Estimating the Probability of a TimelyTraffic-Hazard Warning via Simulation

Nils Müllner, Sibylle Fröschle, Martin Fränzle

Interdisciplinary Research Center onCritical Systems Engineering for

Socio-Technical Systems

CA RLVON

OSS I ET Z KY

January 12, 2015

Brief Problem Outline Practical Application Conclusion

Agenda I

1 Brief Problem Outline

2 Practical Application

3 Conclusion

Nils Müllner, Sibylle Fröschle, Martin Fränzle 2/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 3/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 3/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 3/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 3/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 3/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 4/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 4/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 4/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 4/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 5/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 5/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 5/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 5/13

Brief Problem Outline Practical Application Conclusion

Underlying question

I How reliable are hazard warning systems?I A car approaches a hazard.I A hazard on its path is a safety threat.I The threat can only be assessed on close range.I Cars between ego-car and hazard can propagate a

warning.

ego-car hazard

r

r

Nils Müllner, Sibylle Fröschle, Martin Fränzle 5/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 6/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 6/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 6/13

Brief Problem Outline Practical Application Conclusion

Approach

Simulation:I specify fixed parameters: distance to hazard, velocity of

ego car, communication range of carsI specify dynamic parameters: velocity of other cars,

number of other carsI goal: determine how reliability depends on (dynamic)

parametersI reliability: successful relay of warning message via other

cars before ego car reaches safety threshold in front ofhazard (i.e. breaking distance)

Nils Müllner, Sibylle Fröschle, Martin Fränzle 6/13

Brief Problem Outline Practical Application Conclusion

Three (+1) settings

1. How many trials are necessary to get resilient results?2. How does the velocity interval of other cars influence the

results?3. How does the communication range of cars influence

results?4. How does this all scale with the number of cars deployed

between ego-car and hazard?

Nils Müllner, Sibylle Fröschle, Martin Fränzle 7/13

Brief Problem Outline Practical Application Conclusion

Three (+1) settings

1. How many trials are necessary to get resilient results?2. How does the velocity interval of other cars influence the

results?3. How does the communication range of cars influence

results?4. How does this all scale with the number of cars deployed

between ego-car and hazard?

Nils Müllner, Sibylle Fröschle, Martin Fränzle 7/13

Brief Problem Outline Practical Application Conclusion

Three (+1) settings

1. How many trials are necessary to get resilient results?2. How does the velocity interval of other cars influence the

results?3. How does the communication range of cars influence

results?4. How does this all scale with the number of cars deployed

between ego-car and hazard?

Nils Müllner, Sibylle Fröschle, Martin Fränzle 7/13

Brief Problem Outline Practical Application Conclusion

Three (+1) settings

1. How many trials are necessary to get resilient results?2. How does the velocity interval of other cars influence the

results?3. How does the communication range of cars influence

results?4. How does this all scale with the number of cars deployed

between ego-car and hazard?

Nils Müllner, Sibylle Fröschle, Martin Fränzle 7/13

Brief Problem Outline Practical Application Conclusion

Setting 1: The necessary number of trials

20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1probabilitydofdwarningdsuccessdvs.dnumberdofdcars

numberdofdcars

pro

bab

ilit

ydof

dtim

elyd

war

nin

g

20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90meandwarningddistanced(ifdsuccess)dvs.dnumberdofdcars

numberdofdcars

mea

ndw

arn

ingd

dis

tan

ce

Figure: 10 trials

Nils Müllner, Sibylle Fröschle, Martin Fränzle 8/13

Brief Problem Outline Practical Application Conclusion

Setting 1: The necessary number of trials

20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1probabilitydofdwarningdsuccessdvs.dnumberdofdcars

numberdofdcars

pro

bab

ilit

ydof

dtim

elyd

war

nin

g

20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100meandwarningddistanced(ifdsuccess)dvs.dnumberdofdcars

numberdofdcars

mea

ndw

arn

ingd

dis

tan

ce

Figure: 1.000 trials

Nils Müllner, Sibylle Fröschle, Martin Fränzle 8/13

Brief Problem Outline Practical Application Conclusion

Setting 1: The necessary number of trials

20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1probabilitydofdwarningdsuccessdvs.dnumberdofdcars

numberdofdcars

pro

bab

ilit

ydof

dtim

elyd

war

nin

g

20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70meandwarningddistanced(ifdsuccess)dvs.dnumberdofdcars

numberdofdcars

mea

ndw

arn

ingd

dis

tan

ce

Figure: 100.000 trials

Nils Müllner, Sibylle Fröschle, Martin Fränzle 8/13

Brief Problem Outline Practical Application Conclusion

Setting 2: The velocity interval

20 30 40 50 60 70 80 90 1000

20

40

velocityNintervalN[0.5,1.5]

numberNofNcarsNaN

Nsta

nd

ard

Ndev

iati

on

20 30 40 50 60 70 80 90 1000

20

40

velocityNintervalN[0.7,1.3]

numberNofNcars

NaN

Nsta

nd

ard

Ndev

iati

on

20 30 40 50 60 70 80 90 1000

20

40

velocityNintervalN[0.9,1.1]

number of carsNaN

Nsta

nd

ard

Ndev

iati

on

Nils Müllner, Sibylle Fröschle, Martin Fränzle 9/13

Brief Problem Outline Practical Application Conclusion

Setting 3: The communication range

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

number of cars

pro

bab

ilit

y fo

r ti

mel

y w

arn

ing

r = 3r = 4r = 5r = 6r = 7

Nils Müllner, Sibylle Fröschle, Martin Fränzle 10/13

Brief Problem Outline Practical Application Conclusion

Lessons learned

I Number of simulations should not be fixed.I The velocity interval has minor influence on results.I The radio range has major influence on results.I The number of cars need a critical mass based on other

parameters for warning mechanisms to be effective.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 11/13

Brief Problem Outline Practical Application Conclusion

Lessons learned

I Number of simulations should not be fixed.I The velocity interval has minor influence on results.I The radio range has major influence on results.I The number of cars need a critical mass based on other

parameters for warning mechanisms to be effective.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 11/13

Brief Problem Outline Practical Application Conclusion

Lessons learned

I Number of simulations should not be fixed.I The velocity interval has minor influence on results.I The radio range has major influence on results.I The number of cars need a critical mass based on other

parameters for warning mechanisms to be effective.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 11/13

Brief Problem Outline Practical Application Conclusion

Lessons learned

I Number of simulations should not be fixed.I The velocity interval has minor influence on results.I The radio range has major influence on results.I The number of cars need a critical mass based on other

parameters for warning mechanisms to be effective.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 11/13

Brief Problem Outline Practical Application Conclusion

Future work

I Employ Hoeffding to determine number of simulations.I Switch to SUMO & OMNET++ for better traffic simulation.I Determine security weak spots caused by unequal

distributions (e.g. traffic backlog).I Tackle larger and realistic scenarios.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 12/13

Brief Problem Outline Practical Application Conclusion

Future work

I Employ Hoeffding to determine number of simulations.I Switch to SUMO & OMNET++ for better traffic simulation.I Determine security weak spots caused by unequal

distributions (e.g. traffic backlog).I Tackle larger and realistic scenarios.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 12/13

Brief Problem Outline Practical Application Conclusion

Future work

I Employ Hoeffding to determine number of simulations.I Switch to SUMO & OMNET++ for better traffic simulation.I Determine security weak spots caused by unequal

distributions (e.g. traffic backlog).I Tackle larger and realistic scenarios.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 12/13

Brief Problem Outline Practical Application Conclusion

Future work

I Employ Hoeffding to determine number of simulations.I Switch to SUMO & OMNET++ for better traffic simulation.I Determine security weak spots caused by unequal

distributions (e.g. traffic backlog).I Tackle larger and realistic scenarios.

Nils Müllner, Sibylle Fröschle, Martin Fränzle 12/13

Brief Problem Outline Practical Application Conclusion

Questions?

Nils Müllner, Sibylle Fröschle, Martin Fränzle 13/13