micro-simulation based analysis of railway lines...
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Micro-simulation based analysis of railway lines robustness
Fabrizio Cerreto
Department of Transport
Technical University of Denmark
E-mail: [email protected]
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
2 DTU Transport, Technical University of Denmark
A method to benchmark investments
Infrastructure modifications
•Alignment
•Signaling
Rolling stock modifications
•Acceleration
•Max. Speed
•Braking performance
Sets of rules
•Min. Headway
•Time Supplements
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
3 DTU Transport, Technical University of Denmark
Approach
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
4 DTU Transport, Technical University of Denmark
Sensitivity to primary delays and traffic volume
Sensitivity to primary delaysSensitivity to primary delays
• Primary delays deterministic generation (1,…,n)
• Synthetic indices to describe the measurements
Traffic volume increasesTraffic volume increases
• Test timetables generated from a reference timetable up to the maximum capacity consumption
Micro-simulationMicro-simulation
• Running time calculation
• Trains interaction
• Delays measurement
Skimming methodSkimming method
• Reduce the number of simulation runs through the selection of a set of representative trains
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
5 DTU Transport, Technical University of Denmark
Measurements
• Capacity consumption (UIC 406)
Line exploitation
• Total delay
• Settling time (Recovery time)
Measure and description of primary delay effects on the line
• Share of trains delayed
• Average delay per train
Individual impact on trains
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
6 DTU Transport, Technical University of Denmark
Total delay
y = 13,97x2 - 27,848x - 14,067
R² = 0,9907
y = 14,864x2 - 40,542x + 9,5333
R² = 0,9959
y = 23,72x2 - 87,183x + 71,3
R² = 0,9969
y = 32,144x2 - 140,49x + 133,23
R² = 0,9962
y = 47,258x2 - 172x + 119,2
R² = 0,9578
0
500
1000
1500
2000
2500
3000
3500
1 2 3 4 5 6 7 8 9 10
To
tal
dela
y [
s]
Primary delay [min]
A (11 trains/h) B (12 trains/h) C (14 trains/h)
D (16 trains/h) E (18 trains/h)
Index: Regressed parabola Second derivative
Regression to square parabolas
Sum of each train’s delay at every timing point
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
7 DTU Transport, Technical University of Denmark
Settling time (Recovery time)
Applicable also to the Number of trains involved
Index: Amplification factor
Minimum Mean Squared Error
Irregular shape: basic timetable as a reference
Lapse of time until all the trains are on time
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8 9 10
SETTLIN
G T
IM
E [
MIN
]
PRIMARY DELAY [MIN]
a d md*a
Timetable “a”
Timetable “d”
Scaled timetable “a”
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
8 DTU Transport, Technical University of Denmark
Average delay per train
y = 36,84x - 103,67
R² = 0,9255
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10
AV
ER
AG
E T
RA
IN
DELA
Y A
T R
TD
[S
]
PRIMARY DELAY AT GV [MIN]
A B C D E
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
9 DTU Transport, Technical University of Denmark
The skimming method
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 56 57 58 5944 00 01 02 03 04
7:00 – 8:00 TimetableIntercity
Sneltrein
Sprinter
Stoptrein
55 56 57 58 59 05
Gvc
Gv
Gvmv
Rsw
Dt
Dtz
Sdm
Rtm
2'
3'
0,6'
0,6'
0,6'
0,6'
0,6'
0,6'
IC (NS Hispeed)
1900 19002100 21002200 22005100 5100
5000 50009200
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
10 DTU Transport, Technical University of Denmark
The skimming method
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 56 57 58 5944 00 01 02 03 04
7:00 – 8:00 TimetableIntercity
Sneltrein
Sprinter
Stoptrein
55 56 57 58 59 05
Gvc
Gv
Gvmv
Rsw
Dt
Dtz
Sdm
Rtm
2'
3'
0,6'
0,6'
0,6'
0,6'
0,6'
0,6'
IC (NS Hispeed)
1900 19002100 21002200 22005100 5100
5000 50009200
Same amount of primary delay
Different impact
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
11 DTU Transport, Technical University of Denmark
The skimming method
0
200
400
600
800
1000
1200
1400
1600
1800
1 2 3 4 5 6 7 8 9 10
To
tal d
ela
y a
t [s]
Primary delay [min]
1902 Average
Thorough SimulationThorough Simulation
Primary delay to each train
System behaviorSystem behavior
Total delay for each
simulation
Average total delay
Subset selectionSubset
selectionMean Squared
Error
Most representative
subset
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
12 DTU Transport, Technical University of Denmark
The skimming method
Load reduction
– Total number of simulations
𝑛𝑠𝑖 = 𝑛 ∙
𝑗=1
𝑛𝑡𝑡
𝑣𝑗 ∙ 𝑛𝑠𝑐
– Skimmed number of simulation𝑛𝑠𝑖∗ = 𝑛 ∙ 𝑣1 + 𝑛 ∙ 𝑛𝑡𝑡 ∙ 𝑛𝑠𝑐 = 𝑛 𝑣1 + 𝑛𝑡𝑡 ∙ 𝑛𝑠𝑐
– Reduction
𝜂 =𝑛𝑠𝑖 − 𝑛𝑠𝑖
∗
𝑛𝑠𝑖= 1 −
𝑣1 𝑗=1𝑚 𝑣𝑗 ∙ 𝑛𝑠𝑐
+1
𝑣𝑗
Application
5 Timetables
• 11, 12, 14, 16, 18 trains/h
10 Primary delay values
• 1,…,10 minutes
5 Infrastructure scenarios
𝜂 = 89,86%
Subsetselection
Actual simulation
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
13 DTU Transport, Technical University of Denmark
The case study
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
14 DTU Transport, Technical University of Denmark
Case study
ScenarioJunction
stationingTracks in Delft
Speed limit in Delft (km/h)
Status
Phase 1 North Delft 2 (Viaduct) 100 Current state
Phase 2 North Delft 2 (Tunnel) 140 Under construction (2015)
Phase 3 South Delft 4 (Tunnel) 140 Planned
Phase 4 None 4 (Tunnel) 140 Hypothetical
ETCS L1 North Delft 2 (Viaduct) 100 Hypothetical
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
15 DTU Transport, Technical University of Denmark
Case study: Line The Hague – Rotterdam
• 4-2 tracked
• Mixed passenger traffic
• 11 trains/h
• Cyclic timetable
• Primary delay: (1,…,10) min Den Haag HS
• Delay threshold: 60 s
• Timing points: Rotterdam Centraal
• Simulation: OpenTrack
• Dispatching: FCFS
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
16 DTU Transport, Technical University of Denmark
Capacity consumption
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
81%
86%
99% 99% 100%
70%72%
89% 88%
97%
59%60%
76% 76%
86%
61%63%
71%74%
78%
60%
65%
83% 83%
89%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
A (11 trains/h) B (12 trains/h) C (14 trains/h) D (16 trains/h) E (18 trains/h)
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
17 DTU Transport, Technical University of Denmark
Total delay
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
y = 47,258x2 - 172x + 119,2
R² = 0,9578
0
500
1000
1500
2000
2500
3000
3500
1 2 3 4 5 6 7 8 9 10
To
tal
dela
y a
t R
td [
s]
Primary delay at Gv [min]
A (11 trains/h) B (12 trains/h) C (14 trains/h)
D (16 trains/h) E (18 trains/h)
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
No
rm
alized
to
tal
dela
y s
en
sit
ivit
y i
nd
icato
r
Frequency [trains/h]
Phase 1 Phase 2
Phase 3 Phase 4
Signalling works
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
18 DTU Transport, Technical University of Denmark
Settling time
00:00
10:00
20:00
30:00
40:00
50:00
00:00
1 2 3 4 5 6 7 8 9 10
Sett
lin
g t
ime a
t R
td [
min
]
Primary delay at Gv [min]
A B C D E
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
Sett
lin
gti
me a
mp
lifi
cati
on
facto
r
Frequency [train/s]
Phase 1 Phase 2
Phase 3 Phase 4
Signalling Works
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
19 DTU Transport, Technical University of Denmark
Share of trains involved
0
1
2
3
4
5
6
7
8
9
10
11
12
1 2 3 4 5 6 7 8 9 10
Train
s a
rriv
ing
late
at
Rtd
Primary delay at Gv [min]
A B C D E
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
Dela
yed
train
sam
plifi
cati
on
facto
r
Frequency [trains/s]
Phase 1 Phase 2
Phase 3 Phase 4
Signalling Works
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
20 DTU Transport, Technical University of Denmark
Average delay per train
Scenario a b x (y=0)
Phase 1 36,84 -103,67 2,81
Phase 2 37,42 -121,57 3,25
Phase 3 38,00 -120,49 3,17
Phase 4 39,53 -156,26 3,95
ETCS lev. 1 34,18 -90,933 2,66
𝑦 = 𝑎𝑥 + 𝑏
𝑥 𝑦 = 0 = −𝑏
𝑎y = 36,84x - 103,67
R² = 0,9255
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10
Averag
e t
rain
dela
y a
t R
td [
s]
Primary delay at Gv [min]
A B C D E
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
21 DTU Transport, Technical University of Denmark
Robustness indices
• Phase 1: Delft Viaduct – 2 tracks
• Phase 2: Delft Tunnel – 2 tracks
• Phase 3: Delft Tunnel – 4 tracks
• Phase 4: Entirely 4 tracksinfrastructure
• Signalling works: ETCS Level 1
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
Dela
yed
train
s
am
plifi
cati
on
facto
r
Frequency [trains/s]
Share of trains delayed
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5
Cap
acit
y C
on
su
mp
tio
n
Frequency [trains/h]
Capacity consumption UIC406
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
Sett
lin
gti
me a
mp
lifi
cati
on
facto
r
Frequency [train/s]
Recovery time
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
11 12 13 14 15 16 17 18
No
rm
alized
to
tal d
ela
y s
en
sit
ivit
y
ind
icato
r
Frequency [trains/h]
Total delay
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
22 DTU Transport, Technical University of Denmark
Conclusionsand further work
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
23 DTU Transport, Technical University of Denmark
Conclusions
Infrastructure scenarios comparison
Traffic volume increase: + Total delay
+ Share of trains involved
≈ Recovery Time
= Average delay per train
Capacity consumption (UIC 406)
not exhaustive for robustness
The less timetable allowance, the wider indices spread
Micro-simulation based depends on timetables
Computational load
Dispatching on open line Vs. routing within at stations
26/03/2015Fabrizio Cerreto – Micro-simulation based analysis of railway lines robustness
24 DTU Transport, Technical University of Denmark
Future work
Timetable generation
Dispatching / rerouting / rescheduling
Correlation between Capacity consumption – Timetable allowance and the indicators spread
Quantification of the loss in information given by the skimming method
Go stochastic
17/04/2008Presentation name25 DTU Transport, Technical University of Denmark
Tunnel Inaugurated 28/2/2015
Viaduct Tunnel