1. Train scheduling based on speed profiles
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

2. 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

3. 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

4. Condensation vs. compensation zones
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
Focus of this talk

5. Micro scheduling in compensation zone
Micro scheduling in compensation zone ZG LZ
Entrance point
Flexible speed
and travel time
Fixed
speed profile
Fixed
speed profile
Exit point t

6. Micro train scheduling - Objectives
Conflict-free assignment of track paths to the trains
Fulfill safety requirements on the micro level
Meeting portal (boundary) conditions
Additional quality criteria: Energy, time reserve distribution

7. Two step approach to micro scheduling
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
Conflict-free track path assignment

8. 1. Trackpath generation Enumerate meaningful route alternatives
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

9. 2. Speed profile generation
Generate ®-speed profile „drive as fast as it is allowed“  minimal travel time
Calculate time reserve based on ®-speedprofile
Generate several speed profiles by distributing the time reserve among track sections

11. Example of speed profile generation
Example of speed profile generation
... distributed over K track sections 1 2 1 2 s
®-speedprofile
Diagram
Illustrate
Time reserve is divided by a parameter N=6 parts and … }
Portaltime t

12. S1 Lucerne – Zug:
- ®-profile
- Track section split

13. Conflict-free trackpath assignment
Optimisation model assigns a track path per train.
Resource tree conflict graph
Multicommodity flow
Constrain flow (conflict free)
Integer linear program
Optimise for a quality criteria
Models train dynamics and detailed safety system

14. The optimal solution considers all trains, not only this train!
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!

15. Testcase

16. Testcase – continued
Based on SBB 2008 timetable we derive a service intention
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

17. 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.

18. 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

19. Thank You!
Time for questions! 19