB

4 A1

3

inter-arrival

A1

delays


A1

B1

2

rendezvous

B1 BB

4 A1

3

inter-arrival

A1

delays

Implementation



•  Measure delay •  Append delay to

acknowledgments



Implementation



•  Measure delay •  Append delay to

acknowledgments


A1

B1

2

rendezvous

B1 BB

4 A1

3

inter-arrival

A1

delays


Tight bound

Effects of a delay (ε) in the measurements on the estimation error (e)

Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period


Tight bound

1.  To reduce the error we want ρ to be as small as possible. A longer delay ε, increases the estimation error (under-estimation).


Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period


Tight bound

2.  Given a fixed delay, a shorter period increases the estimation error


Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period


Tight bound

3.  Given a fixed delay, with more devices, the estimation error increases


Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period


Tight bound

4.  Estreme requires sub-millisecond accuracy. Example: Period = 1 s, n = 100 neighbors, ε = 1 ms à 9% error


Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period


Implementation

• T-Estreme (Time) •  Periodically measure the

inter-arrival times

•  Average the last measured samples (n)

Nodes must collect several inter-arrival times (samples) to estimate the cardinality

2

3 2 3 4 3

1

2 2 1 3 2

B

A


Implementation

• T-Estreme (Time) •  Periodically measure the

inter-arrival times

• S-Estreme (Space) •  Periodically exchange

average inter-arrivals

Nodes must collect several inter-arrival times (samples) to estimate the cardinality

2

3 2 3 4 3

1

2 2 1 3 2

B

A

2

3


Evaluation


Evaluation

020406080

100

card

inal

ity

node positions

L R

Our testbed consists of 100 nodes with MSP430 processors and CC1101 transceivers


Evaluation

020406080

100

card

inal

ity

node positions

L R

It offers a wide range of neighborhood cardinalities


Evaluation

020406080

100

card

inal

ity

node positions

L R

And a long transmission range. This means high cardinalities, but also drastic changes!


Evaluation

•  Inspired by most recent works in group testing protocols • On-demand cardinality estimator based on rounds

•  Each round, nodes answer with a decreasing probability •  Count number of non-empty rounds (RSSI)

PROS: fast and resilient to collisions CONS: sensitive to noise, only one estimator

Compared Estreme to a state-of-the-art technique (Baseline)


Accuracy in static scenarios

1) At low cardinalities, Estreme is comparable to state-of-the-art techniques

10 15 20 30 40 50 60 80 1000

0.2

0.4

0.6

neighborhood cardinality

rela

tive

erro

r

T−Estreme S−Estreme Baseline



2) At higher cardinalities, Estreme is way better than the state-of-the-art

10 15 20 30 40 50 60 80 1000

0.2

0.4

0.6


rela

tive

erro

r




3) Estreme’ s accuracy is stable across different cardinalities

10 15 20 30 40 50 60 80 1000

0.2

0.4

0.6


rela

tive

erro

r



Tight bound

3.  Given a fixed delay, with more devices, the estimation error increases


Ε[e]=Θ −ρ1+ ρ

$

%&

'

() , ρ =

ε (n+1)period



Why is the estimation accuracy stable across all the densities?

0

200 10 15 20

0

200 30 40 50

−40 0 400

200 60

−40 0 40

80

−40 0 40

100

Coun

t

Deviation from expected value [ms]

Cardinality


Estimation characteristics

S-Estreme provide a smoother signal, but suffers when the cardinality changes in space

0

50

100

150

nodes

card

inal

ity

L R

T−Estreme S−Estreme Ground truth


Adaptability to changes

Under network dynamics, Estreme adapts to sudden cardinality changes in few minutes

0 15 30 45 60 75 900

50

100

150

time (minutes)

card

inal

ity

T−Estreme S−Estreme Ground truth


Adaptability to changes

An hybrid solution provides the right trade-off between crispness and smoothness

0 5 10 15 20 25 30 35 40 450

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150

L R

time (minutes)

card

inal

ity

T−Estreme S−Estreme Hybrid G.Truth


Conclusions

Problem Neighborhood Cardinality Estreme Generic Framework Implementation Cooperative Behaviors Evaluation Accurate and Agile

Lightweight Neighborhood Cardinality Estimation in Dynamic Wireless Networks (IPSN 2014)

Technology

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