Rail Zürich, 11.2.2009 Train scheduling based on speed profiles © ETH Zürich | M. Fuchsberger Martin Fuchsberger, ETH Zurich RailZurich, 11. February 2009 D. Burkolter, G. Caimi, T. Herrmann, S. Roos, R. Wüst
Dec 22, 2015
Rail Zürich, 11.2.2009
Train scheduling based on speed profiles
© ETH Zürich | M. Fuchsberger
Martin Fuchsberger, ETH Zurich
RailZurich, 11. February 2009
D. Burkolter, G. Caimi, T. Herrmann, S. Roos, R. Wüst
2Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
3Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
Two-level approach reduces complexity
Macro scheduling:
Find a timetable that fulfills trip
time, connection and macro level
safety requirements
Micro scheduling:
Find locally a conflict free
schedule, fulfilling detailed safety
requirements for a given macro
schedule
Focus of this talk
4Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
5Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
Micro scheduling in compensation zone
ZG LZ
Fixed speed profile
Fixed speed profile
t
Flexible speedand travel time
Entrance point
Exit point
6Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
7Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
8Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
9Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
10Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
11Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
Time reserve is divided by a parameterN=6 parts and …
}
Example of speed profile generation
t
0 1 2 1 2s
®-speedprofile
Portaltime
... distributed over K track sections
12Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
S1 Lucerne – Zug:- ®-profile- Track section split
13Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
Conflict-free trackpath assignment
14Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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!
16Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
17Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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.
18Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected]
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
19Rail Zürich, 11.2.2009 M.Fuchsberger / IFOR ETHZ [email protected] 19
Thank You!
Time for questions!