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1Challenge the future
Neighborhood Cardinality Estimation
in Dynamic Wireless Networks
Marco Cattani, M. Zuniga, A. Loukas...
2Challenge the future
Motivations
Improve safety of people during an outdoor
festival
© Alex Prager
3Challenge the future
Motivations
Helping people to avoid areas where density
crosses dangerous thresholds
© Alex Prager
4Challenge the future
Requirements
•  Providing each participant
with a compact, battery
powered device
•  Concurrently es...
5Challenge the future
Requirements
•  Providing each participant
with a compact, battery
powered device
•  Concurrently es...
6Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
Existing works on cardinality estimation do
not ...
7Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Existing works on card...
8Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 -...
9Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 -...
10Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 ...
11Challenge the future
Existing solutions
Error Scale Energy Concur. Speed
RFID Low 1000 Low No Fast
Group testing Low 10 ...
12Challenge the future
Estreme’s mechanism
13Challenge the future
The basic idea
When a room get crowded, the more persons
the less is the personal space (in orange)...
14Challenge the future
The basic idea
When a room get crowded, the more persons
the less is the personal space (in orange)
15Challenge the future
The basic idea
When a room get crowded, the more persons
the less is the personal space (in orange)
16Challenge the future
The same idea applies in time.
17Challenge the future
The basic idea
The more devices (that periodically generate
an event), the shorter is the inter-arr...
18Challenge the future
The basic idea
The more devices (that periodically generate
an event), the shorter is the inter-arr...
19Challenge the future
The basic idea
The more devices (that periodically generate
an event), the shorter is the inter-arr...
20Challenge the future
The basic idea
The more devices (that periodically generate
an event), the shorter is the inter-arr...
21Challenge the future
Model
E(n) = ( period / cardinality )
Given N devices (that periodically generate an
event), the e...
22Challenge the future
Model
E(n) = ( period / cardinality )
inverting
Cardinality = ( period / n ) – 1
Given N devices ...
23Challenge the future
Model
E(n) = ( period / cardinality )
inverting
Cardinality = ( period / n ) – 1
Given N devices ...
24Challenge the future
Implementation
25Challenge the future
Implementation
•  Duty cycling
Apply Estreme
•  Periodic event: wakeup
We implemented Estreme in Co...
26Challenge the future
Implementation
•  Duty cycling
•  Low-power listening
•  First (next) awake neighbor
Apply Estreme
...
27Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
Nodes must r...
28Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
•  Accurate ...
29Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
•  Accurate ...
30Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
•  Accurate ...
31Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
•  Accurate ...
32Challenge the future
A1
B1
2
rendezvous
B1 BB
4 A1
3
inter-
arrival
A1
delays
Implementation
•  Detect collision
•  Retr...
33Challenge the future
Implementation
•  Detect collision
•  Retransmit the last ACK with
a given probability
•  Accurate ...
34Challenge the future
Tight bound
Effects of a delay (ε) in the measurements on
the estimation error (e)
Ε[e]= Θ −
ρ
1+ ρ...
35Challenge the future
Tight bound
1.  To reduce the error we want ρ to be as small as possible.
A longer delay ε, increas...
36Challenge the future
Tight bound
2.  Given a fixed delay, a shorter period increases the
estimation error
Effects of a d...
37Challenge the future
Tight bound
3.  Given a fixed delay, with more devices, the estimation error
increases
Effects of a...
38Challenge the future
Tight bound
4.  Estreme requires sub-millisecond accuracy. Example:
Period = 1 s, n = 100 neighbors...
39Challenge the future
Implementation
•  T-Estreme (Time)
•  Periodically measure the
inter-arrival times
•  Average the l...
40Challenge the future
Implementation
•  T-Estreme (Time)
•  Periodically measure the
inter-arrival times
•  S-Estreme (Sp...
41Challenge the future
Evaluation
42Challenge the future
Evaluation
0
20
40
60
80
100
cardinality
node positions
L R
Our testbed consists of 100 nodes with
...
43Challenge the future
Evaluation
0
20
40
60
80
100
cardinality
node positions
L R
It offers a wide range of neighborhood
...
44Challenge the future
Evaluation
0
20
40
60
80
100
cardinality
node positions
L R
And a long transmission range. This mea...
45Challenge the future
Evaluation
•  Inspired by most recent works in group testing protocols
•  On-demand cardinality est...
46Challenge the future
Accuracy in static scenarios
1) At low cardinalities, Estreme is comparable
to state-of-the-art tec...
47Challenge the future
Accuracy in static scenarios
2) At higher cardinalities, Estreme is way
better than the state-of-th...
48Challenge the future
Accuracy in static scenarios
3) Estreme’ s accuracy is stable across
different cardinalities
10 15 ...
49Challenge the future
Tight bound
3.  Given a fixed delay, with more devices, the estimation error
increases
Effects of a...
50Challenge the future
Accuracy in static scenarios
Why is the estimation accuracy stable across
all the densities?
0
200
...
51Challenge the future
Estimation characteristics
S-Estreme provide a smoother signal, but
suffers when the cardinality ch...
52Challenge the future
Adaptability to changes
Under network dynamics, Estreme adapts to
sudden cardinality changes in few...
53Challenge the future
Adaptability to changes
An hybrid solution provides the right
trade-off between crispness and smoot...
54Challenge the future
Conclusions
Problem
Neighborhood Cardinality
Estreme
Generic Framework
Implementation
Cooperative B...
55Challenge the future
Conclusions
Problem
Neighborhood Cardinality
Estreme
Generic Framework
Implementation
Cooperative B...
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Lightweight Neighborhood Cardinality Estimation in Dynamic Wireless Networks (IPSN 2014)

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

  1. 1. 1Challenge 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. 2. 2Challenge the future Motivations Improve safety of people during an outdoor festival © Alex Prager
  3. 3. 3Challenge the future Motivations Helping people to avoid areas where density crosses dangerous thresholds © Alex Prager
  4. 4. 4Challenge 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. 5. 5Challenge 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. 6. 6Challenge the future Existing solutions Error Scale Energy Concur. Speed Existing works on cardinality estimation do not fit our requirements
  7. 7. 7Challenge 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. 8. 8Challenge 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. 9. 9Challenge 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. 10. 10Challenge 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. 11. 11Challenge 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. 12. 12Challenge the future Estreme’s mechanism
  13. 13. 13Challenge the future The basic idea When a room get crowded, the more persons the less is the personal space (in orange) Person Personal space
  14. 14. 14Challenge the future The basic idea When a room get crowded, the more persons the less is the personal space (in orange)
  15. 15. 15Challenge the future The basic idea When a room get crowded, the more persons the less is the personal space (in orange)
  16. 16. 16Challenge the future The same idea applies in time.
  17. 17. 17Challenge the future The basic idea The more devices (that periodically generate an event), the shorter is the inter-arrival time 1 2 7 Period Inter-arrival time Event
  18. 18. 18Challenge the future The basic idea The more devices (that periodically generate an event), the shorter is the inter-arrival time 1 2 3 7
  19. 19. 19Challenge the future The basic idea The more devices (that periodically generate an event), the shorter is the inter-arrival time 1 2 4 5 3 7
  20. 20. 20Challenge the future The basic idea The more devices (that periodically generate an event), the shorter is the inter-arrival time 1 2 4 5 3 6 7
  21. 21. 21Challenge the future Model E(n) = ( period / cardinality ) Given N devices (that periodically generate an event), the expected inter-arrival length (n) is
  22. 22. 22Challenge the future Model 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. 23. 23Challenge the future Model 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. 24. 24Challenge the future Implementation
  25. 25. 25Challenge 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. 26. 26Challenge 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. 27. 27Challenge 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. 28. 28Challenge 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. 29. 29Challenge 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. 30. 30Challenge 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. 31. 31Challenge 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. 32. 32Challenge 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. 33. 33Challenge 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. 34. 34Challenge the future Tight bound Effects of a delay (ε) in the measurements on the estimation error (e) Ε[e]= Θ − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  35. 35. 35Challenge 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 − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  36. 36. 36Challenge 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 − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  37. 37. 37Challenge 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 − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  38. 38. 38Challenge 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 − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  39. 39. 39Challenge 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. 40. 40Challenge 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. 41. 41Challenge the future Evaluation
  42. 42. 42Challenge the future Evaluation 0 20 40 60 80 100 cardinality node positions L R Our testbed consists of 100 nodes with MSP430 processors and CC1101 transceivers
  43. 43. 43Challenge the future Evaluation 0 20 40 60 80 100 cardinality node positions L R It offers a wide range of neighborhood cardinalities
  44. 44. 44Challenge the future Evaluation 0 20 40 60 80 100 cardinality node positions L R And a long transmission range. This means high cardinalities, but also drastic changes!
  45. 45. 45Challenge 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. 46. 46Challenge 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 80 100 0 0.2 0.4 0.6 neighborhood cardinality relativeerror T−Estreme S−Estreme Baseline
  47. 47. 47Challenge 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 80 100 0 0.2 0.4 0.6 neighborhood cardinality relativeerror T−Estreme S−Estreme Baseline
  48. 48. 48Challenge the future Accuracy in static scenarios 3) Estreme’ s accuracy is stable across different cardinalities 10 15 20 30 40 50 60 80 100 0 0.2 0.4 0.6 neighborhood cardinality relativeerror T−Estreme S−Estreme Baseline
  49. 49. 49Challenge 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 − ρ 1+ ρ $ % & ' ( ) , ρ = ε(n +1) period
  50. 50. 50Challenge 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 40 0 200 60 −40 0 40 80 −40 0 40 100 Count Deviation from expected value [ms] Cardinality
  51. 51. 51Challenge the future Estimation characteristics S-Estreme provide a smoother signal, but suffers when the cardinality changes in space 0 50 100 150 nodes cardinality L R T−Estreme S−Estreme Ground truth
  52. 52. 52Challenge the future Adaptability to changes Under network dynamics, Estreme adapts to sudden cardinality changes in few minutes 0 15 30 45 60 75 90 0 50 100 150 time (minutes) cardinality T−Estreme S−Estreme Ground truth
  53. 53. 53Challenge 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 45 0 50 100 150 L R time (minutes) cardinality T−Estreme S−Estreme Hybrid G.Truth
  54. 54. 54Challenge the future Conclusions Problem Neighborhood Cardinality Estreme Generic Framework Implementation Cooperative Behaviors Evaluation Accurate and Agile
  55. 55. 55Challenge the future Conclusions Problem Neighborhood Cardinality Estreme Generic Framework Implementation Cooperative Behaviors Evaluation Accurate and Agile

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