1February 2009

Analysis of capacity on double-track railway lines

Olov LindfeldtFebruary 2008

2February 2009

Disposition

• Introduction – freight capacity question

• TVEM (model)

• Infrastructure modeling

• Application- Three-pattern case

• Conclusions

3February 2009

Freight capacity question

• What is the capacity for freight traffic on existing lines if high speed lines are constructed?

It depends on the timetable!

Ways to find the timetable for 2050: - Assume one- Make more general assumptions an generate a large number

of timetables

Develop an algorithm that generates timetables and evaluate freight capacity as a distribution…

Disregard disturbances (delays)

4February 2009

Freight capacity question

• What is the capacity for freight traffic on existing lines if high speed lines are constructed?

• It depends on the timetable!

Ways to find the timetable for 2050: - Assume one- Make more general assumptions an generate a large number

of timetables

Develop an algorithm that generates timetables and evaluate freight capacity as a distribution…

Disregard disturbances (delays)

5February 2009

Freight capacity question

• What is the capacity for freight traffic on existing lines if high speed lines are constructed?

• It depends on the timetable!

• Ways to find the timetable for 2050: - Assume one- Make more general assumptions and generate a large

number of timetables

Develop an algorithm that generates timetables and evaluate freight capacity as a distribution…

Disregard disturbances (delays)

6February 2009

Freight capacity question

• What is the capacity for freight traffic on existing lines if high speed lines are constructed?

• It depends on the timetable!

• Ways to find the timetable for 2050: - Assume one- Make more general assumptions and generate a large

number of timetables

Develop an algorithm that generates timetables and evaluate freight capacity as a distribution…

Disregard disturbances (delays)

7February 2009

Research view

Aim• How do the infrastructure and the timetable affect

capacity?

Method• Combinatorial analysis of infrastructure designs and

timetable structures.

TVEM: Timetable Variant Evaluation Model

8February 2009

TVEM: Assumptions

• Passenger traffic operated with a periodic timetable Train patterns

• All patterns are scheduled according to a priority order.

• A train with higher priority is never given scheduled delay for a train with lower priority.

9February 2009

TVEM: Structure

Infrastructure

Train patterns Scheduling algorithm

Evaluation of results

Scheduling order

10February 2009

TVEM: Variables

• Run times between overtaking stations(infrastructure + vehicle)

• Deceleration and acceleration supplements(for overtaking situations)

• Regular stops

• Track dispositions at stations

• Frequency of service

• Scheduling order

11February 2009

TVEM: Calculation scheme

• Periodic timetable train patterns

• Scheduling order for train patterns

• Time step: 1 minute

• Last pattern: as many freight trains as possible

Schedule as many trains as possible in pattern N

Search and store alternative paths for pattern n, given paths for pattern 1,…, n-1

Chose first path for pattern n

If n = N

Scheduling of pattern 1 (n=1)

n = n + 1

If n < N

n = n + 1

n = n - 1

Unused alternative paths for pattern n remaining?

Chose next unused path alternative for pattern n

If n = N

Yes No n = n - 1

If n > 1

If n = 1

All variants scheduled. Brake.

If n < N N

Search and store alternative paths for pattern n, given paths for pattern 1,…, n-1

n = n + 1 Chose first path for pattern n

12February 2009

Infrastructure modelling (1/2)

• Real distribution for inter-station distance.

• Fitted Weibull distribution (M-L).

• Mean: 22,7 km Std: 109 km2.

0 10 20 30 40 50 60 700

0.01

0.02

0.03

0.04

0.05

0.06

Den

sity

0 10 20 30 40 50 60 700

1

2

3

4

5

6

Distance between adjacent overtaking stations [km]

Num

ber

of o

ccas

ions

13February 2009

• Effect of additional overtaking stations?

• Halve the greatest distance repeatedly. relationship between parameters

Infrastructure modelling (2/2)

0 10 20 30 40 50 60 700

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Inter-station distance [km]

Den

sity

0 2 4 6 8 10 12 14 16 18 20 22 240

2

4

6

8

10

12

Mean [km]

Sta

ndar

d de

viat

ion

[km

]

14February 2009

Application: Three-pattern case

High-speed, regional and freight trains

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

12

Number of passenger trains/h

Num

ber

of f

reig

ht t

rain

s/h

Mean number of trains (capacity):

• Two speed combinations - 160/115 km/h (dotted)

- 210/160 km/h (solid)

• Two infrastructure layouts.Inter-station distance:- mean 22 km (lower)- mean 17 km (upper)

15February 2009

Conclusions

• Combinatorial / deterministic approach TVEM

• Infrastructure treated as a variable. Modeled stochastically (replications)

• Regular passenger timetable train pattern combinatorial timetable analysis

• Evaluation: mean capacity, variance caused by:- Infrastructure- Timetable

16February 2009

Thank You for the attention!

Hallsberg - GöteborgAntal godståg per timme

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

Referens 2008

2020 pt hög

Number of freight trains/h