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Delft University of Technology
Toward operationally feasible railway timetables (PPT)
Bešinović, Nikola; Goverde, Rob
Publication date2016Document VersionFinal published version
Citation (APA)Bešinović, N., & Goverde, R. (2016). Toward operationally feasible railway timetables (PPT). 2016INFORMS Annual Meeting, Nashville, United States.
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Introduction Problem description Methodology Experimental results Conclusions
Towards operationally feasible railway timetables
Nikola Besinovic, Rob M.P. Goverde
Delft University of Technology, The Netherlands
INFORMS 2016, Nashville, Tennessee
Introduction Problem description Methodology Experimental results Conclusions
Outline
1 Introduction
2 Problem description
3 Methodology
4 Experimental results
5 Conclusions
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 1 / 31
Introduction Problem description Methodology Experimental results Conclusions
Current state in railway traffic
� Constant growth of demand for passenger and freight railwaytransport
� Heavily congested networks
� Reaching maximum available infrastructure capacity
� Experiencing delays
� Existing need for better planning to satisfy a high level of service
(ERA, UIC, IMs, RUs...)
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 2 / 31
Introduction Problem description Methodology Experimental results Conclusions
Current state in railway traffic
� Constant growth of demand for passenger and freight railwaytransport
� Heavily congested networks
� Reaching maximum available infrastructure capacity
� Experiencing delays
� Existing need for better planning to satisfy a high level of service
(ERA, UIC, IMs, RUs...)
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 2 / 31
Introduction Problem description Methodology Experimental results Conclusions
Timetable planning
Infrastructure Line plan Timetable Rollingstock Crew
INPUT:
� Train line requests (OD, stops, frequencies, rolling stock)
� Track topology
� Rolling stock with dynamic characteristics
� Passenger connections and rolling stock turn-arounds
OUTPUT:
� Timetable: arrival, departure and passing times at timetable points
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 3 / 31
Introduction Problem description Methodology Experimental results Conclusions
Timetable planning
Goals:
� Efficiency - short travel times and seamless connections
� Realizability - scheduled RT > minimum RT
� (Operational) Feasibility - no conflicts
� Stability - acceptable capacity occupation in corridors and stations
� Robustness - cope with system stochasticity
Operationally feasible timetable
An operationally feasible timetable has no conflicts on the microscopiclevel (block and track detection sections) between train’s blocking times.
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 4 / 31
Introduction Problem description Methodology Experimental results Conclusions
Timetable planning
Goals:
� Efficiency - short travel times and seamless connections
� Realizability - scheduled RT > minimum RT
� (Operational) Feasibility - no conflicts
� Stability - acceptable capacity occupation in corridors and stations
� Robustness - cope with system stochasticity
Operationally feasible timetable
An operationally feasible timetable has no conflicts on the microscopiclevel (block and track detection sections) between train’s blocking times.
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 4 / 31
Introduction Problem description Methodology Experimental results Conclusions
Time-distance diagram
Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehv
0
10
20
30
40
50
60
Time distance diagram for corridor Ut−Ehv
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 5 / 31
Introduction Problem description Methodology Experimental results Conclusions
Blocking time diagram
Question:
� How to guarantee the operational feasibility in timetabling models?
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 6 / 31
Introduction Problem description Methodology Experimental results Conclusions
Blocking time diagram
Question:
� How to guarantee the operational feasibility in timetabling models?
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 6 / 31
Introduction Problem description Methodology Experimental results Conclusions
Minimum headway time
Minimum headway time (Hansen and Pachl, 2014)
A minimum headway time is the time separation between two trains atcertain positions that enable conflict-free operation of trains.
Minimum headway time Lij depends on:
� infrastructure characteristics: block lengths
� signalling system
� train engine characteristics
� (scheduled) train running times
� not a single value
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 7 / 31
Introduction Problem description Methodology Experimental results Conclusions
Minimum headway time
Minimum headway time (Hansen and Pachl, 2014)
A minimum headway time is the time separation between two trains atcertain positions that enable conflict-free operation of trains.
Minimum headway time Lij depends on:
� infrastructure characteristics: block lengths
� signalling system
� train engine characteristics
� (scheduled) train running times
� not a single value
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 7 / 31
Introduction Problem description Methodology Experimental results Conclusions
Minimum headway time
Minimum headway time (Hansen and Pachl, 2014)
A minimum headway time is the time separation between two trains atcertain positions that enable conflict-free operation of trains.
Minimum headway time Lij depends on:
� infrastructure characteristics: block lengths
� signalling system
� train engine characteristics
� (scheduled) train running times
� not a single value
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 7 / 31
Introduction Problem description Methodology Experimental results Conclusions
State-of-the-art
So far:
� Efficiency
� Realizability
� (Operational) Feasibility
� Stability -
� Robustness -
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 8 / 31
Introduction Problem description Methodology Experimental results Conclusions
Periodic event scheduling problem (PESP)
Serafini & Ukovich (1989)Periodic timetable with cycle time TPeriodic events: arrival & departure times πi ∈ [0,T )
Constraints:
lowerBoundij ≤ πj − πi + zijT ≤ upperBoundij
Period shift: zij - define the order of trains
a1 d1
d2a2
[13,16]T
[11,14]T
[1,3]T
[1,3]T
[3,57]T [3,8]T
[22,26]T
[19,22]T
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 9 / 31
Introduction Problem description Methodology Experimental results Conclusions
Periodic event scheduling problem (PESP)
Serafini & Ukovich (1989)Periodic timetable with cycle time TPeriodic events: arrival & departure times πi ∈ [0,T )Constraints:
lowerBoundij ≤ πj − πi + zijT ≤ upperBoundij
Period shift: zij - define the order of trains
a1 d1
d2a2
[13,16]T
[11,14]T
[1,3]T
[1,3]T
[3,57]T [3,8]T
[22,26]T
[19,22]T
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 9 / 31
Introduction Problem description Methodology Experimental results Conclusions
Periodic event scheduling problem (PESP)
Serafini & Ukovich (1989)Periodic timetable with cycle time TPeriodic events: arrival & departure times πi ∈ [0,T )Constraints:
lowerBoundij ≤ πj − πi + zijT ≤ upperBoundij
Period shift: zij - define the order of trains
a1 d1
d2a2
[13,16]T
[11,14]T
[1,3]T
[1,3]T
[3,57]T [3,8]T
[22,26]T
[19,22]T
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 9 / 31
Introduction Problem description Methodology Experimental results Conclusions
Periodic event scheduling problem (PESP)
Serafini & Ukovich (1989)Periodic timetable with cycle time TPeriodic events: arrival & departure times πi ∈ [0,T )Constraints:
lowerBoundij ≤ πj − πi + zijT ≤ upperBoundij
Period shift: zij - define the order of trains
a1 d1
d2a2
[13,16]T
[11,14]T
[1,3]T
[1,3]T
[3,57]T [3,8]T
[22,26]T
[19,22]T
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 9 / 31
Introduction Problem description Methodology Experimental results Conclusions
Solving PESP
(PESP − N) Min f (π, z)
such that
lij ≤ πj − πi + zijT ≤ uij ∀(i , j) ∈ A
0 ≤ πi < T , ∀izij binary
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 10 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computing operationally feasible timetables
Solving PESP-N:
� Fixed minimum headways
� Can be violated when scheduled running time increases
How to include microscopic details in timetable planning models?
� Iterative approach
� Integrated approach
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 11 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computing operationally feasible timetables
Solving PESP-N:
� Fixed minimum headways
� Can be violated when scheduled running time increases
How to include microscopic details in timetable planning models?
� Iterative approach
� Integrated approach
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 11 / 31
Introduction Problem description Methodology Experimental results Conclusions
Iterative micro-macro framework (Transp. Res. B, 2016)
Macro Micro
Micro model (Comp-aided Civil and Inf. Eng., 2016):
� Compute operational train speed profiles
� Conflict detection
� Update headways
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 12 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
Can we add microscopic details directly to the macroscopic level?
Yes.
Introduce flexible minimum headways in PESP
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 13 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
Can we add microscopic details directly to the macroscopic level? Yes.
Introduce flexible minimum headways in PESP
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 13 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
Can we add microscopic details directly to the macroscopic level? Yes.
Introduce flexible minimum headways in PESP
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 13 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
(PESP − N) Min f (π, z)
such that
lij ≤ πj − πi + zij · T ≤ uij ∀(i , j) ∈ A
0 ≤ πi < T , ∀izij binary
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 14 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
(PESP − FlexHeadways) Min f (π, z)
such that
lij ≤ πj − πi + zij · T ≤ uij ∀(i , j) ∈ Arun ∪ Adwell
Lij ≤ πj − πi + zij · T ≤ Uij ∀(i , j) ∈ Aheadway
0 ≤ πi < T , ∀izij binary
Lij = F(running times of two trains)
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 15 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
For each train pair at each timetable point:
� vary running speeds = amount of time supplements
� compute minimum headway time for each trains-speeds variations
� get functional relationship between given time supplements andminimum headways → Lij
Expected: bigger speed difference → bigger minimum headway time
� more homogenized running times → smaller minimum headway time
� second train faster → minimum headway increases
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 16 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
For each train pair at each timetable point:
� vary running speeds = amount of time supplements
� compute minimum headway time for each trains-speeds variations
� get functional relationship between given time supplements andminimum headways → Lij
Expected: bigger speed difference → bigger minimum headway time
� more homogenized running times → smaller minimum headway time
� second train faster → minimum headway increases
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 16 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
runik - running time supplement of the first train (in %)runjl - running time supplement of the second train (in %)Rij - relative difference between time supplements of two trains (in %)
Rij = runik − runjl
runik = rik/r ik − 1 runjl = rjl/r jl − 1
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 17 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
runik - running time supplement of the first train (in %)runjl - running time supplement of the second train (in %)Rij - relative difference between time supplements of two trains (in %)
Rij = runik − runjl
runik = rik/r ik − 1 runjl = rjl/r jl − 1
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 17 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
−0.2 −0.1 0 0.1 0.2
80
90
100
110
120
130
140
150
Running time difference runi−run
j [s]
Min
imum
hea
dway
tim
e L ij [s
]
Headway relation for train lines 6001 and 16001 at station Cl
1.05
1.1
1.15
runik − runjl > 0: the first train is faster*runik − runjl < 0: the second train is faster** Assuming the same category trainsN.Besinovic ([email protected]) Feasible timetabling November 17, 2016 18 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
−0.2 −0.1 0 0.1 0.2
80
90
100
110
120
130
140
150
Running time difference runi−run
j [s]
Min
imum
hea
dway
tim
e L ij [s
]
Headway relation for train lines 6001 and 16001 at station Cl
1.05
1.1
1.15
run1 − run2 > 0: the first train is faster*run1 − run2 < 0: the second train is faster** Assuming the same category trainsN.Besinovic ([email protected]) Feasible timetabling November 17, 2016 19 / 31
Introduction Problem description Methodology Experimental results Conclusions
Lij = F (running times of two trains)
Linear dependency between runik and runjl
Lij = αij · Rij + l0
αij - slope of LijRij - relative difference between time supplements of two trains (in %)l0 - minimum headway time for runik = runjl
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 20 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated approach
(PESP − FlexHeadways) Min f (π, z)
such that
lij ≤ πj − πi + zij · T ≤ uij ∀(i , j) ∈ Arun ∪ Adwell
αij · Rij + l0 ≤ πj − πi + zij · T ≤ uij ∀(i , j) ∈ Aheadway
Rij = runik − runjl
0 ≤ πi < T , ∀izij binary
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 21 / 31
Introduction Problem description Methodology Experimental results Conclusions
Case studies
Case network: Utrecht - Eindhoven network (two intersecting corridors)
� 15 stations and junctions
� 40 trains/h
� 96 events and 148 activities
Minimum running time supplement: 5%Maximum running time supplement: 20%Minimum dwell times: 60-120 s
Test: Iterative micro-macro and integrated PESP-FlexHeadway models
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 22 / 31
Introduction Problem description Methodology Experimental results Conclusions
Case 1: Utrecht-Eindhoven network
Figure: Line plan
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 23 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computed timetables
Table: Solutions obtained after the first iteration
Model # of conflicts Total time Scheduled time[train pairs] in conflicts [s] supplements [s]
Iterative micro-macro* 4 160 10Integrated PESP-FlexHeadway 0 0 382
*After first iteration
Iterative micro-macro framework finished after 10 iterationsPESP-FlexHeadway allocated more time supplements to satisfy newheadwaysCPU times are comparable
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 24 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computed timetables
Table: Solutions obtained after the first iteration
Model # of conflicts Total time Scheduled time[train pairs] in conflicts [s] supplements [s]
Iterative micro-macro* 4 160 10Integrated PESP-FlexHeadway 0 0 382
*After first iterationIterative micro-macro framework finished after 10 iterations
PESP-FlexHeadway allocated more time supplements to satisfy newheadwaysCPU times are comparable
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 24 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computed timetables
Table: Solutions obtained after the first iteration
Model # of conflicts Total time Scheduled time[train pairs] in conflicts [s] supplements [s]
Iterative micro-macro* 4 160 10Integrated PESP-FlexHeadway 0 0 382
*After first iterationIterative micro-macro framework finished after 10 iterationsPESP-FlexHeadway allocated more time supplements to satisfy newheadways
CPU times are comparable
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 24 / 31
Introduction Problem description Methodology Experimental results Conclusions
Computed timetables
Table: Solutions obtained after the first iteration
Model # of conflicts Total time Scheduled time[train pairs] in conflicts [s] supplements [s]
Iterative micro-macro* 4 160 10Integrated PESP-FlexHeadway 0 0 382
*After first iterationIterative micro-macro framework finished after 10 iterationsPESP-FlexHeadway allocated more time supplements to satisfy newheadwaysCPU times are comparable
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 24 / 31
Introduction Problem description Methodology Experimental results Conclusions
Iterative micro-macro framework
Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet EbEhv
0
10
20
30
40
50
60
Time distance diagram for corridor Ut−Ehv
Distance [stations]
Tim
e [
min
]
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 25 / 31
Introduction Problem description Methodology Experimental results Conclusions
Iterative micro-macro framework
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 26 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated framework: PESP-FlexHeadway
Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehv
0
10
20
30
40
50
60
Time distance diagram for corridor Ut−Ehv
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 27 / 31
Introduction Problem description Methodology Experimental results Conclusions
Integrated framework: PESP-FlexHeadway
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 28 / 31
Introduction Problem description Methodology Experimental results Conclusions
Some more headways...
−0.2 −0.1 0 0.1 0.280
90
100
110
120
130
Running time difference runi−run
j [s]
Min
imum
hea
dway
tim
e L ij [s
]Headway relation for train lines 3501 and 801 at station Htn
1.05
1.1
1.15
−0.2 −0.1 0 0.1 0.2
70
80
90
100
110
120
Running time difference runi−run
j [s]
Min
imum
hea
dway
tim
e L ij [s
]
Headway relation for train lines 800 and 3500 at station Btl
1.05
1.1
1.15
−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
140
150
160
170
180
190
Running time difference run2−run
1 [s]
Min
imum
hea
dway
tim
e L ij [s
]
Headway relation for train lines 800 and 6000 at station Htn
1.05
1.1
1.15
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 29 / 31
Introduction Problem description Methodology Experimental results Conclusions
Conclusions
Main observations:
� We can compute operationally feasible timetables
� Iterative approach solves within a limited number of iterations
� Minimum headway times as a function of running times
� Macroscopic Flexible minimum headway model formulation generates(almost) operationally feasible solutions
Pursuing the (passenger) happiness
� Is linear approximation always good? Piecewise linear?
� Include stability and robustness in the objective function
� Test the model on bigger instances
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 30 / 31
Introduction Problem description Methodology Experimental results Conclusions
Conclusions
Main observations:
� We can compute operationally feasible timetables
� Iterative approach solves within a limited number of iterations
� Minimum headway times as a function of running times
� Macroscopic Flexible minimum headway model formulation generates(almost) operationally feasible solutions
Pursuing the (passenger) happiness
� Is linear approximation always good? Piecewise linear?
� Include stability and robustness in the objective function
� Test the model on bigger instances
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 30 / 31
Introduction Problem description Methodology Experimental results Conclusions
Thank you for your attention
Iterative micro-macro framework
Figure: Micro-macro iterations
N.Besinovic ([email protected]) Feasible timetabling November 17, 2016 1 / 1