Minimizing Bus Bunching   Results from a new strategy that cuts waittimes, improve comfort and brings reliability to      ...
Santiago, Chile
Time-space trajectories                                 Line 201, March 25th, 2009                  35                 32....
Boston, MA; line 1 during winter
Boston, MA; line 1 during summer
Is keeping regular headways that             difficult?          Transit Leaders Roundtable   MIT, June 2011
Bus Operations without Control                              BusWaitingPassengers        Stop                              ...
Bus Operations without Control a small perturbation…WaitingPassengers        Stop   Bus                           Bus   St...
Bus Operations without ControlWhile one bus is still loading passengers the other bus already left itslast stop         St...
Bus Operations without Control                     BusStop                                 Bus   Stop                  Ric...
Bus Operations without ControlWithout bus control, bus bunching occurs!!!   Stop                                       Sto...
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...
Bus bunching isspecially serious,where bus capacityis an activeconstraint.
Bus bunching Severe problem if not controlled   Most passengers wait longer than they should for crowded     buses   Re...
2. Objective Propose a headway control mechanism for a high frequency & capacity-  constrained corridor. Consider a sing...
3. ApproachBased on real-time information (or estimations) about:       Bus position.       Bus loads.       # of Passenge...
4. Experiment: Simulation Scenarios           One-way loop Transit corridor with 30 Stops    Scenario            Bus capac...
Estrategias de control simuladas  4. Experiment: Control strategiesNo controlSpontaneous evolution of the system.Buses dis...
5. Results: Simulation Animation                  Simulation includes events randomness      2 hours of bus operation. 15 ...
5. Results: Time savings                         No      Threshold    HRT                       control    control        ...
5. Results: Time-space trajectories                                   s2 NETS sc corrida17                                ...
5. Results: Time-space trajectories                     s2 NETS sc corrida17                                  10          ...
5. Results: Bus Loads                            Scenario 1 HBLRT alpha=05 Beta=05                                        ...
5. Results: Bus Loads                                         Scenario 1 HBLRT alpha=05 Beta=05                           ...
5. Results: Cycle Time                                 No control                                                    HRT 0...
5. Results: Cycle Time                                              No control                         350                ...
5. Results: Waiting time Distribution                                  % of passengers that have to wait between:         ...
6. Impact of implementation failures                           Disobeying            Technological                        ...
Common disobedience rate across drivers          Total Waiting Time [Min]                                     15000       ...
Common disobedience rate across drivers                       HRT                                            HRT, 50% obed...
Full disobedience of a set of drivers                                 16000                                 15000         ...
Full disobedience of a set of drivers   a) HRT                                                                           b...
7. Implementation• The first pilot plan consisted in implemnting our holding  tool in buses of line 210 of SuBus from Tran...
Plan Description
ImplementationReal time GPS                   Program optimizinginformation of                  dispatch times for eacheac...
Control Points
The results were very promisingeven though the conditions were far             from ideal
Input Data              • Trajectories of given GPS data (on a regular day)                                               ...
Input Data            • The trajectiories traveled by buses can be              inferred as:                              ...
Pilot Analysis              • Trajectories of our experiment                                                          Pilo...
Pilot Analysis             • Again… versus a regular day                                                           Correct...
The speeds we used need fine-tuning• Difference between the projected departure  time and the actual departure time       ...
The speeds we used need fine-tuning• Difference between the projected departure  time and the actual departure time       ...
Main results• Transantiago computes an indicator for  regularity based on intervals exceeding twice  the expected headway ...
Main results: cycle times             3:36:00             3:28:48             3:21:36             3:14:24                 ...
Unexpected result• The demand captured by the line grew!
Can we quantify this impact?      • Line 210 captured an extra 20% demand!           106.000           104.000           1...
This pilot plan can improve significantly1) GPS errors can be corrected2) Run the Optimization more often (from 3.5 to 2 m...
8. ConclusionsDeveloped a tool for headway control using Holding in real time reachingtime savings of over 50%Extending it...
Publications and working papers•   Delgado, F., Muñoz, J.C., Giesen, R., Cipriano, A. (2009) Real-Time Control of    Buses...
Roles for Richer Data and Better   Analysis in Improving theEffectiveness of Transit Systems         Nigel H.M. Wilson    ...
Minimizing Bus Bunching   Results from a new strategy that cuts waittimes, improve comfort and brings reliability to      ...
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Webinar: Minimizing Bus Bunching – Results from a new strategy that cuts wait times, improve comfort and brings reliability to bus services

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2012 12-14

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Webinar: Minimizing Bus Bunching – Results from a new strategy that cuts wait times, improve comfort and brings reliability to bus services

  1. 1. Minimizing Bus Bunching Results from a new strategy that cuts waittimes, 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. 2. Santiago, Chile
  3. 3. Time-space trajectories Line 201, March 25th, 2009 35 32.5 30 27.5 25 22.5 20Posición (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. 4. Boston, MA; line 1 during winter
  5. 5. Boston, MA; line 1 during summer
  6. 6. Is keeping regular headways that difficult? Transit Leaders Roundtable MIT, June 2011
  7. 7. Bus Operations without Control BusWaitingPassengers Stop Stop Waiting Passengers Bus Ricardo Giesen ©
  8. 8. Bus Operations without Control a small perturbation…WaitingPassengers Stop Bus Bus Stop Waiting Passengers Ricardo Giesen ©
  9. 9. Bus Operations without ControlWhile one bus is still loading passengers the other bus already left itslast stop Stop Bus Stop Bus Ricardo Giesen ©
  10. 10. Bus Operations without Control BusStop Bus Stop Ricardo Giesen ©
  11. 11. Bus Operations without ControlWithout bus control, bus bunching occurs!!! Stop Stop Bus Bus Ricardo Giesen ©
  12. 12. Stable versus unstable equilibrium
  13. 13. Stable versus unstable equilibrium
  14. 14. Stable versus unstable equilibrium
  15. 15. Stable versus unstable equilibrium
  16. 16. Stable versus unstable equilibrium
  17. 17. Stable versus unstable equilibrium
  18. 18. + - + - + - +
  19. 19. + - + - + - +
  20. 20. + - + - + - +
  21. 21. + - + - + - +And so on so forth.Our challenge is to keep an inherently unstable system: buses evenly spacedNow, if we want to prevent bunching from occurring … when is the right time to intervene?
  22. 22. Bus bunching isspecially serious,where bus capacityis an activeconstraint.
  23. 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 busesContribution: Control Mechanism to Avoid Bus Bunching!
  24. 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. 25. 3. ApproachBased 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 busreaches 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. 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. 27. Estrategias de control simuladas 4. Experiment: Control strategiesNo controlSpontaneous evolution of the system.Buses dispatched from terminal as soon as they arrive or until the design headway isreached.No other control action is taken along the route.Threshold controlMyopic 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 boardinglimits.
  28. 28. 5. Results: Simulation Animation Simulation includes events randomness 2 hours of bus operation. 15 minutes “warm-up” period.
  29. 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. 30. 5. Results: Time-space trajectories s2 NETS sc corrida17 Scenario 1 threshold run17 10 10 9 9 8 8 7 7Distance (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. 31. 5. Results: Time-space trajectories s2 NETS sc corrida17 10 9 8 Scenario 1 threshold run17No 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 2Threshold 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. 32. 5. Results: Bus Loads Scenario 1 HBLRT alpha=05 Beta=05 Scenario 1 HBLRT alpha=05 Beta=05 120 120 100 100 80 80Load (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. 33. 5. Results: Bus Loads Scenario 1 HBLRT alpha=05 Beta=05 120 100 Scenario 1 HBLRT alpha=05 Beta=05No 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 20Threshold 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. 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 250Frequency 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. 35. 5. Results: Cycle Time No control 350 300 mean =33.64No 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 =35.62Threshold 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. 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. 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. 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. 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. 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. 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. 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. 43. Plan Description
  44. 44. ImplementationReal time GPS Program optimizinginformation of dispatch times for eacheach bus bus from each stopText messages were sent Buses are held according toautomatically to each person the text message instructionsin each of the 24 stops (never more than one minute)
  45. 45. Control Points
  46. 46. The results were very promisingeven though the conditions were far from ideal
  47. 47. Input Data • Trajectories of given GPS data (on a regular day) Trajectories 60 50Kilometers 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. 48. Input Data • The trajectiories traveled by buses can be inferred as: Corrected Trajectories for a typical day 60 50Kilometers 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. 49. Pilot Analysis • Trajectories of our experiment Pilot Corrected Trajectories 60Kilometers 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. 50. Pilot Analysis • Again… versus a regular day Corrected Trajectories 60 50Kilometers 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. 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. 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. 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. 54. Main results: cycle times 3:36:00 3:28:48 3:21:36 3:14:24 Piloto 1 Prueba10Cycle 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. 55. Unexpected result• The demand captured by the line grew!
  56. 56. Can we quantify this impact? • Line 210 captured an extra 20% demand! 106.000 104.000 102.000Demand 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. 57. This pilot plan can improve significantly1) GPS errors can be corrected2) Run the Optimization more often (from 3.5 to 2 min)3) Calibrate speeds and arrival rates4) Check data inputs before feeding the systemAnd more importantly:5) Bypass the person at the stop. Communicate to drivers
  58. 58. 8. ConclusionsDeveloped a tool for headway control using Holding in real time reachingtime savings of over 50%Extending it to green time extension and boarding limits savings can reachover 60% with only minor impact on car usersHuge improvements in comfort and reliabilityThe 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. 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. 60. Roles for Richer Data and Better Analysis in Improving theEffectiveness of Transit Systems Nigel H.M. Wilson January 25, 2013 11:00 AM (Boston time)
  61. 61. Minimizing Bus Bunching Results from a new strategy that cuts waittimes, 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

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