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

Santiago, Chile

Time-space trajectories Line 201, March 25th, 2009

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 3000

2.5

5

7.5

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27.5

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32.5

35

Tiempo (minutos)

Posic

ión (

Km

.)

6:30 AM 8:30 AM

Boston, MA; line 1 during winter

Boston, MA; line 1 during summer

Is keeping regular headways that

difficult?

Transit Leaders Roundtable MIT, June 2011

Ricardo Giesen ©

Bus

Bus

Stop Stop

Waiting

Passengers

Waiting

Passengers

Bus Operations without Control

Ricardo Giesen ©

Bus Bus Stop Stop

a small perturbation…

Waiting

Passengers

Waiting

Passengers

Bus Operations without Control

Ricardo Giesen ©

Bus

Bus

Stop Stop

While one bus is still loading passengers the other bus already left its

last stop

Bus Operations without Control

Ricardo Giesen ©

Bus

Bus Stop Stop

Bus Operations without Control

Ricardo Giesen ©

Bus

Bus

Stop Stop

Without bus control, bus bunching occurs!!!

Bus Operations without Control

Stable versus unstable equilibrium

Stable versus unstable equilibrium

Stable versus unstable equilibrium

Stable versus unstable equilibrium

Stable versus unstable equilibrium

Stable versus unstable equilibrium

+ - + - + - +

+ - + - + - +

+ - + - + - +

+ - + - + - +

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?

Bus bunching is

specially serious,

where bus capacity

is an active

constraint.

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!

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.

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

4. Experiment: Simulation Scenarios

Scenario Bus capacity is

reached

Service frequency

1 Yes High

2 No High

3 Yes Medium

4 No Medium

One-way loop Transit corridor with 30 Stops

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.

Estrategias de control simuladas 4. Experiment: Control strategies

5. Results: Simulation Animation

Simulation includes events randomness

2 hours of bus operation. 15 minutes “warm-up” period.

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

5. Results: Time savings

5. Results: Time-space trajectories

No Control Threshold

0 20 40 60 80 100 1200

1

2

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7

8

9

10s2 NETS sc corrida17

Dis

tance (

Km

)

Time(minutes)0 20 40 60 80 100 120

0

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7

8

9

10Scenario 1 threshold run17

Dis

tance (

Km

)

Time(minutes)

5. Results: Time-space trajectories

No

Co

ntr

ol

Th

resh

old

0 20 40 60 80 100 1200

1

2

3

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5

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7

8

9

10s2 NETS sc corrida17

Dis

tance (

Km

)

Time(minutes)

0 20 40 60 80 100 1200

1

2

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4

5

6

7

8

9

10Scenario 1 threshold run17

Dis

tance (

Km

)

Time(minutes)

HRT

0 20 40 60 80 100 1200

1

2

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4

5

6

7

8

9

10Scenario 1 threshold run17

Dis

tance (

Km

)

Time(minutes)

5. Results: Bus Loads

No Control Threshold

0 5 10 15 20 25 300

20

40

60

80

100

120Scenario 1 HBLRT alpha=05 Beta=05

Load (

Pax.)

Stop0 5 10 15 20 25 30

0

20

40

60

80

100

120Scenario 1 HBLRT alpha=05 Beta=05

Load (

Pax.)

Stop

5. Results: Bus Loads

0 5 10 15 20 25 300

20

40

60

80

100

120Scenario 1 HBLRT alpha=05 Beta=05

Load (

Pax.)

Stop

0 5 10 15 20 25 300

20

40

60

80

100

120Scenario 1 HBLRT alpha=05 Beta=05

Load (

Pax.)

Stop

No

Co

ntr

ol

Th

resh

old

HRT

0 5 10 15 20 25 300

20

40

60

80

100

120Scenario 1 HBLRT alpha=05 Beta=05

Load (

Pax.)

Stop

5. Results: Cycle Time

No Control Threshold

25 30 35 40 450

50

100

150

200

250

300

350

mean =33.64

Std.Dev. =3.51

No control

Fre

quency

Cycle Time (Minutes)25 30 35 40 45

0

50

100

150

200

250

300

350

mean =35.62

Std.Dev. =1.38

HRT 05

Fre

quency

Cycle Time (Minutes)

5. Results: Cycle Time

25 30 35 40 450

50

100

150

200

250

300

350

mean =33.64

Std.Dev. =3.51

No control

Fre

quency

Cycle Time (Minutes)

25 30 35 40 450

50

100

150

200

250

300

350

mean =35.62

Std.Dev. =1.38

HRT 05

Fre

quency

Cycle Time (Minutes)

No

Co

ntr

ol

Th

resh

old

25 30 35 40 450

50

100

150

200

250

300

350

mean =32.11

Std.Dev. =1.2

HRT 05

Fre

quency

Cycle Time (Minutes)

HRT

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

Disobeying Drivers

Similar disobedience across all drivers

A subset of drivers never obey

Technological

Disruption

Random signal fail

Failure in the signal receptor equipment

Signal-less zone

Homogeneous distribution across buses

Concentration in certain buses

Concentration in certain stops

6. Impact of implementation failures

Common disobedience rate across drivers

8000

9000

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15000

0%10%20%30%40%50%60%70%80%90%100%

Tota

l W

aiti

ng

Tim

e [M

in]

Obedience rate

HRT, Beta=0,5

Sin Control

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Dis

tancia

[K

m]

Tiempo [Minutos]0 20 40 60 80 100 120

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tan

cia

[K

m]

Tiempo [Minutos]

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tancia

[K

m]

Tiempo [Minutos]0 20 40 60 80 100 120

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Dis

tancia

[K

m]

Tiempo [Minutos]

HRT, 50% obedience HRT

HRT, 20% obedience No Control

Common disobedience rate across drivers

Full disobedience of a set of drivers

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Tota

l W

aiti

ng T

ime

[Min

]

Deaf Buses from a total of 15 buses

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tan

cia

[K

m]

Tiempo [Minutos]

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tan

cia

[K

m]

Tiempo [Minutos]0 20 40 60 80 100 120

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tan

cia

[K

m]

Tiempo [Minutos]

b) HRT, 3 deaf buses a) HRT

c) HRT, 6 deaf buses d) No Control

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tan

cia

[K

m]

Tiempo [Minutos]

Full disobedience of a set of drivers

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.

Plan Description

Implementation

Real time GPS information of each bus

Program optimizing dispatch times for each bus from each stop

Text messages were sent automatically to each person in each of the 24 stops

Buses are held according to the text message instructions (never more than one minute)

Control Points

The results were very promising even though the conditions were far

from ideal

Input Data

• Trajectories of given GPS data (on a regular day)

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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

Kilo

met

ers

fro

m T

erm

inal

Time

Trajectories

Input Data • The trajectiories traveled by buses can be

inferred as:

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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

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erm

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Corrected Trajectories for a typical day

Pilot Analysis

• Trajectories of our experiment

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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

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me

ters

fro

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erm

inal

Time

Pilot Corrected Trajectories

Pilot Analysis

• Again… versus a regular day

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Kilo

met

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erm

inal

Time

Corrected Trajectories

• Difference between the projected departure time and the actual departure time

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20

-96

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-66

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-12

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Mo

re

Fre

cue

nci

a

Diferencia (s)

Parada 2/(M) Mirador

The speeds we used need fine-tuning

Unbiased prediction

Significant dispersion

• Difference between the projected departure time and the actual departure time

The speeds we used need fine-tuning

0

2

4

6

8

10

12

14

16

-10

20

-96

0

-90

0

-84

0

-78

0

-72

0

-66

0

-60

0

-54

0

-48

0

-42

0

-36

0

-30

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-24

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-18

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-12

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-60 0

60

12

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78

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84

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90

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96

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Mo

re

Fre

cue

nci

a

Diferencia (s)

Parada 2/ (M) Santa Isabel

Biased prediction

Significant dispersion

Main results

• Transantiago computes an indicator for regularity based on intervals exceeding twice the expected headway (and for how much).

0

2

4

6

8

10

12

14

Piloto1 Prueba8 Prueba9 Prueba10 Prueba11 Prueba12 Prueba13 Prueba14 Prueba15 Prueba16 Prueba17

ICR Aproximado PM y TPM (UF)

Fines due to regularity on that day dropped around 50%

Main results: cycle times

2:24:00

2:31:12

2:38:24

2:45:36

2:52:48

3:00:00

3:07:12

3:14:24

3:21:36

3:28:48

3:36:00

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

Cyc

le t

ime

Dispatch time

Piloto 1

Prueba10

Prueba12

Prueba13

Prueba15

Prueba16

Prueba17

No significant differences for cycle times

Unexpected result

• The demand captured by the line grew!

Can we quantify this impact?

• Line 210 captured an extra 20% demand!

94.000

96.000

98.000

100.000

102.000

104.000

106.000

7.400 7.600 7.800 8.000 8.200 8.400 8.600 8.800

Demand for Line 210 (pax)

Demand on All lines

(pax)

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

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.

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.

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)

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