Content uploaded by Luca Corolli
Author content
All content in this area was uploaded by Luca Corolli on Jan 01, 2025
Content may be subject to copyright.
Punctuality and Capacity in Railway Investment:
A Socio-Economic Assessment for Finland
Luca Corolli a, 1, Giorgio Medeossi a, 2, Saara Haapala b, 3,
Jukka-Pekka Pitkänen b, 4, Tuomo Lapp b, 5, Aki Mankki b, 6, Alex Landex c
a TRENOlab s.r.l.s., via Maniacco 7/A, 34170 Gorizia, Italy, Phone: +39 0481 30031
E-mail: 1 l.corolli@trenolab.com, 2 g.medeossi@trenolab.com
b Ramboll Finland, Espoo, Finland, E-mail: 3 saara.haapala@ramboll.fi,
4 jukka-pekka.pitkanen@ramboll.fi, 5 tuomo.lapp@ramboll.fi, 6 aki.mankki@ramboll.fi
c Ramboll Denmark, Copenhagen S, Denmark, E-mail: alex.landex@ramboll.dk
Abstract
This paper presents two methods designed to provide quantitative data for analysing the
socio-economic impacts of rail network improvements developed for the Finnish Transport
Agency. The first is a capacity estimation method; it adapts the UIC 406 method to the
characteristics of the Finnish rail network. The second method estimates delay propagation
based on the key characteristics of lines; in this case distinct formulas were developed using
regression for single- and double-track lines. The proposed methods were evaluated based
on actual and simulated data from Finland and the UK. They provide network saturation
and delay data for evaluation of capital improvements by network managers. The study
results were approved and adopted by the Finnish Transport Agency.
Keywords
Capacity estimation, Delay propagation, UIC 406, Mathematical regression, Finland.
1. Introduction
The Finnish Transport Agency (FTA) requires preparation of socio-economic assessments
for all major infrastructure investments. This requirement covers many types of railway
projects from track rehabilitation to major network improvements. Unfortunately, there is
currently no established quantitative method for assessing the capacity and traffic
punctuality impacts of railway investments, and therefore they are only assessed
qualitatively.
This paper presents results of research conducted for the FTA to develop quantitative
methods for assessing the capacity and traffic punctuality impacts of railway investments
for use in FTA’s socio-economic assessments (Finnish Transport Agency, 2018). The first
method assesses railway line capacity, enabling the rail network manager to determine line
saturation, and thereby estimate the effect of investments on capacity. The second method
evaluates delay propagation given a set of line parameters, enabling the network manager
to estimate the effect of investments on train punctuality. Both methods were developed
with the aim of being easy to apply by non-experts in socio-economic analyses.
This paper is organised as follows: Section 2 describes the capacity analysis method,
focusing on its interpretation for Finland and results obtained by applying it to a real single-
track line. Section 3 describes the delay propagation methods developed using regression
for use on single- and double-track lines. Finally, Section 4 presents conclusions.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 270
2. Capacity analysis method
The main concern in socio-economic assessments is railway network utilisation, making
capacity consumption the key performance indicator. Railway capacity can be defined as the
maximum throughput of a given set of trains on a specific line section or station area. Many
methods have been developed to estimate railway line capacity including UIC 405 (UIC,
1996), CAPACITY (Pitkänen, 2005), and CAP1/CAP2 (Moreira et al., 2004). A basic way
to calculate capacity consumption is to determinate the share of time reserved for train
operations during a given time period. The result is a percentage, as shown in Equation (1):
(1)
The most widely used method for estimating capacity consumption in Europe is UIC 406
(UIC, 2004). A key shortcoming of this method is that it does not clearly define many
important parameters, leading to a wide room for interpretation (Lindner, 2011). As a result,
multiple interpretations have been proposed including the UK’s Capacity Utilisation Index
(CUI) and Denmark’s Train Mix (Landex, 2008).
An alternative method for capacity consumption estimation uses capacity indices. For
example, heterogeneity indices have been developed based on the observation that
heterogeneity has a clear negative correlation to disturbance tolerance (Vromans, 2005).
Similarly, rail yard conflict indices have been developed based on railway layout, conflict
probability, or minimum train headways (Pitkänen, 2005).
In addition to timetable-based calculation methods, capacity can also be estimated using
microscopic simulation. Simulation is typically used when detailed information on the
impact of various alternative infrastructure scenarios or fault situations is needed. An
advantage of simulation models is that they can take human behaviour into account using
stochastic parameters. A drawback is that they typically require users to define a complete
microscopic model, which can be time consuming.
In the Finnish context, a study (Pitkänen, 2005) was aimed at calibrating the SBB’s
CAPACITY method for application in Finland. An important finding during model
calibration was that results are always dependent on specific infrastructure, rolling stock
and timetable assumptions, making it very difficult to study independent measures. In socio-
economic assessments, these parameters frequently differ between alternatives, making
comparison impossible.
An important requirement of the socio-economic assessments being considered in this
research is that they should be tackled using macroscopic analysis. Therefore, microscopic
methods (i.e., simulation) are not suitable. As a result, it was decided to develop an
interpretation of the UIC 406 method based on characteristics of the Finnish rail network.
The goal of developing a UIC 406 interpretation for Finland was to create a simple and
accurate method for estimating capacity applicable to both single- and double-track lines.
2.1 UIC 406 interpretation for Finland
Developing an interpretation of UIC 406 for Finland started with Equation (1). Defining the
equation denominator (the time period) is straightforward; defining the numerator (the time
reserved for train operations) is more complicated.
Determining the time reserved for train operations depends on many parameters
including features of the Finnish interlocking system and rolling stock. These parameters are
listed and discussed in Table 1.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 271
Parameter
Description
Notes
Capacity consumption
Measured in percentage
Analysed time period
Suggested value is 60 minutes
Sum of minimum
headway times
Sum of the time intervals between two
consecutive trains running in the same
direction
Sum of driving time
differences
Sum of time intervals between two
consecutive trains running in the same
direction with different driving times
Sum of occupation times
Sum of time intervals between two
consecutive trains running in opposite
directions on a single-track line
Earliest possible
departure time, compared
with the beginning of the
time period
Time interval referring to the impact of
partial trains in the beginning of the time
period
Sum of supplementary
time for maintenance
Time that the line section is not available for
normal operations due to maintenance
Sum of station and
crossing times
Amount of time needed for switch turning
operations during the time period
Table 1. Parameters used to determinate time reserved for train operations.
All time measurements are expressed in minutes.
Using the parameters listed in Table 1, Equation (1) can be expressed as:
(2)
The first step in calculating this equation is to define the set of trains to be analysed.
Next, the data must be prepared for each of the parameters. This is described below.
Definition of the set of trains to be analysed. Capacity consumption is typically calculated
for hourly time periods. Trains are assigned to time periods based on the time of departure
from the first station they leave in the studied area. For double-track sections, areas can span
over multiple locations (i.e., stations, halts, or junctions). Single-track sections, on the other
hand, are only defined between two consecutive locations.
Calculation of minimum headway times (). Minimum headway times depend on the
driving speed and signalling. Block sections can vary by direction and therefore headway
values must be calculated separately for each direction. Theoretically, the minimum
headway time depends on the driving speeds of two consecutive trains. Defining:
block sections factor: for single block sections, for multiple block
sections
average block section length, in km
weighted average speed, in km/h
Let us denote with the minimum headway time for a train i, that is . For each
train i, headway is calculated as shown in Equation (3) (notice that 60 = mins/hour):
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 272
(3)
Calculation of running time differences (). The running time difference describes the
extra time needed when a slow train is followed by a faster train. This calculation, for
double-track sections, depends on the operations of consecutive trains. Let us denote with
the additional headway to be assigned to a train i. If a train i is followed by a slower or
equally fast train, there is no additional headway: . Otherwise, is calculated as the
difference between the running times of the two trains over the area being analysed. The
total value is then calculated as the sum of all values, i.e. .
Calculation of occupation times (). In this context, the term occupation time describes
the reserved period after an operation on a single-track line. It is equal to the train running
time on the line section being analysed.
Calculation of earliest possible departure times (). This parameter is used to describe
the impact of trains that only partially operate during the analysed time period, i.e. that span
over multiple time periods in the studied area. In the following, we call such trains “partial
trains”. Four cases can be identified:
1. There is no partial train in the analysed time period:
2. There is only one partial train t in the scenario, departing before the beginning of
the scenario and arriving at destination during the timetable period:
where:
• arrival time of train i
• hl headway of the last line section
• running time of first train i’
• bg beginning of the time period
3. Multiple partial trains (arriving during the considered period) are present in the
scenario: only the last partial train is considered.
4. There is at least one train running through the scenario, i.e. departing before and
arriving after the scenario period: is set to the length of the time period,
resulting in full capacity consumption (100%).
Calculation of station and junction crossing times (). Station and junction crossing
times consist of the extra occupation time needed to account for turning a switch between
two train operations. They are location-specific and should be provided by a signalling
specialist. is calculated as the sum of these values.
Calculation of supplementary time for maintenance (). Timetables may or may not
include planned capacity reservations for maintenance work or shuntings. If these
operations are planned and known, they can be included in the analysis by simply adding
their total duration, in minutes, to the parameter.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 273
Figure 1. Capacity consumption in different single-track line sections.
2.2 Capacity consumption analysis results
Once capacity consumption values are defined for all line segments and time periods being
analysed, the consumption value for the whole line can be determined. Line capacity is
given by the largest value during the considered time period. For single-track sections, both
directions are considered together, so the maximum value between the two directions is
taken. For double-track sections, the two directions are considered separately.
When capacity consumption values are calculated over a full day, peak times typically stand
out. The sharpness of these peaks gives important information on the likelihood of delays
on track sections. For track sections with both passenger and freight trains, UIC has set two
threshold values for congestion: 75% in peak hours, and 60% off-peak.
Figure 1 illustrates capacity consumption for different sections of a single-track line
with mixed operations in Finland. Each line depicts the variation in capacity consumption
over the whole day for a particular line segment. The thick black line highlights maximum
values, while the two red straight lines indicate the UIC threshold values. As shown in
Figure 1, during peak hours there is congestion in multiple areas, with capacity consumption
remaining above 75% for three hours. This indicates a high risk of unpunctuality and little
room for effective delay recovery. Similarly, the 60% off-peak threshold is exceeded three
times.
3. Delay propagation method
The second method developed to better quantify socio-economic assessments of railway
investments was a delay propagation method. This method calculates the relationship
between capacity-related parameters and delays. Several well-accepted methods using
capacity to calculate delays are already available for double-track lines (Landex, 2008).
Conversely, for single-track lines, no direct relationship can be consistently identified
following the theoretical evidences first identified by Potthoff (Potthoff, 1962). As a result,
single- and double-track lines must be analysed separately using ad-hoc methods. These
methods require large sets of data with a wide range of capacity usage. Such data can be
obtained by either analysing operational data from several lines (including some heavily
used lines) or using simulation (which allows testing several increasing traffic density
scenarios and analysing the corresponding simulated delays). The next two sections
describe the distinct methods for analysing delay on single- and double-track lines.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 274
3.1 Single-track line delay propagation method
Based on theoretical considerations and an analysis of actual Finnish data, the delay
propagation P for a group of trains on a single-track line can be defined as a function of:
• the number of crossings in the timetable
• the margin (it is a function of the running time: 10% for passenger trains, and
12.5% for freight trains)
• the initial delay , with early- and late-running trains accounted for separately:
and
. Notice that early arriving trains are considered as trains with negative
initial delay, i.e. they contribute to the
parameter.
Since initial delay is the delay given as input and final delay is delay given as output, in the
following text we call them “input delay” and “output delay”, respectively. Both input and
output delays include all delays regardless of the cause of the delay. For input delays this is
not an issue since infrastructure investments can only affect delays that propagate in the
track section affected by the investment. For output delays, days with heaviest delay
propagation within each line need to be filtered out of the data set since they include major
train or infrastructure failures, which are not related to railway investments.
As part of this research, one year’s worth of input data were aggregated by day and line.
These data were supplemented by simulation data since historical data do not cover all
possible parameter combinations. The simulations were run using OpenTrack software
(Nash and Huerlimann, 2004) on timetables with 12 different numbers of crossings per train
(each corresponding to a specific headway value) and 5 different input delay values. This
showed how delays changed altering one parameter at a time. One hundred simulations
were run for each combination of crossings and input delay, for a total of
simulations.
The simulation results are illustrated in Figure 2 which shows the relationship between
input delay (x-axis) and output delay (y-axis). The lines show the output delay variation for
a given headway (in seconds), while the vertical bars show the average output delay across
all headway values. As shown in Figure 2 the relationship between output and input delay
appears to be slightly super-linear.
Figure 2. Simulation results analysis: output delay vs input delay
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 275
Figure 3. Simulation results analysis: output delay vs crossings.
Figure 3 illustrates the relationship between number of crossings and output delays. For
small numbers of crossings there is no appreciable tendency for delays to increase. At
approximately 3 crossings/train output delay starts increasing, and after 4 crossings/train it
rapidly grows. The growth in output delay does not continue beyond 7 crossings/train since
deadlocks in the simulation prevent trains from arriving at all.
The delay propagation model was developed to obtain a mathematical formula for
estimating output delays based on input delays and crossings. In this case mathematical
regression, an approach consistent with other railway delay propagation research (Marković
et al., 2015) was used to develop the formula.
The first step in a regression analysis is to examine the data to determine the type of
relationship. Figure 4 illustrates a quadratic trend line plotted for the relationship between
input delay and output delay, while Figure 5 illustrates a quadratic trend line plotted for the
relationship between crossings/train and output delay. In both cases quadratic
approximations appear to be reasonable. Since quadratic equations are also easy for non-
experts to apply, they were chosen for use in developing the assessment method.
Figure 4. Output delay vs input delay: quadratic trend line.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 276
Figure 5. Output delay vs crossings per train: quadratic trend line.
The regression model for the single-track case is a combination of two quadratic
formulas: one considering positive input delays and one considering the number of
crossings. Denoting with the average number of crossings per train, and with
the regression parameters, the total expected output delay for a group of trains can be
calculated with Equation (4):
(4)
The parameters were obtained by running a regression on the simulation results using
the XLSTAT data analysis Excel add-on. The parameters found were: ,
, , . Next a goodness of fit indicator was calculated to
evaluate results. Denoting with
the observed (measured) positive output delays,
goodness is defined in Equation (5):
(5)
The goodness measure was calculated using the identified parameters and Finnish
historical data from 12 railway lines. The goodness was equal to just 10.8%, calling for an
alternative approach. Thus, a mixed approach was studied. In the mixed approach,
simulated data were used to estimate crossings parameters and (since real data do not
have a sufficient range of crossings values), and real data were used to determine the input
delay parameters and . The regression analysis of real input delay data resulted in a
negligible value for (so it was removed from the formula), and . The goodness
measure calculated with these parameters was equal to 61.0% which is reasonable. The final
proposed formula for estimating total output delay for a group of trains on a single-track
line is presented in Equation (6):
(6)
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 277
3.2 Double-track line delay propagation method
The key parameters used to evaluate delay propagation on a double-track line are:
• the buffer times, i.e. the additional spacing between trains provided to reduce the
risk of delay propagation. It is especially important to examine cases when the
buffer time is limited (so called “critical headways”). Buffer times are included
using a set denoted with B, with buffer thresholds. Buffer thresholds are
indices to denote buffers of size . Each buffer, measured in minutes, ranges from
a minimum to a maximum , thus
• the initial delay (referred to as “input delay” in the following text)
• the running and stop time margins and
As for the single-track case, the formula for estimating output delays for a group of trains
from a set of input parameters can be obtained using mathematical regression. First, the
input data were prepared aggregating values for all parameters for each line, direction, day,
and time-band. The total expected output delay for a group of trains can be calculated using
Equation (7):
(7)
Parameter is the number of buffers in a threshold b, and is the weight
associated to buffer b. Thus, the effect of buffer times is evaluated considering the criticality
of having a small buffer time, with defined to reflect this criticality:
.
Input data include 10 double-track lines with both directions separately accounted for.
One-year worth of traffic data were considered, defining one train group per day/line. Buffer
thresholds were subdivided into five 1-minute wide groups, from 0 up to 5 minutes. Train
groups without buffers between 0 and 1 minute (the most critical ones) were not considered.
Regression performed on the input data provided the following parameter values:
, , , and . All parameters have a reasonable
practical interpretation, and the corresponding goodness is 73.91%. Thus, they may be used
in Equation (7) to create Equation (8) for estimating delay propagation on double-track
lines:
(8)
Regression results were tested to evaluate the impact of timetable changes, by applying
the proposed delay propagation formula to 4 scenarios from the UK’s Crossrail project. The
input delay was set at zero to simplify the analysis. Results showing the estimated effect of
all timetable-dependent parameters on output delay are illustrated in Table 2.
Scenario
SC0
SC1
SC2
SC3
Number of trains
40
48
22
11
0–1 min buffers
397
559
37
0
Buffer weight
210.668
291.219
36.688
0
Margin
547.5
678
0
0
Expected delay [s/train/day]
100.4
114.1
36.4
0
Table 2. Validation of the double-track line delay propagation method.
Scenario N is denoted with SCN (e.g. SC0 = Scenario 0)
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 278
The base scenario (SC0) represents the current timetable. SC1 adds 8 trains to the base
timetable, resulting in a large number of small buffers. SC2 and SC3 have lighter traffic
levels: SC2 has about half the trains from the base scenario, and SC3 further divides the
number of trains in half. This test case study shows that the proposed mathematical model
is sensitive to train frequency and provides reasonable results.
4. Conclusions
This paper discusses research carried out for the Finnish Transport Agency to develop
quantitative methods for evaluating the socio-economic impacts of railway investments.
Two methods were developed, the first determines capacity consumption and the second
determines delay propagation. These methods are designed to provide railway network
managers with simple formulas for evaluating the impacts of railway line investments
without performing complex simulations.
The capacity consumption method was developed by applying the characteristics of the
Finnish railway (e.g., interlocking, rolling stock) to the UIC 406 capacity formula. The
paper describes the development of the parameters and highlights the differences between
single- and double-track line cases. The method was then applied to a Finnish line to
illustrate use of capacity over the course of a day.
The delay propagation forecasting method was developed using mathematical
regression with both simulated and historical traffic data. The regression results were
evaluated using a goodness measure. Separate methods were developed for the single- and
double-track line cases to account for the different factors triggering delay propagation.
References
• Finnish Transport Agency, 2018. “Capacity and Punctuality in Railway Investment
Socio-Economic Assessment”. Technical report.
• International Union of Railways (UIC), 1996. “Links between railway infrastructure
capacity and the quality of operations” (UIC code 405 OR). Paris, France.
• International Union of Railways (UIC), 2004. “UIC leaflet 406”, France
• Landex, A., 2008. “Methods to estimate railway capacity and passenger delays”. PhD
thesis, Copenhagen, Technical University of Denmark.
• Lindner, T., 2011. “Applicability of the analytical UIC Code 406 compression method
for evaluating line and station capacity”. Journal of Rail Transport Planning &
Management 1, pp.49-57.
• Marković, N., Milinković, S., Tikhonov, K.S., Schonfeld, P., 2015. “Analyzing
passenger train arrival delays with support vector regression”. Transportation Research
Part C: Emerging Technologies, vol. 56, pp.251-262.
• Moreira, N., Garcia, L., Catarrinho, P., 2004. “Network Capacity”. Computers in
Railways IX Conference, Dresden, Germany.
• Nash, A., Huerlimann, D., 2004. “Railroad simulation using OpenTrack”; Computers in
Railways IX, WIT Press, Southampton, pp. 45-54.
• Pitkänen, J-P., 2005, “Radan välityskyvyn mittaamisen ja tunnuslukujen kehittäminen”.
Helsinki: Ratahallintokeskus, Liikennejärjestelmäosasto (in Finnish language).
• Potthoff, G., 1962. “Verkehrsströmungslehre I - Die zugfolge auf Strecken und in
Bahnhöfen”, Transpress, Berlin, Germany (in German language).
• Vromans, M., 2005. “Reliability of Railway Systems”. Rotterdam: The Netherlands
TRAIL School.
8th International Conference on Railway Operations Modelling and Analysis - RailNorrk¨oping 2019 279
