Towards operationally feasible railway timetables

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

Outline

1 Introduction

2 Problem description

3 Methodology

4 Experimental results

5 Conclusions

N.Besinovic (n.besinovic@tudelft.nl) Feasible timetabling November 17, 2016 1 / 31

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...)

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...)

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

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.

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.

Time-distance diagram

Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehv

Time distance diagram for corridor Ut−Ehv

Blocking time diagram

Question:

� How to guarantee the operational feasibility in timetabling models?

Blocking time diagram

Question:

� How to guarantee the operational feasibility in timetabling models?

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

State-of-the-art

So far:

� Efficiency

� Realizability

� (Operational) Feasibility

� Stability -

� Robustness -

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

[13,16]T

[11,14]T

[1,3]T

[3,57]T [3,8]T

[22,26]T

[19,22]T

Serafini & Ukovich (1989)Periodic timetable with cycle time TPeriodic events: arrival & departure times πi ∈ [0,T )Constraints:

[13,16]T

[11,14]T

[1,3]T

[3,57]T [3,8]T

[22,26]T

[19,22]T

[13,16]T

[11,14]T

[1,3]T

[3,57]T [3,8]T

[22,26]T

[19,22]T

[13,16]T

[11,14]T

[1,3]T

[3,57]T [3,8]T

[22,26]T

[19,22]T

Solving PESP

(PESP − N) Min f (π, z)

such that

lij ≤ πj − πi + zijT ≤ uij ∀(i , j) ∈ A

0 ≤ πi < T , ∀izij binary

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

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

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

Integrated approach

Can we add microscopic details directly to the macroscopic level?

Introduce flexible minimum headways in PESP

Integrated approach

Can we add microscopic details directly to the macroscopic level? Yes.

Integrated approach

Can we add microscopic details directly to the macroscopic level? Yes.

Integrated approach

(PESP − N) Min f (π, z)

such that

lij ≤ πj − πi + zij · T ≤ uij ∀(i , j) ∈ A

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

Lij = F(running times of two trains)

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

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

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

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 %)

runik = rik/r ik − 1 runjl = rjl/r jl − 1

−0.2 −0.1 0 0.1 0.2

Running time difference runi−run

e L ij [s

Headway relation for train lines 6001 and 16001 at station Cl

runik − runjl > 0: the first train is faster*runik − runjl < 0: the second train is faster** Assuming the same category trainsN.Besinovic (n.besinovic@tudelft.nl) Feasible timetabling November 17, 2016 18 / 31

−0.2 −0.1 0 0.1 0.2

e L ij [s

Headway relation for train lines 6001 and 16001 at station Cl

run1 − run2 > 0: the first train is faster*run1 − run2 < 0: the second train is faster** Assuming the same category trainsN.Besinovic (n.besinovic@tudelft.nl) Feasible timetabling November 17, 2016 19 / 31

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

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

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

Case 1: Utrecht-Eindhoven network

Figure: Line plan

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

Computed timetables

*After first iterationIterative micro-macro framework finished after 10 iterations

PESP-FlexHeadway allocated more time supplements to satisfy newheadwaysCPU times are comparable

Computed timetables

*After first iterationIterative micro-macro framework finished after 10 iterationsPESP-FlexHeadway allocated more time supplements to satisfy newheadways

CPU times are comparable

Computed timetables

*After first iterationIterative micro-macro framework finished after 10 iterationsPESP-FlexHeadway allocated more time supplements to satisfy newheadwaysCPU times are comparable

Iterative micro-macro framework

Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet EbEhv

Distance [stations]

Integrated framework: PESP-FlexHeadway

Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehv

Integrated framework: PESP-FlexHeadway

Some more headways...

−0.2 −0.1 0 0.1 0.280

e L ij [s

]Headway relation for train lines 3501 and 801 at station Htn

−0.2 −0.1 0 0.1 0.2

e L ij [s

Headway relation for train lines 800 and 3500 at station Btl

−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

Running time difference run2−run

e L ij [s

Headway relation for train lines 800 and 6000 at station Htn

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

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

Thank you for your attention

Figure: Micro-macro iterations

Towards operationally feasible railway timetables

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