1. LT1: Development, calibration and validation of
bus-following model to support analysis and
evaluation of alternative BRT strategies under
different scenarios
Luis Antonio Lindau
Paula Manoela dos Santos

2. Mile-
OUTPUTS
stones
M1 Do vehicle-following literature review
M2 Check potential of existing models to represent bus behavior
M3 Select data collection technique
M4 Plan field data collection
M5 Collect data
M6 Process data
M7 Define bus-following model
M8 Final report
Transit Leaders Roundtable MIT, June 2011

3. Comparing: GHR and Gipps
GHR reveled unstable for typical Gipps is attractive for successive
bus stopping maneuvers. stopping buses.
1 0,6
0,5 0,4
0 0,2
acceleration (m/s²)
0 20 40 60 80 100 120 140
acceleration (m/s²))
-0,5 0
0 50 100 150 200
-1 -0,2
-1,5 -0,4
-2 -0,6
-2,5
time (s) -0,8
time (s)

4. Data collection (manual vs. automatic)
Reported last
year

5. Solution: image recognition software Kinovea 0.8.15
• Developed
for studying
athletic
techniques
• free and
open source
• 33 info/s

6. Paralaxis correction
𝐶1 +𝐶2 𝑋 𝑓 +𝐶3 𝑌 𝑓 𝐶6 +𝐶7 𝑋 𝑓 +𝐶8 𝑌 𝑓
𝑋𝑟 = 𝐶4 𝑋 𝑓 +𝐶5 𝑌 𝑓 +1
𝑌𝑟 = 𝐶4 𝑋 𝑓 +𝐶5 𝑌 𝑓 +1
Bleyl, R. L. (1972) Traffic analysis of time lapse photographs without employing a perspective grid. Traffic
Engineering, p. 29-31.

7. Methodology
Find a setting to film Locate and measure 4 reference points
Film making (with vehicle loading Film analysis with image recognition
estimation) software
Data collection (distance vs. time) Calibration of parameters

8. Calibrated models
FREE FLOW
𝑣(𝑡)
𝑎 𝑡 + 𝑑𝑡 = 𝐴 𝑚𝑎𝑥 × 1 −
𝑉 𝑑𝑒𝑠
BUS STOPPING
𝑣𝑛 𝑡 + 𝑇 = 𝑏𝑛 × 𝑇 + 𝑏 𝑛 2 × 𝑇 2 − 𝑏 𝑛 × 2 × 𝑥 𝑡𝑎𝑟𝑔𝑒𝑡 − 𝑥 𝑛 (𝑡) − 𝑣 𝑛 (𝑡) × 𝑇
Static target:
next station

9. Data analysis
Software output Real distance calculation
Track
Label : 18:39:03 corrected parameters
Coords (x,y:px; t:time)
t (s) Xv (m) Yv (m) h (m) d (m)
x y t
0 5,1242567 6,0919539 7,96052191 0
23 27 0
0,5 5,07053561 5,88621922 7,76903521 0,1914867
23 26 500
0,634 4,8952569 5,84434539 7,62364173 0,33688018
22 26 634
22 25 834 0,834 4,84202476 5,63956763 7,43302945 0,52749246
21 25 1067 1,067 4,66758358 5,59817115 7,28874863 0,67177328
21 24 1101 1,101 4,61483563 5,39434269 7,09898873 0,86153319
21 23 1334 1,334 4,56224048 5,19110469 6,91097722 1,04954469
20 23 1401 1,401 4,38895678 5,15053206 6,766899 1,19362291
20 22 1535 1,535 4,3368393 4,94823141 6,57975449 1,38076742
19 22 1668 1,668 4,16437691 4,90812353 6,43674697 1,52377494
19 21 1701 1,701 4,1127325 4,70675283 6,25044725 1,71007466

10. Data analysis
Real distance calculation Model distance calculation
(from the linear acceleration model)
Real Model
t (s) Xv (m) Yv (m) h (m) d (m) a (m/s²) min²(m/s)
v d d (m)
0 5,1242567 6,0919539 7,96052191 0 0 0 0 0
0,5 5,07053561 5,88621922 7,76903521 0,1914867 0,89368685 0,446843423
0,001019845 0,22342171
0,634 4,8952569 5,84434539 7,62364173 0,33688018 0,86023957 0,562115526
0,001454277 0,29874519
0,834 4,84202476 5,63956763 7,43302945 0,52749246 0,85161119 0,732437764
0,00676666 0,44523275
1,067 4,66758358 5,59817115 7,28874863 0,67177328 0,83886217 0,92789265
0,000106948 0,66143173
1,101 4,61483563 5,39434269 7,09898873 0,86153319 0,82423192 0,955916535
0,028089857 0,69393289
1,334 4,56224048 5,19110469 6,91097722 1,04954469 0,82213426 1,147473819
0,007788133 0,96129429
1,401 4,38895678 5,15053206 6,766899 1,19362291 0,80779575 1,201596134
0,023049822 1,04180124
1,535 4,3368393 4,94823141 6,57975449 1,38076742 0,80374457 1,309297907
0,026738876 1,21724716
1,668 4,16437691 4,90812353 6,43674697 1,52377494 0,79568284 1,415123726
0,013998753 1,40545861
1,701 4,1127325 4,70675283 6,25044725 1,71007466 0,78776154 1,441119856
0,06607938 1,45301557
Minimize the sum of squared differences toAmax the
𝑣(𝑡) obtain Vdes
𝑎 𝑡 + 𝑑𝑡 = 𝐴 𝑚𝑎𝑥 × 1 −
best alignment𝑉 𝑑𝑒𝑠 0,83413911 15,9777749

11. Data analysis: acceleration
8 50
observed acceleration
45
7 observed speed
speed (m/s) – acceleration (m/s²)
real distance 40
6
35
5
distance (m)
30
4 25
20
3
15
2
10
1
5
0 0
0 2 4 6 8 10 12
time (s)

12. Data analysis: acceleration
8 50
observed speed 45
7
speed modeled
speed (m/s) – acceleration (m/s²)
40
observed acceleration
6
acceleration modeled 35
real distance
5
distance (m)
distance modeled 30
4 25
20
3
15
2
10
1
5
0 0
0 2 4 6 8 10 12
time (s)

13. Acceleration by occupancy level
1,60
1,40
level 1
1,20
acceleration (m/s²)
level 2
1,00
level 3
0,80
0,60 level 4
0,40 level 5
0,20 average
0,00
0 1 2 3 4 5 6
bus load levels
Level 1 Level 2 Level 3 Level 4 Level 5
Acceleration 1,07 0,94 0,92 0,81 0,80
(m/s²) (0,11) (0,16) (0,09) (0,17) (0,14)
Time to reach 33 35 34 40 49
60km/h (s) (7,49) (7,00) (3,60) (7,74) (16,74)

14. Data analysis: deceleration
25
distance (m) – speed (m/s)
20
15
10
observed distance
5
observed speed
0
0 2 4 6 8 10 12 14
time (s)

15. Data analysis: deceleration
25
distance (m) – speed (m/s)
20
15
10
modeled distance
modeled speed
5 observed distance
observed speed
0
0 2 4 6 8 10 12 14
time (s)

16. Deceleration by occupancy level
7,00
6,00 level 1
5,00
deceleration (m/s²)
level 2
4,00
level 3
3,00
level 4
2,00
1,00 average
0,00
0 1 2 3 4 5
bus load levels
Level 1 Level 2 Level 3 Level 4
τ=1s 1,80 1,58 1,44 1,29
(0,52) (0,78) (0,63) (0,52)
Deceleration (m/s²)
τ=0,66s 2,13 1,97 1,70 1,51
(0,66) (1,20) (2,20) (2,69)