2012 12-14

1. Minimizing Bus Bunching
Results from a new strategy that cuts wait
times, improve comfort and brings reliability to
bus services
Juan Carlos Muñoz, Felipe Delgado, Ricardo Giesen
Sergio Ariztía, Daniel Hernández, Felipe Ortiz and William Phillips
Department of Transport Engineering and Logistics
Pontificia Universidad Católica de Chile

2. Santiago, Chile

3. Time-space trajectories
Line 201, March 25th, 2009
35
32.5
30
27.5
25
22.5
20
Posición (Km.)
17.5
15
12.5
10
7.5
5
2.5
0
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Tiempo (minutos)
6:30 AM 8:30 AM

4. Boston, MA; line 1 during winter

5. Boston, MA; line 1 during summer

6. Is keeping regular headways that
difficult?
Transit Leaders Roundtable MIT, June 2011

7. Bus Operations without Control
Bus
Waiting
Passengers
Stop Stop
Waiting
Passengers
Bus
Ricardo Giesen ©

8. Bus Operations without Control
a small perturbation…
Waiting
Passengers
Stop Bus Bus Stop
Waiting
Passengers
Ricardo Giesen ©

9. Bus Operations without Control
While one bus is still loading passengers the other bus already left its
last stop
Stop Bus Stop
Bus
Ricardo Giesen ©

10. Bus Operations without Control
Bus
Stop Bus Stop
Ricardo Giesen ©

11. Bus Operations without Control
Without bus control, bus bunching occurs!!!
Stop Stop
Bus
Bus
Ricardo Giesen ©

12. Stable versus unstable equilibrium

13. Stable versus unstable equilibrium

14. Stable versus unstable equilibrium

15. Stable versus unstable equilibrium

16. Stable versus unstable equilibrium

17. Stable versus unstable equilibrium

18. + - + - + - +

19. + - + - + - +

20. + - + - + - +

21. + - + - + - +
And so on so forth.
Our challenge is to keep an inherently unstable system: buses evenly spaced
Now, if we want to prevent bunching from occurring … when is the right time to intervene?

22. Bus bunching is
specially serious,
where bus capacity
is an active
constraint.

23. Bus bunching
 Severe problem if not controlled
 Most passengers wait longer than they should for crowded
buses
 Reduces reliability affecting passengers and operators
 Affects Cycle time and capacity
 Creates frictions between buses (safety)
 Put pressure in the authority for more buses
Contribution: Control Mechanism to Avoid Bus Bunching!

24. 2. Objective
 Propose a headway control mechanism for a high frequency & capacity-
constrained corridor.
 Consider a single control strategies: Holding
 Explore its impact in waiting, reliability, capacity and comfort
 Identify scenarios where the control strategy is recommended.

25. 3. Approach
Based on real-time information (or estimations) about:
Bus position.
Bus loads.
# of Passengers waiting at each stop.
We run a rolling-horizon optimization model each time a bus
reaches a stop or every certain amount of time (e.g. 2 minutes)
The model minimizes:
Time waiting for first bus + time waiting for subsequent buses +
+ time held + penalty for being prevented from boarding

26. 4. Experiment: Simulation Scenarios
One-way loop Transit corridor with 30 Stops
Scenario Bus capacity is Service frequency
reached
1 Yes High
2 No High
3 Yes Medium
4 No Medium

27. Estrategias de control simuladas
4. Experiment: Control strategies
No control
Spontaneous evolution of the system.
Buses dispatched from terminal as soon as they arrive or until the design headway is
reached.
No other control action is taken along the route.
Threshold control
Myopic rule of regularization of headways between buses at every stop.
A bus can be held at every stop to reach a minimum headway with the previous bus.
Holding (HRT)
Solve the rolling horizon optimization model not including green extension or boarding
limits.

28. 5. Results: Simulation Animation
Simulation includes events randomness
2 hours of bus operation. 15 minutes “warm-up” period.

29. 5. Results: Time savings
No Threshold HRT
control control
Wfirst 4552.10 1220.47 805.33
Std. Dev. 459.78 310.43 187.28
% reduction -73.19 -82.31
Wextra 1107.37 661.70 97.49
Std. Dev. 577.01 1299.95 122.59
% reduction -40.25 -91.20
Win-veh 270.57 6541.56 1649.28
Std. Dev. 36.00 868.74 129.56
% reduction 2317.74 509.57
Tot 5930.03 8423.73 2552.10
Std. Dev. 863.80 2377.11 390.01
% reduction 42.05 -56.96

30. 5. Results: Time-space trajectories
s2 NETS sc corrida17 Scenario 1 threshold run17
10 10
9 9
8 8
7 7
Distance (Km)
6
Distance (Km)
6
5 5
4 4
3 3
2 2
1 1
0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Time(minutes) Time(minutes)
No Control Threshold

31. 5. Results: Time-space trajectories s2 NETS sc corrida17
10
9
8 Scenario 1 threshold run17
No Control
10
7
9
Distance (Km)
6
5
8
4
7
3
Distance (Km)
2 6
1
5
0
0 20 40 60 80 100 120
Time(minutes) run17 4
Scenario 1 threshold
10
3
9
8 2
Threshold
7 1
Distance (Km)
6
0
5 0 20 40 60 80 100 120
Time(minutes)
4
3 HRT
2
1
0
0 20 40 60 80 100 120
Time(minutes)

32. 5. Results: Bus Loads
Scenario 1 HBLRT alpha=05 Beta=05 Scenario 1 HBLRT alpha=05 Beta=05
120 120
100 100
80 80
Load (Pax.)
Load (Pax.)
60 60
40 40
20 20
0 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30
Stop Stop
No Control Threshold

33. 5. Results: Bus Loads
Scenario 1 HBLRT alpha=05 Beta=05
120
100 Scenario 1 HBLRT alpha=05 Beta=05
No Control
120
80
100
Load (Pax.)
60
80
40
Load (Pax.)
20
60
0
0 5 10 15 20 25 30
Stop
Scenario 1 HBLRT alpha=05 Beta=05 40
120
20
Threshold
100
80
0
0 5 10 15 20 25 30
Load (Pax.)
60 Stop
40
HRT
20
0
0 5 10 15 20 25 30
Stop

34. 5. Results: Cycle Time
No control HRT 05
350 350
300 mean =33.64 300 mean =35.62
Std.Dev. =3.51 Std.Dev. =1.38
250 250
Frequency
Frequency
200 200
150 150
100 100
50 50
0 0
25 30 35 40 45 25 30 35 40 45
Cycle Time (Minutes) Cycle Time (Minutes)
No Control Threshold

35. 5. Results: Cycle Time
No control
350
300 mean =33.64
No Control
Std.Dev. =3.51 HRT 05
250
350
Frequency
200
150
300 mean =32.11
Std.Dev. =1.2
100 250
50
Frequency
200
0
25 30 35 40 45
HRT 05
Cycle Time (Minutes) 150
350
100
300 mean =35.62
Threshold
Std.Dev. =1.38
250 50
Frequency
200
0
25 30 35 40 45
150 Cycle Time (Minutes)
100 HRT
50
0
25 30 35 40 45
Cycle Time (Minutes)

36. 5. Results: Waiting time Distribution
% of passengers that have to wait between:
Period 15-25 Period 25-120
0-2 min 2-4 min > 4 min 0-2 min 2-4 min > 4 min
No Control 57.76 29.60 12.64 63.46 27.68 8.86
Threshold Control 78.15 20.64 1.21 82.52 16.46 1.02
HRT 79.24 20.29 0.47 87.30 12.62 0.08

37. 6. Impact of implementation failures
Disobeying Technological
Drivers Disruption
Homogeneous Similar
Random signal
distribution across disobedience
buses
fail
across all drivers
Concentration in A subset of Failure in the
certain buses drivers never signal receptor
obey equipment
Concentration in
Signal-less
certain stops
zone

38. Common disobedience rate across drivers
Total Waiting Time [Min]
15000
14000
13000
12000
11000
10000
HRT, Beta=0,5
9000
Sin Control
8000
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
Obedience rate

39. Common disobedience rate across drivers
HRT HRT, 50% obedience
10 10
9 9
8 8
7 7
Distancia [Km]
Distancia [Km]
6 6
5 5
4 4
3 3
2 2
1 1
0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Tiempo [Minutos] Tiempo [Minutos]
HRT, 20% obedience No Control
10 10
9 9
8 8
7 7
Distancia [Km]
Distancia [Km]
6 6
5 5
4 4
3 3
2 2
1 1
0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Tiempo [Minutos] Tiempo [Minutos]

40. Full disobedience of a set of drivers
16000
15000
14000
Total Waiting Time [Min]
13000
12000
11000
10000
9000
8000
0 1 2 3 4 5 6 7
Deaf Buses from a total of 15 buses

41. Full disobedience of a set of drivers
a) HRT b) HRT, 3 deaf buses
10 10
9 9
8 8
7 7
Distancia [Km]
Distancia [Km]
6 6
5 5
4 4
3 3
2 2
1 1
0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Tiempo [Minutos] Tiempo [Minutos]
c) HRT, 6 deaf buses d) No Control
10 10
9 9
8 8
7 Distancia [Km] 7
Distancia [Km]
6 6
5 5
4 4
3 3
2 2
1 1
0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Tiempo [Minutos] Tiempo [Minutos]

42. 7. Implementation
• The first pilot plan consisted in implemnting our holding
tool in buses of line 210 of SuBus from Transantiago
(Santiago, Chile) along its full path from 7:00 to 9:30 AM.
• We chose 24 out of 130 stops to hold buses
• One person in each of these 24 stops received text
messages (from a central computer) into their cell
phones indicating when each bus should depart from the
stop.

43. Plan Description

44. Implementation
Real time GPS Program optimizing
information of dispatch times for each
each bus bus from each stop
Text messages were sent Buses are held according to
automatically to each person the text message instructions
in each of the 24 stops (never more than one minute)

45. Control Points

46. The results were very promising
even though the conditions were far
from ideal

47. Input Data
• Trajectories of given GPS data (on a regular day)
Trajectories
60
50
Kilometers from Terminal
40
30
20
10
0
6:00:00 6:28:48 6:57:36 7:26:24 7:55:12 8:24:00 8:52:48 9:21:36 9:50:24
Time

48. Input Data
• The trajectiories traveled by buses can be
inferred as:
Corrected Trajectories for a typical day
60
50
Kilometers from Terminal
40
30
20
10
0
6:00:00 6:28:48 6:57:36 7:26:24 7:55:12 8:24:00 8:52:48 9:21:36 9:50:24
Time

49. Pilot Analysis
• Trajectories of our experiment
Pilot Corrected Trajectories
60
Kilometers from Terminal
50
40
30
20
10
0
6:00:00 6:28:48 6:57:36 7:26:24 7:55:12 8:24:00 8:52:48 9:21:36 9:50:24
Time

50. Pilot Analysis
• Again… versus a regular day
Corrected Trajectories
60
50
Kilometers from Terminal
40
30
20
10
0
6:00:00 6:28:48 6:57:36 7:26:24 7:55:12 8:24:00 8:52:48 9:21:36 9:50:24
Time

51. The speeds we used need fine-tuning
• Difference between the projected departure
time and the actual departure time
Parada 2/(M) Mirador
10
9
8
7 Unbiased prediction
6
Significant dispersion
Frecuencia
5
4
3
2
1
0
780
120
180
240
300
360
420
480
540
600
660
720
840
900
960
-60
1020
-960
-900
-840
-780
-720
-660
-600
-540
-480
-420
-360
-300
-240
-180
-120
0
-1020
60
More
Diferencia (s)

52. The speeds we used need fine-tuning
• Difference between the projected departure
time and the actual departure time
Parada 2/ (M) Santa Isabel
16
14
12
10
Biased prediction
Frecuencia
8
Significant dispersion
6
4
2
0
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
-60
1020
-960
-900
-840
-780
-720
-660
-600
-540
-480
-420
-360
-300
-240
-180
-120
0
-1020
60
More
Diferencia (s)

53. Main results
• Transantiago computes an indicator for
regularity based on intervals exceeding twice
the expected headway (and for how much).
ICR Aproximado PM y TPM (UF)
14
12
Fines due to regularity on that day
10 dropped around 50%
8
6
4
2
0
Piloto1 Prueba8 Prueba9 Prueba10 Prueba11 Prueba12 Prueba13 Prueba14 Prueba15 Prueba16 Prueba17

54. Main results: cycle times
3:36:00
3:28:48
3:21:36
3:14:24 Piloto 1
Prueba10
Cycle time
3:07:12
3:00:00 Prueba12
2:52:48 Prueba13
2:45:36 Prueba15
2:38:24 Prueba16
2:31:12 Prueba17
2:24:00
5:52:48 6:00:00 6:07:12 6:14:24 6:21:36 6:28:48 6:36:00 6:43:12 6:50:24 6:57:36
Dispatch time
 No significant differences for cycle times

55. Unexpected result
• The demand captured by the line grew!

56. Can we quantify this impact?
• Line 210 captured an extra 20% demand!
106.000
104.000
102.000
Demand on
All lines
100.000
(pax)
98.000
96.000
94.000
7.400 7.600 7.800 8.000 8.200 8.400 8.600 8.800
Demand for Line 210 (pax)

57. This pilot plan can improve significantly
1) GPS errors can be corrected
2) Run the Optimization more often (from 3.5 to 2 min)
3) Calibrate speeds and arrival rates
4) Check data inputs before feeding the system
And more importantly:
5) Bypass the person at the stop. Communicate to drivers

58. 8. Conclusions
Developed a tool for headway control using Holding in real time reaching
time savings of over 50%
Extending it to green time extension and boarding limits savings can reach
over 60% with only minor impact on car users
Huge improvements in comfort and reliability
The tool is fast enough for real time applications. It had been tested
successfully in simulations (for the Insurgentes corridor in Mexico city)
and in the streets (line 210 in Santiago, Chile) with very promising results.

59. Publications and working papers
• Delgado, F., Muñoz, J.C., Giesen, R., Cipriano, A. (2009) Real-Time Control of
Buses in a Transit Corridor Based on Vehicle Holding and Boarding Limits.
Transportation Research Record, Vol 2090, 55-67
• Munoz, J.C. and Giesen, R. (2010). Optimization of Public Transportation
Systems. Encyclopedia of Operations Research and Management Science, Vol
6, 3886-3896.
• Delgado, F., J.C. Muñoz and R. Giesen (2012) How much can holding and
limiting boarding improve transit performance? Trans Res Part B, , vol.46
(9), 1202-1217
• Muñoz, J.C., C. Cortés, F. Delgado, F. Valencia, R. Giesen, D. Sáez and A.
Cipriano (2011) Comparison of dynamic control strategies for transit
operations. Submitted to Trans Res Part C.

60. Roles for Richer Data and Better
Analysis in Improving the
Effectiveness of Transit Systems
Nigel H.M. Wilson
January 25, 2013
11:00 AM (Boston time)

61. Minimizing Bus Bunching
Results from a new strategy that cuts wait
times, improve comfort and brings reliability to
bus services
Juan Carlos Muñoz, Felipe Delgado, Ricardo Giesen
William Phillips, Sergio Ariztía and Daniel Hernández
Department of Transport Engineering and Logistics
Pontificia Universidad Católica de Chile