Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Towards a Better Train Timetable for Denmark,
Reducing Total Expected Passenger Time
Peter Sels 1,2,3 , Dirk Cattrysse2 , Pieter Vansteenwegen2
1
Logically Yours BVBA,
Plankenbergstraat 112 bus L7, 2100 Antwerp, Belgium
e-mail: [email protected], corresponding author
2
Katholieke Universiteit Leuven,
Leuven Mobility Research Centre, CIB,
Celestijnenlaan 300, 3001 Leuven, Belgium
3
Infrabel, Traffic Management & Services,
Fonsnylaan 13, 1060 Brussels, Belgium
July 22nd 2015
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Table of Contents
1
Optimising Timetables
2
Reflowing Results
3
Retiming Results
Deterministic Results
Stochastic Results
4
Conclusions & Future Work
5
Questions / Next Steps
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Optimising Timetables
Challenge / Puzzle
Danish Infrastructure Management Company: Banedanmark:
Improve timetable in terms of expected passenger travel time
(includes: ride, dwell, transfer time and primary and secondary delays)
Fixed:
Infrastructure, train lines, halting pattern, primary delay distributions
Variable:
Timing: supplements times at every ride, dwell, transfer action,
⇒ variable inter-train heading times ⇒ variable train orders
Note:
Includes primary and secondary delays ⇒ opt. efficiency vs. robustness
Specifics:
One busy day, morning peak hour
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Reflowing Results
Reflowing Results: via OD-Based Passenger Routing
!( Frederikshavn
25
!(
Thisted
!(
Aalborg
34
24
Struer
!(
32
!( Holstebro
31
!(
!
!( Langå
Herning
!(
35
Grenaa
Aarhus H
!( Helsingør
!( Skanderborg
!(
Skjern
33
10
23
Lersøen
Vejle!(
Taulov
Esbjerg
!(
!(
Bramming
29
Lunderskov
!(
!(
!(
!(
5
Roskilde
!(
!( Fredericia
!(
!(
Nyborg
!(
1
Korsør
Ringsted
!(
4
!( Næstved
26
21
!(
Tinglev
!(
28
Svendborg
!( Sønderborg
2
!( Padborg
!( Nykøbing F
!(
Rødby Færge
Østerport
7 !(!(!(København H
!(
6
11 Kastrup
Snoghøj
Odense
30
Tønder!(
Kalundborg
3
!( Gedser
Validity period:
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
Retiming Results for Hard Constraints:
Minimum Run Time Violations?
Table 1: Realisability. Reduction of the number and size of minimum runtime
violations from timetable Orig. → Opt.
timetable:
Orig.
Orig.
distribution: #
6s
12s
18s
107
88
44
72s
78s
84s
2
0
0
actions with
24s
30s
22
6
90s
96s
0
1
a violation per size of violation
36s
42s
48s
56s
6
5
0
3
102s
108s
114s 120s
0
1
0
0
in seconds
60s
66s
1
0
126s
132s
1
1
Table 2: Realisability. Reduction (elimination) of total and average violation
from timetable Orig. → Opt.
timetable
Orig.
Opt.
weighted sum (s)
4452
0
tot.#
288
0
avg. (s)
15.5
0
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
Retiming Results for Hard Constraints:
Realisability?
From headway histograms:
Only Orig. has minimum run time violations.
So Orig. is not realisable.
Opt. is realisable.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
2500
2500
Retiming Results for Hard Constraints:
Headway Conflicts?
2000
tot=13880660.00
1500
1000
#edges * 1
avg=300.47
0
0
500
1000
1500
avg=305.00
500
#edges * 1
2000
tot=14089810.00
0
100
200
300
400
500
Orig_KO_flow1_planned_ms_in_6s_units
600
0
100
200
300
400
500
600
Opt_KO_flow1_planned_ms_in_6s_units
Figure 2: #Edges per Planned headway. m + s < 30 and T − 30 < m + s, are
problematic. Orig: NOK, Opt OK.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
4e+06
3e+06
avg=305.15
0e+00
0e+00
1e+06
2e+06
avg=304.37
tot=19581138508.48
2e+06
#edges * flow
3e+06
tot=19531660476.46
1e+06
#edges * flow
4e+06
Retiming Results for Hard Constraints:
Headway Conflicts?
0
100
200
300
400
500
Orig_KO_flowf_planned_ms_in_6s_units
600
0
100
200
300
400
500
600
Opt_KO_flowf_planned_ms_in_6s_units
Figure 3: #Passengers per Planned headway. m + s < 30 and T − 30 < m + s,
are problematic. Orig: NOK, Opt OK.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
Retiming Results for Hard Constraints:
Macroscopically Feasible?
From headway histograms:
Only Orig. has minimum headway time violations.
So Orig. is not macroscopically feasible = not conflict-less.
Opt. is macroscopically feasible = conflict-less.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
60000
Retiming Results in the Planned Train Time Domain
12.90%
40000
50000
10.69%
30000
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
87.10%
10000
20000
89.31%
0
reduction:−2.53%
orig.m
original
orig.s
Plan_Train_Time
opt.m
optimal
opt.s
Figure 4: Increase of 2.53% of total planned train time from Orig. to Opt.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Deterministic Results
Retiming Results in the Planned Train Time Domain
Bargraphs show: Orig. → Opt.
Same planned train minimum ride + dwell time:
due to same number of trains and same minima in Orig. and Opt.
timetables,
(relatively) more planned train ride + dwell supplement time:
steered by objective function trading off efficiency with robustness,
effectiveness for passenger service of this is to be judged in expected
passenger time domain.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Stochastic Results
8e+07
Results in the Expected Passenger Time Domain
3.14%
0.00%
1.39%
2.59%
0.68%
0.00%
8.62%
8.88%
7.26%
0.22%
7.51%
2.72%
0.00%
KnockOn(s)
KnockOn(m)
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
4e+07
6e+07
5.75%
2.64%
0.00%
72.84%
2e+07
70.73%
0.47%
4.57%
0e+00
improvement:2.90%
orig.m
original
orig.s
Exp_FullPssngr_Curved_Time
opt.m
optimal
opt.s
Figure 5: Reduction by 2.90% of total exp. passenger time from Orig. to Opt.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Retiming Results
Stochastic Results
Results in the Expected Passenger Time Domain
Bargraphs show: Orig. → Opt.
= same (expected) minimum ride + dwell time due to:
same train line plan
passengers (still) taking same routes
+ less expected ride + dwell supplement time → more efficient
+ lowered expected knock-on delay → better robustness
- increased expected transfer time due to:
difficulty for solver to plan many transfers with few passengers
+ overall reduction of 2.90% in expected passenger time
Reduction of missed transfer probability from 11.34% to 2.45%
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Conclusions & Future Work
Conclusions
practical method to optimise timetables (in 65 minutes)
objective = minimal expected passenger time
showed Orig. → Opt. reduction of 2.90% in exp. passenger. time
evaluation reports on hard constraints, deterministic
stability (ride & dwell & transfers)
feasibility = conflict freeness (headways)
evaluation reports on soft constraints, stochastic
efficiency versus robustness
does not consider resilience
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Conclusions & Future Work
Railway Timetable Performance Indicators
Table 3: Railway Timetable Performance Indicators
deterministic
stable
timetableinternal
delays
settle
some
supplements
can be negative
but some are
compensatingly
positive
stochastic
feasible
robust
resilient
property in realised domain
no
timetabletimetable
timetable
internal
absorbs common
allows dispatching
delays
prim. & sec.
to absorb
delays
more rare delays
cause or measure taken in planned domain
no
supplements
timetablesupplements
are sufficiently
tuned
are negative
large
dispatching
measures
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Conclusions & Future Work
International Comparison
Table 4: Current Quality Levels of some European Railway Timetables
Level
0
1
2
3
4
?,?
stable
v
v
v
v
stable
v,v
deterministic
................feasible................
realiasable no µ-HW-conflicts
v
v
v
realiasable
v,v
v
v
v
no 3-́HW-conflicts
v,v
stochastic
robust resilient
v
v
robust
v,v
Country
FR,IT,BE,DK
NL,UK
DE
CH,SE
v
resilient
Country
BE 0∗ , DK 0∗
Black text above [Goverde and Hansen(2013)], based on inquiries
and timetable process descriptions of 2013, may be incorrect.
[Sels et al.(2015a)Sels, Cattrysse, and Vansteenwegen]
[Sels et al.(2015b)Sels, Dewilde, Cattrysse, and Vansteenwegen]
[Sels et al.(2015c)Sels, Dewilde, Cattrysse, and Vansteenwegen]
µ-HW = microscopically calculated min. headway times.
3-́HW = 3 minute macroscopically assumed min. headway times.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Conclusions & Future Work
Future Work
evaluate over only real transfers ← data?
vary parameter ’a’ value: 1% .. 5%
add parameter ’r’
r% of passengers benefit from temporal spreading of trains
parameter ’r’ value: 0% .. 100%
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Questions / Next Steps
Questions / Next Steps
Your questions?
here and now, or ...
[email protected]
www.LogicallyYours.com/research/
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Questions / Next Steps
0.36%
1.36%
12.49%
10.69%
8e+07
60000
8e+07
Results in all Time Domains
6e+07
6e+07
4e+07
0.00%
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
70.74%
3.34%
68.58%
10000
2e+07
70.63%
10.43%
6.96%
3.44%
2e+07
71.83%
6.62%
0.00%
4e+07
50000
87.51%
20000
89.31%
0.00%
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
2.56%
2.64%
10.74%
7.07%
6.39%
3.09%
1.99%
6.72%
0.00%
40000
30000
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
0.35%
8.62%
4.23%
2.25%
2.02%
1.34%
8.36%
8.61%
8.76%
orig.s
Plan_Train_Time
opt.m
optimal
opt.s
orig.m
original
orig.s
Plan_OptPssngr_Time
0e+00
opt.m
optimal
opt.s
60000
8e+07
original
0.00%
original
2.11%
0.50%
0.00%
4e+07
86.76%
20000
88.77%
optimal
opt.s
2.04%
0.49%
1.37%
0.00%
9.03%
6e+07
7.21%
2.62%
0.00%
0.10%
7.41%
2.76%
0.00%
KnockOn(s)
KnockOn(m)
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
70.28%
0.16%
4.22%
74.08%
10000
2e+07
76.72%
2e+07
71.74%
0.17%
4.37%
4e+07
6e+07
40000
30000
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
2.16%
0.00%
KnockOn(s)
KnockOn(m)
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
opt.m
6.13%
4.62%
0.10%
7.56%
Plan_FullPssngr_Time
8.57%
9.35%
4.83%
2.02%
0.00%
orig.s
3.53%
0.00%
1.40%
8.74%
50000
orig.m
3.60%
13.24%
11.23%
reduction:−3.15%
8e+07
0
orig.m
reduction:−1.69%
0e+00
reduction:−2.05%
Exp_Train_Lin_Time
opt.m
optimal
opt.s
orig.m
original
orig.s
Exp_OptPssngr_Lin_Time
optimal
opt.s
60000
orig.m
3.20%
13.39%
11.29%
improvement:5.14%
0e+00
opt.m
8e+07
orig.s
original
8e+07
0
original
improvement:6.49%
0e+00
improvement:−2.33%
orig.m
0.00%
2.78%
0.58%
0.00%
1.39%
4e+07
86.61%
20000
88.71%
6e+07
opt.s
2.68%
0.56%
8.90%
2.64%
0.00%
7.30%
0.22%
7.51%
2.73%
0.00%
KnockOn(s)
KnockOn(m)
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
70.73%
0.44%
4.35%
73.04%
10000
2e+07
75.56%
2e+07
72.14%
0.46%
4.51%
4e+07
6e+07
50000
40000
30000
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
2.13%
0.00%
KnockOn(s)
KnockOn(m)
Sink(s)
Sink(m)
Transfer(s)
Transfer(m)
Source(s)
Source(m)
Dwell(s)
Dwell(m)
Ride(s)
Ride(m)
optimal
5.75%
4.78%
0.23%
7.66%
opt.m
0.00%
8.62%
9.21%
4.52%
2.03%
0.00%
Exp_FullPssngr_Lin_Time
3.14%
0.00%
1.42%
8.79%
orig.s
original
orig.s
Exp_Train_Curved_Time
opt.m
optimal
opt.s
orig.m
original
orig.s
Exp_OptPssngr_Curved_Time
improvement:3.16%
0e+00
0
orig.m
improvement:4.53%
0e+00
improvement:−2.42%
opt.m
optimal
opt.s
orig.m
original
orig.s
Exp_FullPssngr_Curved_Time
opt.m
optimal
opt.s
Figure 6: Reduction by 3.16% of total exp. passenger time from Orig. to Opt.
Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time
Questions / Next Steps
Goverde, R., Hansen, I., 2013. Performance indicators for railway
timetables. Proceedings of IEEE International Conference on Intelligent
Rail Transportation: ICIRT2013, August 30-September 1, 2013, Beijing,
China., 301–306.
Sels, P., Cattrysse, D., Vansteenwegen, P., Jul. 2015a. Practical
Macroscopic Evaluation and Comparison of Railway Timetables.
Proceedings of the 18th Euro Working Group on transportation
(EWGT2015), 14-16 July 2015, Delft, The Netherlands. URL
http://4c4u.com/ED2015.pdf.
Sels, P., Dewilde, T., Cattrysse, D., Vansteenwegen, P., 2015b. Reducing
the Passenger Travel Time in Practice by the Automated Construction of
a Robust Railway Timetable. submitted to Transportation Research Part B
URL http://4c4u.com/TRB2015.pdf.
Sels, P., Dewilde, T., Cattrysse, D., Vansteenwegen, P., Jul. 2015c.
Towards a Better Train Timetable for Denmark, Reducing Total Expected
Passenger Time. Proceedings of the 13th Conference on Advanced
Systems in Public Transport (CASPT2015), 19-23 July 2015, Rotterdam,
The Netherlands. URL http://4c4u.com/CR2015.pdf.