LinTim. A Toolbox for the Experimental Evaluation of the Interaction of Different Planning Stages in Public Transportation

Transcription

1 A Toolbox for the Experimental Evaluation of the Interaction of Different Planning Stages in Public Transportation Institute for Numerical and Applied Mathematics, University of Göttingen, Germany OptALI Industry Workshop, Auckland February 25, 2014

2 Outline 1 General Overview The Purpose and Implementation of 2 Specific Problems and Their Implementation Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

3 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling 4 Vehicle Scheduling 5 Delay Management Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

4 Planning Stages in Public Transportation 1 Network Design - Where to place stations and edges, i.e. tracks? 2 Line Planning 3 Timetabling 4 Vehicle Scheduling 5 Delay Management Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

5 Planning Stages in Public Transportation 1 Network Design 2 Line Planning - Which line should go where with what frequency? 3 Timetabling 4 Vehicle Scheduling 5 Delay Management Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

6 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling - At what time shall the train be where? 4 Vehicle Scheduling 5 Delay Management Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

7 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling 4 Vehicle Scheduling - How to combine trips by the same vehicles? 5 Delay Management Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

8 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling 4 Vehicle Scheduling 5 Delay Management - To wait or not to wait? - How to deal with delays? Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

9 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling 4 Vehicle Scheduling 5 Delay Management Each step is already hard but well investigated. Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

10 Planning Stages in Public Transportation 1 Network Design 2 Line Planning 3 Timetabling 4 Vehicle Scheduling 5 Delay Management Each step is already hard but well investigated. Possibility of integrating these steps. Input Ex. PTN Ex. Edges Ex. Stops Demand Generate OD\Pool OD Pool Per. Timetabling Per. Timetable Rollout Network Design PTN Line Planning Line Concept Build EAN EAN Aper. Timetable Aper. Timetabling Vehicle Scheduling Rolling Stock Delays Generator Delays Delay Managment Disposition Timetable

11 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

12 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

13 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularly Study correlation between different steps Develop integrated models Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

14 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularly Study correlation between different steps Develop integrated models Obtain results for real world data sets Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

15 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularily Study correlation between different steps Develop integrated models Obtain results for real world data sets Implementation:

16 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularily Study correlation between different steps Develop integrated models Obtain results for real world data sets Implementation: Text file based data handling

17 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularily Study correlation between different steps Develop integrated models Obtain results for real world data sets Implementation: Text file based data handling High degree of freedom in terms of programming styles

18 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularily Study correlation between different steps Develop integrated models Obtain results for real world data sets Implementation: Text file based data handling High degree of freedom in terms of programming styles Modular design Single step evaluation

19 Purpose and Implementation of Purpose: Investigation of dependencies between different planning steps. Downwards in general Sequential process Upwards particularily Study correlation between different steps Develop integrated models Obtain results for real world data sets Implementation: Text file based data handling High degree of freedom in terms of programming styles Modular design Single step evaluation Command prompt Graphical user interface Documetation

20 PTN Data Toy Goettingen Data numbers: Toy: 8 stations, 8 tracks, 22 OD Athens: 51 st., 52 tr., 2,385 OD Goettingen Bus: 257 st., 548 tr., 65,668 OD Netherlands: Only EAN data Athens Netherlands

21 PTN Data Data numbers: German Rail 1: 250 st., 326 tr., 24,421 OD German Rail 2: German Rail 1 German Rail 3 German Rail 2 German Rail st., 354 tr., 30,555 OD German Rail 3: 295 st., 393 tr., 34,142 OD German Rail 4: 319 st., 452 tr., 38,939 OD Jonas Harbering, Anita Scho bel

22 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

23 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management my.opera.com/vikaskhan/albums/showpic.dml?album= &picture=

24 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management my.opera.com/vikaskhan/albums/showpic.dml?album= &picture=

25 Network Design p 1 p 3 p 2

26 Network Design p 1 r p 3 p 2

27 Network Design p 1 p 3 p 2

28 Network Design p 1 p 3 p 2

29 Network Design p 1 p 3 p 2

30 Network Design Feasible Stop Location Given a set of m demand points P R 2, a set S of possible station locations, a radius r R and an existing PTN G = (V, E) consisting of nodes V and edges E. Then the aim is to find a set of points S S V such that all demand points are covered.

31 Network Design Feasible Stop Location Given a set of m demand points P R 2, a set S of possible station locations, a radius r R and an existing PTN G = (V, E) consisting of nodes V and edges E. Then the aim is to find a set of points S S V such that all demand points are covered. Objectives: Minimize number of stations built, i.e. min S

32 Network Design Feasible Stop Location Given a set of m demand points P R 2, a set S of possible station locations, a radius r R and an existing PTN G = (V, E) consisting of nodes V and edges E. Then the aim is to find a set of points S S V such that all demand points are covered. Objectives: Minimize number of stations built, i.e. min S Minimize traveling time (two formulations)

33 as Analysis Tool - Comparing Models

34 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

35 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management pic.epicfail.com/wp-content/uploads/2010/11/epic-personal-space-fail-train.jpg

36 Example

37 Example

38 Example

39 Example

40 Example

41 Example f =2 l f l=1 f l=4 f l=1

42 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ).

43 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models

44 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models Direct Travellers Approach Maximize the number of direct travelers on all shortest paths

45 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models Direct Travellers Approach Multicriteria Cost Model Direct Travelers Approach

46 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models Direct Travellers Approach Multicriteria Cost Model Direct Travelers Approach Game Theoretic Model

47 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models Direct Travellers Approach Multicriteria Cost Model Direct Travelers Approach Game Theoretic Model Traveling Time Model Minimize the overall traveling time of all passengers at their final station

48 Line Planning Feasible Line Concept Given a Public Transportation Network (PTN)= (V, E), a line pool L 0, lower and upper frequencies fe min fe max for all e E, find a feasible line concept (L, f ). Solution Methods: Cost Models Direct Travellers Approach Multicriteria Cost Model Direct Travelers Approach Game Theoretic Model Traveling Time Model Minimizing Changes Model

49 as Analysis Tool - Multicriteria Comparison bahn-01 lc direct travelers Cost WLP3 Direct Travellers lc cost 10 4

50 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

51 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

52 Timetabling Feasible Periodic Timetable Given an Event-Activity-Network N = (E, A), intervals [L a, U a ] a A and a period T N, find a feasible Timetable Π, i.e. values Π i for all i E, such that (Π j Π i ) mod T [L a, U a ] for all a = (i, j) A

53 Timetabling Feasible Periodic Timetable Given an Event-Activity-Network N = (E, A), intervals [L a, U a ] a A and a period T N, find a feasible Timetable Π, i.e. values Π i for all i E, such that (Π j Π i ) mod T [L a, U a ] for all a = (i, j) A Traveling Time Oriented Model Given c a, aim: min a=(i,j) A c a(π j Π i ) mod T

54 as Analysis Tool - Estimate Validation 5.6e+08 game cost-heuristic cost-exact direct rerouted travel times 5.5e e e e e e+08 6e e+08 estimated travel times

55 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

56 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

57 Vehicle Scheduling wait dep l1,s 1 drive arr l1,s 0 dep l1,s 0 arr l1,s 3 End of trip Start of trip dep l2,s 2 arr l2,s 0 dep l2,s 0 arr l2,s 4

58 Vehicle Scheduling t 1 t 3 dep l1,s 1 arr l1,s 0 dep l1,s 0 arr l1,s 3 dep l2,s 2 arr l2,s 0 dep l2,s 0 arr l2,s 4 t 2 t 4

59 Vehicle Scheduling t 1 t 3 t 2 t 4

60 Vehicle Scheduling π arrl1,s 0 = 5 t 1 π depl1,s 0 = 35 t 3 π arrl2,s 0 = 30 t 2 π depl2,s 0 = 12 t 4

61 Vehicle Scheduling π arrl1,s 0 = 5 t 1 π depl1,s 0 = 35 t 3 π arrl2,s 0 = 30 t 2 π depl2,s 0 = 12 t 4 Sum of Waiting Times: 72 minutes

62 Vehicle Scheduling π arrl1,s 0 = 5 t 1 π depl1,s 0 = 35 t 3 π arrl2,s 0 = 30 t 2 π depl2,s 0 = 12 t 4 Sum of Waiting Times: 12 minutes

63 Vehicle Scheduling Feasible Vehicle Schedule Given a set of trips T, start and end times for every trip πt start i, πt end i i = 1,..., T and possible connecting empty rides (defined by a relation β) between two trips. Then a feasible vehicle schedule is searched, such that every trip is served.

64 Vehicle Scheduling Feasible Vehicle Schedule Given a set of trips T, start and end times for every trip πt start i, πt end i i = 1,..., T and possible connecting empty rides (defined by a relation β) between two trips. Then a feasible vehicle schedule is searched, such that every trip is served. Cost Oriented Models Influencing cost parameters: operating vehicles and empty meters

65 as Analysis Tool - Iterative Solving

66 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management

67 Public Transportation Planning Steps Network Design Line Planning Timetabling Vehicle Scheduling Delay Management Crowd.jpg

68 Model: event-activity network station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive station 1 station 1 station 2 station 2 arrival wait departure arrival drive wait departure drive changing activity: delete or not?

69 Model: event-activity network station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive change station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive station 1 station 1 station 2 station 2 arrival wait departure arrival drive wait departure drive changing activity: delete or not?

70 Model: event-activity network station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive change station 1 arrival wait station 1 departure drive station 2 arrival wait station 2 departure drive station 1 station 1 station 2 arrival wait departure drive arrival wait station 2 departure drive headway constraint: which one? changing activity: delete or not?

71 Delay Management Feasible Disposition Timetable Given an Event-Activity-Network N = (E, A), intervals [L a, U a ] a A, d i 0 for all i E. Find a feasible timetable, i.e. times x i for all i E, such that minimal driving times, taking into account the delays, are respected for all activities.

72 Delay Management Feasible Disposition Timetable Given an Event-Activity-Network N = (E, A), intervals [L a, U a ] a A, d i 0 for all i E. Find a feasible timetable, i.e. times x i for all i E, such that minimal driving times, taking into account the delays, are respected for all activities. Minimizing the disruption Given c a, aim: min i E c a(x i Π i ) + a A change z a c a T

73 as Analysis Tool - Influence Detection

74 Conclusion - Problem Solving

75 Conclusion - as Analysis Tool Problem Solving Comparing Models Multicriteria Evaluation Estimate Validation Iterative Solving Influence Detection...

76 Conclusion - as Analysis Tool Problem Solving Comparing Models Multicriteria Evaluation Estimate Validation Iterative Solving Influence Detection... Thank you for your attention! Questions? Remarks?

77 Line Planning: Cost Model min f l cost l l L 0 s.t. fe min f l fe max l L 0,e l f l N 0 for all l L 0 for all e E

78 Line Planning: Direct Travelers s.t. max l L 0 i,j V P ij l d ijl d ijl C ij for all i, j V l L 0 P ij l i,j V e P ij l d ijl A f l for all e E, l L 0 f min e l L 0,e l f l f max e for all e E f l, d ijl N 0 for all i, j V, l L 0

79 Timetabling: Minimizing Traveling Time min c a (Π j Π i ) mod T a=(i,j) A s.t. (Π j Π i ) mod T U a for all a = (i, j) A (Π j Π i ) mod T L a for all a = (i, j) A Π i N 0 for all i E

80 Vehicle Scheduling: Minimizing Costs s.t. T T T min c i,j x i,j i=1 j=1 x i,j = 1, for i = 1,..., T i=1 T x i,j = 1, for j = 1,..., T j=1 x i,j {0, 1}

81 Delay Management: Minimizing Disruption min i E c a (x i Π i ) + s.t. x i Π i + d i for all i E a A change z a c a T x j x i L a + d a for all a A drive A wait Mz a + x j x i L a for all a = (i, j) A change Mg ij + x j x i L ij for all a = (i, j) A headway x i N 0 for all i E z a {0, 1} for all a A change g ij {0, 1} for all (i, j) A headway