Date post: | 03-Jul-2015 |
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Technology |
Upload: | marco-cattani |
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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
2 Challenge the future
Motivations
Improve safety of people during an outdoor festival
© Alex Prager
3 Challenge the future
Motivations
Helping people to avoid areas where density crosses dangerous thresholds
© Alex Prager
4 Challenge the future
Requirements
• Providing each participant with a compact, battery powered device
• Concurrently estimate and communicate the density of the crowd
Helping people to avoid areas where density crosses dangerous thresholds
5 Challenge the future
Requirements
• Providing each participant with a compact, battery powered device
• Concurrently estimate and communicate the density of the crowd neighborhood cardinality
Helping people to avoid areas where density crosses dangerous thresholds
6 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
Existing works on cardinality estimation do not fit our requirements
7 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Existing works on cardinality estimation do not fit our requirements
8 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 - No V. Fast
Existing works on cardinality estimation do not fit our requirements
9 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 - No V. Fast
Neigh. Discovery Low 10 Low Yes Slow
Existing works on cardinality estimation do not fit our requirements
10 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 - No V. Fast
Neigh. Discovery Low 10 Low Yes Slow
Mobile phones High 10 High Yes Fast
Existing works on cardinality estimation do not fit our requirements
11 Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 - No V. Fast
Neigh. Discovery Low 10 Low Yes Slow
Mobile phones High 10 High Yes Fast
Estreme Low 100s Low Yes Fast
Existing works on cardinality estimation do not fit our requirements
12 Challenge the future
Estreme’s mechanism
13 Challenge the future
The basic idea
When a room get crowded, the more persons the less is the personal space (in orange)
Person
Personalspace
14 Challenge the future
The basic idea
When a room get crowded, the more persons the less is the personal space (in orange)
15 Challenge the future
The basic idea
When a room get crowded, the more persons the less is the personal space (in orange)
16 Challenge the future
The same idea applies in time.
17 Challenge the future
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
18 Challenge the future
The basic idea
The more devices (that periodically generate an event), the shorter is the inter-arrival time
123
7
19 Challenge the future
The basic idea
The more devices (that periodically generate an event), the shorter is the inter-arrival time
12
45
3
7
20 Challenge the future
The basic idea
The more devices (that periodically generate an event), the shorter is the inter-arrival time
12
45
3
67
21 Challenge the future
Model
12
45
3
67
E(n) = ( period / cardinality )
Given N devices (that periodically generate an event), the expected inter-arrival length (n) is
22 Challenge the future
Model
12
45
3
67
E(n) = ( period / cardinality )
inverting
Cardinality = ( period / n ) – 1
Given N devices (that periodically generate an event), the expected inter-arrival length (n) is
23 Challenge the future
Model
12
45
3
67
E(n) = ( period / cardinality )
inverting
Cardinality = ( period / n ) – 1
Given N devices (that periodically generate an event), the expected inter-arrival length (n) is
ESTREME
24 Challenge the future
Implementation
25 Challenge the future
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
26 Challenge the future
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
27 Challenge the future
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
28 Challenge the future
Implementation
• Detect collision • Retransmit the last ACK with
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
29 Challenge the future
Implementation
• Detect collision • Retransmit the last ACK with
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
30 Challenge the future
Implementation
• Detect collision • Retransmit the last ACK with
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
31 Challenge the future
Implementation
• Detect collision • Retransmit the last ACK with
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
32 Challenge the future
A1
B1
2
rendezvous
B1 BB
4 A1
3
inter-arrival
A1
delays
Implementation
• Detect collision • Retransmit the last ACK with
a given probability • Accurate timing
• Measure delay • Append delay to
acknowledgments
Still, due to delays, the rendezvous time is longer than the inter-arrival time
33 Challenge the future
Implementation
• Detect collision • Retransmit the last ACK with
a given probability • Accurate timing
• Measure delay • Append delay to
acknowledgments
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
34 Challenge the future
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
35 Challenge the future
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).
Effects of a delay (ε) in the measurements on the estimation error (e)
Ε[e]=Θ −ρ1+ ρ
$
%&
'
() , ρ =
ε (n+1)period
36 Challenge the future
Tight bound
2. Given a fixed delay, a shorter period increases the estimation error
Effects of a delay (ε) in the measurements on the estimation error (e)
Ε[e]=Θ −ρ1+ ρ
$
%&
'
() , ρ =
ε (n+1)period
37 Challenge the future
Tight bound
3. Given a fixed delay, with more devices, the estimation error increases
Effects of a delay (ε) in the measurements on the estimation error (e)
Ε[e]=Θ −ρ1+ ρ
$
%&
'
() , ρ =
ε (n+1)period
38 Challenge the future
Tight bound
4. Estreme requires sub-millisecond accuracy. Example: Period = 1 s, n = 100 neighbors, ε = 1 ms à 9% error
Effects of a delay (ε) in the measurements on the estimation error (e)
Ε[e]=Θ −ρ1+ ρ
$
%&
'
() , ρ =
ε (n+1)period
39 Challenge the future
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
40 Challenge the future
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
41 Challenge the future
Evaluation
42 Challenge the future
Evaluation
020406080
100
card
inal
ity
node positions
L R
Our testbed consists of 100 nodes with MSP430 processors and CC1101 transceivers
43 Challenge the future
Evaluation
020406080
100
card
inal
ity
node positions
L R
It offers a wide range of neighborhood cardinalities
44 Challenge the future
Evaluation
020406080
100
card
inal
ity
node positions
L R
And a long transmission range. This means high cardinalities, but also drastic changes!
45 Challenge the future
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)
46 Challenge the future
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
47 Challenge the future
Accuracy in static scenarios
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
neighborhood cardinality
rela
tive
erro
r
T−Estreme S−Estreme Baseline
48 Challenge the future
Accuracy in static scenarios
3) Estreme’ s accuracy is stable across different cardinalities
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
49 Challenge the future
Tight bound
3. Given a fixed delay, with more devices, the estimation error increases
Effects of a delay (ε) in the measurements on the estimation error (e)
Ε[e]=Θ −ρ1+ ρ
$
%&
'
() , ρ =
ε (n+1)period
50 Challenge the future
Accuracy in static scenarios
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
51 Challenge the future
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
52 Challenge the future
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
53 Challenge the future
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
50
100
150
L R
time (minutes)
card
inal
ity
T−Estreme S−Estreme Hybrid G.Truth
54 Challenge the future
Conclusions
Problem Neighborhood Cardinality Estreme Generic Framework Implementation Cooperative Behaviors Evaluation Accurate and Agile
55 Challenge the future
Conclusions
Problem Neighborhood Cardinality Estreme Generic Framework Implementation Cooperative Behaviors Evaluation Accurate and Agile