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Capacity planning for railway systemsLeo Kroon Jan 17, 2002

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Conclusions

• Capacity planning at several levels• Relevant resources are:

¶ Infrastructure¶ Rolling stock¶ Personnel¶ . . .

• All relevant resources are scarce• Effective utilization of resources is required• OR models can provide useful support

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Dutch railway quantities

1.000.000 passengers per workday14.000.000.000 passenger kilometers per year5000 timetabled trains per workday

2800 kilometers of tracks380 stations

2650 wagons

3000 train drivers4000 conductors (and assistants)

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050

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UtHmlaWdGdCps NwkRtaRtnRtd VtnMda Gdg

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Hourly Pattern for the track Rotterdam - Utrecht

2800

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Platform Occupation Chart

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UtrechtCentral

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Dis-punctualiteit in procent

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Utilization of the infrastructure (%)

Price per pkm in cents (Dfl)Dispunctuality (%)

Source: KoppelingDec 16, 2000

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Capacity aspects (infrastructure)

• Passengers vs. Cargo vs. Maintenance• Significant increase in demand is expected• Stations are a major bottle-neck• # Trains or # Passengers/Tons?• Utilization vs. Robustness

Different kinds of capacity (OptiRail)• Theoretical capacity• Practical capacity• Planned capacity

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Capacity aspects (infrastructure: tracks)

• # Parallel tracks• Heterogeneity of traffic• # Take-over facilities• Safety system (length of blocks)• Energy system (diesel/electric)• Rolling stock characteristics• Rolling stock capacity (per wagon/unit) • Environment (noise)• . . . .

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Capacity aspects (infrastructure: stations)

• # Platforms• # Parallel/simultaneous routes • Platform occupation times (length of return times)• # Shunting movements • # (Cross-platform) connections • Length of platforms• Rail-side vs. City-side• . . . .

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Traditional system

time

A B C D E F

5 trains

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Clustered

time

7 trains

A B C D E F

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A B C D E F

Take-over

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9 trains

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Homogeneous system

time

A B C D E F

8 trains

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A B C D E F

2 tracks per direction

time

15 trains

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Capacity analysis and utilization

DONS/SIMONE: Feasibility and robustness(dependent on timetable)

Model Huisman: Network of queuing systems(independent of timetable)

OptiRail: Network flow model with discrete resources (independent of timetable)

B & B: Benutten & Bouwen (Utilize & Expand)

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Rolling stock

• In rush hours: Allocation of scarce capacity

• Outside rush hours: Efficiency

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Mat’64 with 2 or 4 wagons

Koploper with 3 or 4 wagons

Double decker with 3 or 4 wagons

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Capacity aspects (Rolling stock)

Increasing demand during last years Additional wagons (units) will be available soon

Rolling stock capacity mainly determined by - available # of wagons (units)- capacity per wagon (unit)- speed of the trains

Available operational rolling stock capacity = (rolling stock capacity) - (maintenance reservation)

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Capacity aspects (Rolling stock)

Required operational capacity mainly determined during the morning rush hours

Allocated capacity per trip => minimally required capacity - shortage

Allocated capacity per trip = # wagons (units) * capacity per wagon (unit)

Maximum train length <= minimum platform length

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Minimally required capacity per trip

• Based on counts by conductors

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15%

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87 9

line 1

line 2

Eight o’clock cross section

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Rolling stock allocation model

Applied to 8 o’clock cross section of all stoptrainsImplemented in ILOG OPL Studio Solved by CPLEX 7.0 on PC (900 MHz, 256 Mb) # variables: 3700# constraints: 9600

Manual solution:Total shortages (2nd class) 4869# trains with shortages 75 (of 188)

Scenarios based on max. # types and subtypes per line:Best solution found: 3958# trains with shortages 71 (of 188)

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0 1Utilization

Wait

ing t

ime

Waiting time vs. Utilization

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Conclusions

• Capacity planning at several levels• Relevant resources are:

¶ Infrastructure¶ Rolling stock¶ Personnel¶ . . .

• All relevant resources are scarce• Effective utilization of resources is required• OR models can provide useful support

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Conference on Optimization in Public TransportMay 23, 2002, Erasmus University Rotterdam

http://www.few.eur.nl/few/research/ecopt/conference

Airline session:• Jacques Desrosiers GERAD and École des Hautes Études Commericales, Montréal• Gerrit Timmer; ORTEC Consultants and Free University Amsterdam

Railway session:• Paolo Toth; DEIS, University of Bologna, Italy• Leo Kroon; NS Reizigers and ECOPT, Erasmus University Rotterdam

Bus session:• Matteo Fischetti; DEI, University of Padua and Double-Click sas, Italy• Dennis Huisman; ECOPT, Erasmus University Rotterdam