Traffic state estimation with multi-sensor data for large networks with macro simulation - part B
1. TRAFFIC STATE ESTIMATIONWITH MULTI-
SENSOR DATA FOR LARGE NETWORSWITH
MACROSIMULATION
PROFESSOR NIKOLAS GEROLIMINIS
SEMESTER PROJECT – SPRING 2015
ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE,
TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY.
YAZAN SAFADI
2. Introduction
▪ Barcelona is ranked as high densely populated
city in Europe (1.6 million people in the 102
km^2 city area).
▪ Study area - Eixamlple district
▪ Number of detectors - 1570
▪ Time window of 2 hours (7:45 – 9:45)
▪ 4 Regions
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 2
3. Demand
Percentage of demand inside every
region and in between the different
region (only with region 4).
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 3
10 20 30 40 50 60 70 80
0
10
20
30
40
50
60
70
Time [Min]
%
Demand In Controller
D14
D41
D24
D42
D34
D43
10 20 30 40 50 60 70 80
0
5
10
15
20
25
30
35
40
45
50
Time [Min]
%
Demand Inside Region
D11
D22
D33
D44
4. Demand
Demand in each region
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TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 4
0 10 20 30 40 50 60 70 80
100
200
300
400
500
600
700
800
Demand
Time [Min]
Demand
[Veh]
D1
D2
D3
D4
5. Demand
Time = 22.5 min[8:12] Time = 105 min[9:30]
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 5
6. Trip Length
Trip length distribution in each
region, we take the average value
for each region as following :
Region 1 – 1.0443
Region 2 – 0.644
Region 3 – 0.846
Region 4 – 1.070
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TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 6
0 0.5 1 1.5
0
5
10
15
20
25
30
Length Trip Distribution Region 1
Trip Length[Km]
0 0.5 1 1.5
0
5
10
15
20
25
30
Length Trip Distribution Region 2
Trip Length[Km]
0 0.5 1 1.5
0
5
10
15
20
25
30
Length Trip Distribution Region 3
Trip Length[Km]
0 0.5 1 1.5
0
5
10
15
20
25
30
Length Trip Distribution Region 4
Trip Length[Km]
Average:1.0443 Average:0.64438
Average:0.846 Average:1.07
7. Flow chart
Model – [i-j] Region
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 7
Input
• Controllers
• Trip Length
• TimeWindow
• Fixed value of
accumulation for
first step
• Production –
Accumulation
relation
Model
• Calculate transfer flow
and accumulation in
time step of 90 second
Output
• Accumulation for
each origin and
destination
8. Model – [i-j] : for each origin and destination
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 8
𝑴𝒊𝒋 =
𝑷𝒊 𝒏𝒊
𝒍𝒊
∗
𝒏𝒊𝒋
𝒏𝒊
Region 1 :
𝒅𝑵𝟏𝟏
𝒅𝒕
= 𝒅𝟏𝟏 + 𝑼𝟒𝟏 ∗ 𝑴𝟒𝟏 − 𝑴𝟏𝟏
𝒅𝑵𝟏𝟐
𝒅𝒕
= 𝒅𝟏𝟐 − 𝑼𝟏𝟒 ∗ 𝑴𝟏𝟐
𝒅𝑵𝟏𝟑
𝒅𝒕
= 𝒅𝟏𝟑 − 𝑼𝟏𝟒 ∗ 𝑴𝟏𝟑
𝒅𝑵𝟏𝟒
𝒅𝒕
= 𝒅𝟏𝟒 − 𝑼𝟏𝟒 ∗ 𝑴𝟏𝟒
𝒊 − 𝒐𝒓𝒊𝒈𝒊𝒏 ; 𝒋 − 𝒅𝒆𝒔𝒕𝒊𝒏𝒂𝒕𝒊𝒐𝒏
11. Result
0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
x 10
4
Acc - Region 1
Time [Min]
Acc
[Veh]
0 20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
Time [Min]
Error
Model-Real
[Veh]
61065
0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
x 10
4
Acc - Region 2
Time [Min]
Acc
[Veh]
0 20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
Time [Min]
Error
Model-Real
[Veh]
5829
0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
x 10
4
Acc - Region 3
Time [Min]
Acc
[Veh]
0 20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
Time [Min]
Error
Model-Real
[Veh]
394956
0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
x 10
4
Acc - Region 4
Time [Min]
Acc
[Veh]
Model
Aimsun
0 20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
Time [Min]
Error
Model-Real
[Veh]
162289
• Full time window prediction –
enormous error
• New approach - testing with
smaller predicted time (7.5min
and 15min).
• Narrowing the time window to
relevant time : 8:12 - 9:30
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TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 11
12. Flow chart
Model – [i-j] Region
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TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 12
Input
• Controllers
• Trip Length
• TimeWindow
• Fixed value of
accumulation for
first step
• Production –
Accumulation
relation
Model
• Calculate transfer flow
and accumulation in
time step of 90 second
Output
• Accumulation for
each origin and
destination
Fixed time window
prediction of 7.5/15 min
13. Model – [i-j]
Accumulation model graphs
compared to Aimsun simulation in
each origin and destination.
Time window prediction – 7.5 min
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TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 13
20 40 60 80 100 120
1000
1500
2000
2500
3000
3500
N-11
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
10
20
30
40
N-12
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
50
100
150
N-13
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
100
200
300
400
500
600
N-14
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
5
10
15
20
25
N-21
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
400
450
500
550
600
N-22
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
10
20
30
40
50
60
N-23
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
50
100
150
200
250
N-24
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
100
200
300
400
N-31
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
20
40
60
80
100
120
N-32
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
N-33
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
200
400
600
800
1000
N-34
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
400
600
800
1000
1200
1400
N-41
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
200
300
400
500
600
700
N-42
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
100
200
300
400
500
600
700
N-43
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
1000
1500
2000
2500
3000
3500
4000
N-44
Time [min]
Accumlation
[Veh]
Model
Aimsun
14. Model – [i-j]
Accumulation model in each
regions.
Error between model to Aimsun
simulation
Time window prediction – 7.5 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 14
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
Time [Min]
Error
Model-Real
[Veh]
6556 7714 23619
Model
Aimsun
93387
16. Model – [i-j]
MFD graphs :
Production calculated in relation to
the relevant accumulation (polyfit
parameters).
Time window prediction – 7.5 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 16
17. Model – [i-j]
Accumulation model in each
regions.
Error between model to Aimsun
simulation
Time window prediction – 15 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 17
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
3500
4000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
3500
4000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
3500
4000
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
3500
4000
Time [Min]
Error
Model-Real
[Veh]
14356 7779 53585
Model
Aimsun
105793
18. Model – [i-j]
Accumulation model graphs
compared to Aimsun simulation in
each origin and destination.
Time window prediction – 15 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 18
20 40 60 80 100 120
1000
1500
2000
2500
3000
3500
N-11
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
5
10
15
20
25
30
N-12
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
50
100
150
N-13
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
100
200
300
400
500
600
N-14
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
5
10
15
20
25
30
N-21
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
400
450
500
550
600
N-22
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
10
20
30
40
50
60
N-23
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
50
100
150
200
250
N-24
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
N-31
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
50
100
150
200
N-32
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
2500
3000
N-33
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
500
1000
1500
2000
N-34
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
200
400
600
800
1000
1200
1400
N-41
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
100
200
300
400
500
600
700
N-42
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
100
200
300
400
500
600
700
N-43
Time [min]
Accumlation
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
N-44
Time [min]
Accumlation
[Veh]
Model
Aimsun
20. Model – [i-j]
MFD graphs :
Production calculated in relation to
the relevant accumulation (polyfit
parameters).
Time window prediction – 15 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 20
21. Flow chart
Model – 4 Region
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 21
Input
• Controllers
• Trip Length
• Time Window
• Fixed value of
accumulation for
first step
• Outflow –
Accumulation
relation
Model
• Calculate outflow and
accumulation in time
step of 90 second
Output
• Accumulation
for each region
Fixed time window
prediction of 7.5/15 min
22. Model – 4 Regions
Region 1:
𝒅𝑵𝟏
𝒅𝒕
= 𝒅𝟏 + 𝑼𝟒𝟏 ∗ 𝑴𝟒𝟏 − 𝑴𝟏𝟏 − 𝑼𝟏𝟒 ∗ 𝑴𝟏𝟒
Region 2:
𝒅𝑵𝟐
𝒅𝒕
= 𝒅𝟐 + 𝑼𝟒𝟐 ∗ 𝑴𝟒𝟐 − 𝑴𝟐𝟐 − 𝑼𝟐𝟒 ∗ 𝑴𝟐𝟒
Region 3:
𝒅𝑵𝟑
𝒅𝒕
= 𝒅𝟑 + 𝑼𝟒𝟑 ∗ 𝑴𝟒𝟑 − 𝑴𝟑𝟑 − 𝑼𝟑𝟒 ∗ 𝑴𝟑𝟒
Region 4:
𝒅𝑵𝟒
𝒅𝒕
= 𝒅𝟒 + 𝑼𝟏𝟒 ∗ 𝑴𝟏𝟒 + 𝑼𝟐𝟒 ∗ 𝑴𝟐𝟒 + 𝑼𝟑𝟒 ∗ 𝑴𝟑𝟒
−𝑴𝟒𝟒 − 𝑼𝟒𝟏 ∗ 𝑴𝟒𝟏 − 𝑼𝟒𝟐 ∗ 𝑴𝟒𝟐 − 𝑼𝟒𝟑 ∗ 𝑴𝟒𝟑
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 22
23. Model – 4 regions
Accumulation model in each
regions.
Error between model to Aimsun
simulation
Time window prediction – 7.5 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 23
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
6640 2545 8911
Model
Aimsun
16310
25. Model – 4 regions
MFD graphs : outflow - accumulation
Time window prediction – 7.5 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 25
26. Model – 4 regions
Accumulation model in each
regions.
Error between model to Aimsun
simulation
Time window prediction – 15 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 26
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
200
400
600
800
1000
1200
1400
1600
Time [Min]
Error
Model-Real
[Veh]
10789 3909 18557
Model
Aimsun
25894
28. Model – 4 regions
MFD graphs : outflow - accumulation
Time window prediction – 15 min
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 28
30. Comparsion
Model – [i-j] Model - 4 regions
Region 1 6556 6640
Region 2 7714 2545
Region 3 23619 8911
Region 4 93387 16310
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
Region 1 Region 2 Region 3 Refion 4
Error
[i,j] 4 regions
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 30
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
20 40 60 80 100 120
0
100
200
300
400
500
600
700
Time [Min]
Error
Model-Real
[Veh]
6640 2545 8911
Model
Aimsun
16310
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 1
Time [Min]
Acc
[Veh]
1500
2000
2500
3000
del-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 2
Time [Min]
Acc
[Veh]
1500
2000
2500
3000
del-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 3
Time [Min]
Acc
[Veh]
1500
2000
2500
3000
del-Real
[Veh]
20 40 60 80 100 120
0
1000
2000
3000
4000
5000
6000
7000
8000
Acc - Region 4
Time [Min]
Acc
[Veh]
1500
2000
2500
3000
del-Real
[Veh]
6556 7714 23619
Model
Aimsun
93387
31. Conclusion
▪ Large time window prediction – big error in both model
▪ Model – [i,j] : MFD error
▪ Model – [i,j] :Transfer flow error
▪ Model – 4 regions : only MFD error, good estimation in 7.5 minutes time window prediction
▪ Even with small time window prediction we aren’t satisfy with the result and we will try different
approach.
▪ We would like to try a model with large time window prediction and to avoid a non liner model.
7/31/2021
TRAFFIC STATE ESTIMATION WITH MULTI-SENSOR DATA FOR LARGE NETWORS WITH MACROSIMULATION 31
