This document describes a study estimating traffic conditions in Barcelona using multi-sensor data and macrosimulation. The study area was divided into 4 regions, with 1570 detectors collecting data over a 2 hour period. A macroscopic model was developed to estimate accumulation values in each region based on production and flow between regions. The model was tested against real accumulation values from Aimsun microsimulation, showing large errors over the full time window but potential for improved accuracy with shorter prediction times.
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).
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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
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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