Train scheduling based on speed profiles 23.07.2018 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

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

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

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

Micro scheduling in compensation zone 23.07.2018 Micro scheduling in compensation zone ZG LZ Entrance point Flexible speed and travel time Fixed speed profile Fixed speed profile Exit point t

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

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

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

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

Example of speed profile generation 23.07.2018 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

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

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

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!

Testcase

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

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.

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

Thank You! Time for questions! 19