Train scheduling based on speed profiles
Martin Fuchsberger, ETH Zurich
RailZurich, 11. February 2009
D. Burkolter, G. Caimi, T. Herrmann, S. Roos, R. Wüst
© ETH Zürich | M. Fuchsberger
Rail Zürich, 11.2.2009
What is train scheduling?
 INPUT:



Train service intention (SI)
Aggregated and detailed track topology of the
network
Rolling stock with dynamic properties
 OUTPUT:

Conflict-free periodic train schedule fulfilling SI
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
[email protected]
2
Two-level approach reduces complexity
Macro scheduling:
Find a timetable that fulfills trip
time, connection and macro level
safety requirements
Focus of this talk
Micro scheduling:
Find locally a conflict free
schedule, fulfilling detailed safety
requirements for a given macro
schedule
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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3
Condensation vs. compensation zones
Focus of this talk
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
Condensation zone:
• Main station area
• Bottleneck
• Maximum speed policy
• Many routes
Compensation zone:
• Regions connecting
main stations
• Time reserves
• Variable speed
• Few routes
Portal:
• Link between zones
• Macroscopic draft
passing times
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Micro scheduling in compensation zone
ZG
LZ
Entrance point
Flexible speed
and travel time
Fixed
speed profile
Fixed
speed profile
Exit point
t
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Micro train scheduling - Objectives
1. Conflict-free assignment of track paths to the
trains
2. Fulfill safety requirements on the micro level
3. Meeting portal (boundary) conditions
4. Additional quality criteria:
Energy, time reserve distribution
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
[email protected]
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Two step approach to micro scheduling
1. Track path generation
Apply two reasonable simplifications:


Approximation of the continuous track path by a
finite chain of <location,time> points
Represent the infinitely many track paths by a
representative finite set of track paths
2. Conflict-free track path assignment
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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1. Trackpath generation
a) Enumerate meaningful route alternatives
b) Generate viable speed profiles for each route,
which:

Are a versatile representation of the infinitely many
speed profiles

Comply with maximum speed limits
Obey dynamic train properties
Meet portal boundary conditions


Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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2. Speed profile generation
a) Generate ®-speed profile
„drive as fast as it is allowed“
 minimal travel time
b) Calculate time reserve based on ®-speedprofile
c) Generate several speed profiles by distributing
the time reserve among track sections
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Example of speed profile generation
... distributed over K track sections
0
1
2
1
2
s
®-speedprofile
}
Portaltime
t
Rail Zürich, 11.2.2009
Time reserve is
divided by a parameter
N=6 parts and …
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S1 Lucerne – Zug:
- ®-profile
- Track section split
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Conflict-free trackpath assignment
Optimisation model assigns a track path per train.
1. Resource tree conflict graph
2. Multicommodity flow
3. Constrain flow (conflict free)
4. Integer linear program
5. Optimise for a quality criteria
Models train dynamics and detailed safety system
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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S1 Lucerne – Zug:
- Min. energy consumption
- Max. time reserve distribution desirability
- Combination of both objectives
Remember:
The optimal solution considers
all trains, not only this train!
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Testcase
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Testcase – continued
1. Based on SBB 2008 timetable we derive a
service intention
2. Solve macroscopic timetable scheduling
 Generates portal times
Schedule contains per hour and direction



2 intercity trains
1 interregio train
2 commuter trains
 10 trains / hour
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Effects of parameters K and N
 Too few track sections (K) lead to:


Less variety of speed profiles
Problem became infeasible
 High granularity partitioning of time reserve (N):


Improves objective value
Increases memory consumption
 Computation times < 30 s
After tuning parameters K and N, trains are swiftly
scheduled and comply with security standards.
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Outlook
Our current research focuses on
 Application of this approach for rescheduling
 Interaction between:

Macro and micro level (2-level approach)

Compensation and condensation zones
 Possible contributions of Operations Research
(OR) to the field of railway rescheduling
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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Thank You!
Time for questions!
Rail Zürich, 11.2.2009
M.Fuchsberger / IFOR ETHZ
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