Probabilistic Aggregation for Data Dissemination in ... - SIGMOBILE
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Probabilistic Aggregation for Data Dissemination in VANETs Christian Lochert
Björn Scheuermann
Martin Mauve
Computer Networks Research Group Heinrich Heine University Düsseldorf
The Fourth ACM International Workshop on Vehicular Ad Hoc Networks September 2007 Montreal, Canada
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 1/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation 15 30 35 10 18 5 10 15 15 26 36 18 5 15 15 30 25 3 5 5 15 15 26 3 18 5 10 3 3 35 5 20
20 12 15 30 3 26 35 20 25 15 30 18 10 25 10 8
8 16 18 36 18 10 35 10 12 20 8 16 25 36 18 18 5 15 10 15 30 8 26 3 36 18 5 35 10 15 20 10 26 5 15 35 15 30 20 26 3 25 12 5 15 16 15 30
5 15 26 18 5 35 20 25 15 30 3 10 8 36 35 20
15 30 3 10 15 10 8 36 35 20 25 12 16 18 10 8
35 10 20 8 25 36 18 5 10 15 12 26 16 18 18 10 10 12 8 16 36 18 18 5 10 15 35 26 15 30 26 3
12 5 15 35 10 12 16 15 30 20 8 16 18 26 3 25 36 18 15 35 10 12 26 5 30 20 8 16 35 15 3 25 36 18 20 26 5 15 35 10 12 18 15 30 20 8 16 10 26 3 25 36 18 25 18 5 15 35 10 12 10 15 30 20 8 16 15 35 10 12 36 18 30 20 8 16 25 36 3 25 36 18 18 5 20 8 16 18 5 15 25 36 18 10 15 30
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
0
15 35 30 20 knowledge
0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
30
15 35 30 20 knowledge
0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
45
15 35 30 20 knowledge
30
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
15 35 30 20 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
15 35 30 20 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
100 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,1) 21
1 0 0 0 0 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,2) 21
1 0 0 0 0 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,3) 21
1 0 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,4) 21
1 1 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,1)
h(17,2)
h(17,3)
h(17,4) 21
1 1 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Computation of Elements
1 1 0 0 1 0 Z=2 Z (S) := min({i ∈ N0 | i < w ∧ si+1 = 0} ∪ {w}) = 2 C(S) :=
2Z (S) 22 = = 5.15773 ρ 0.775351
Accuracy can be improved by using multiple sketches
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 4/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Creating and Merging
Merging Two Aggregates
Car B
Car A
1 1 0 0 1 0
1 1 1 0 1 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 5/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Creating and Merging
Merging Two Aggregates
Car B
Car A
1 1 0 0 1 0 1 1 1 0 1 0
1 1 1 0 1 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 5/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions
small aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions
medium aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110
medium aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110 1...101000100000
medium aggregate
1...101000100000 1...111101100110
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110
medium aggregate
1...111101100110
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Challenges of VANET-Aggregation
Adaptions to VANETs
Values can change often Aggregates have to represent this procedure ⇒ How can elements be erased out of a sketch? Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 7/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Soft-State Sketches Deletion of a specific measurement is not possible, but . . . Measurements can die out after some time Extending static bit-field to more flexible (TTL-) counters Counters are set to maximal value Decrementation of counters emulates die out process If counter = 0 then the ’bit’ is not set
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 8/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Merging Aggregates
Car B
Car A
9 8 0 0 6 0
9 7 4 0 8 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 9/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Merging Aggregates
Car B
Car A
9 8 0 0 6 0 9 8 4 0 8 0
9 7 4 0 8 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 9/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Computation of Elements
9 8 4 0 8 0 Z=3 Z (S) := min({i ∈ N0 | i < w ∧ si+1 = 0} ∪ {w}) = 3 C(S) :=
23 2Z (S) = = 10.3179 ρ 0.775351
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 10/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
VANET Applications
Example VANET Application City scenario Cars count Free parking places Total number of parking places
Aggregation of measured data Periodical dissemination of Local (aggregated) information Aggregates of adjacent cells
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 11/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Technical Standard ns-2 simulation with obstacle modeling City scenario (16 km×16 km, 500 km streets) 10,000 nodes, ca. 2,500 equipped with car2car technology Realistic movement by ns-2/VISSIM coupling Simulation time settling: 3 h simulation: 15 min
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 12/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Methodical
Stochastic process to model occupancy of parking places Sketch counter: 5 Bit ⇒ 31 steps Beacon frequency: 1/5 s
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 13/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Methodical
Soft-State approach compared with True value Based on global knowledge
Optimal reference protocol Cars measure value of their cell No aggregation Unlimited bandwidth assumed
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 14/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Local Accuracy Small Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 15/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Forming Aggregates Large Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 16/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Distributing Aggregates Distant Medium Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 17/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Summary
Sketches for duplicate-sensitive aggregation Soft-state approach for VANET applications Applicable for the dissemination of any kind of sums Parking places Current traffic situations ...
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 18/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Thank you for your attention!
Questions? [email protected]
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 19/19
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Probabilistic Aggregation for Data Dissemination in VANETs Christian Lochert
Björn Scheuermann
Martin Mauve
Computer Networks Research Group Heinrich Heine University Düsseldorf
The Fourth ACM International Workshop on Vehicular Ad Hoc Networks September 2007 Montreal, Canada
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 1/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation 15 30 35 10 18 5 10 15 15 26 36 18 5 15 15 30 25 3 5 5 15 15 26 3 18 5 10 3 3 35 5 20
20 12 15 30 3 26 35 20 25 15 30 18 10 25 10 8
8 16 18 36 18 10 35 10 12 20 8 16 25 36 18 18 5 15 10 15 30 8 26 3 36 18 5 35 10 15 20 10 26 5 15 35 15 30 20 26 3 25 12 5 15 16 15 30
5 15 26 18 5 35 20 25 15 30 3 10 8 36 35 20
15 30 3 10 15 10 8 36 35 20 25 12 16 18 10 8
35 10 20 8 25 36 18 5 10 15 12 26 16 18 18 10 10 12 8 16 36 18 18 5 10 15 35 26 15 30 26 3
12 5 15 35 10 12 16 15 30 20 8 16 18 26 3 25 36 18 15 35 10 12 26 5 30 20 8 16 35 15 3 25 36 18 20 26 5 15 35 10 12 18 15 30 20 8 16 10 26 3 25 36 18 25 18 5 15 35 10 12 10 15 30 20 8 16 15 35 10 12 36 18 30 20 8 16 25 36 3 25 36 18 18 5 20 8 16 18 5 15 25 36 18 10 15 30
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
0
15 35 30 20 knowledge
0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
30
15 35 30 20 knowledge
0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
45
15 35 30 20 knowledge
30
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
15 35 30 20 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
15 35 30 20 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregation for Car-2-Car Applications
Duplicate Sensitive Aggregation
knowledge
80
100 knowledge
50
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 2/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,1) 21
1 0 0 0 0 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,2) 21
1 0 0 0 0 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,3) 21
1 0 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,4) 21
1 1 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Probabilistic Counting Definition (FM-Sketch) Data structure for Probabilistic counting of Distinct elements ID: 17 Value: 4
h(17,1)
h(17,2)
h(17,3)
h(17,4) 21
1 1 0 0 1 0 Prob 1/2
1/4
1/8
1/16 1/32
1/64
18 15
4
20
19
17
16
14
13
h: Hash function with positive integer output, where P(h(x) = i) = 2−i Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 3/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Basic Operation
Computation of Elements
1 1 0 0 1 0 Z=2 Z (S) := min({i ∈ N0 | i < w ∧ si+1 = 0} ∪ {w}) = 2 C(S) :=
2Z (S) 22 = = 5.15773 ρ 0.775351
Accuracy can be improved by using multiple sketches
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 4/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Creating and Merging
Merging Two Aggregates
Car B
Car A
1 1 0 0 1 0
1 1 1 0 1 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 5/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Creating and Merging
Merging Two Aggregates
Car B
Car A
1 1 0 0 1 0 1 1 1 0 1 0
1 1 1 0 1 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 5/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions
small aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions
medium aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110
medium aggregate
1...101000100000
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110 1...101000100000
medium aggregate
1...101000100000 1...111101100110
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Aggregating
Aggregation of Larger Regions medium aggregate
1...111101100110
medium aggregate
1...111101100110
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 6/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Challenges of VANET-Aggregation
Adaptions to VANETs
Values can change often Aggregates have to represent this procedure ⇒ How can elements be erased out of a sketch? Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 7/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Soft-State Sketches Deletion of a specific measurement is not possible, but . . . Measurements can die out after some time Extending static bit-field to more flexible (TTL-) counters Counters are set to maximal value Decrementation of counters emulates die out process If counter = 0 then the ’bit’ is not set
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 8/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Merging Aggregates
Car B
Car A
9 8 0 0 6 0
9 7 4 0 8 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 9/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Merging Aggregates
Car B
Car A
9 8 0 0 6 0 9 8 4 0 8 0
9 7 4 0 8 0
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 9/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Introducing Counters
Computation of Elements
9 8 4 0 8 0 Z=3 Z (S) := min({i ∈ N0 | i < w ∧ si+1 = 0} ∪ {w}) = 3 C(S) :=
23 2Z (S) = = 10.3179 ρ 0.775351
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 10/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
VANET Applications
Example VANET Application City scenario Cars count Free parking places Total number of parking places
Aggregation of measured data Periodical dissemination of Local (aggregated) information Aggregates of adjacent cells
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 11/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Technical Standard ns-2 simulation with obstacle modeling City scenario (16 km×16 km, 500 km streets) 10,000 nodes, ca. 2,500 equipped with car2car technology Realistic movement by ns-2/VISSIM coupling Simulation time settling: 3 h simulation: 15 min
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 12/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Methodical
Stochastic process to model occupancy of parking places Sketch counter: 5 Bit ⇒ 31 steps Beacon frequency: 1/5 s
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 13/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Methodology
Simulation Evaluation – Methodical
Soft-State approach compared with True value Based on global knowledge
Optimal reference protocol Cars measure value of their cell No aggregation Unlimited bandwidth assumed
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 14/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Local Accuracy Small Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 15/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Forming Aggregates Large Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 16/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Main Results
Distributing Aggregates Distant Medium Aggregate 1 Soft-state sketches Optimal reference True value
Estimate
0.8 0.6 0.4 0.2
Measurements exist Area of interest Queried cars
0 0
5
10
15
Time (in minutes) Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 17/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Summary
Sketches for duplicate-sensitive aggregation Soft-state approach for VANET applications Applicable for the dissemination of any kind of sums Parking places Current traffic situations ...
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 18/19
Motivation
FM-Sketches
Soft-State Sketches
Evaluation
Summary
Thank you for your attention!
Questions? [email protected]
Christian Lochert, Björn Scheuermann, Martin Mauve Probabilistic Aggregation for Data Dissemination in VANETs
Heinrich Heine University 19/19
