Acta Polytechnica CTU Proceedings


doi:10.14311/APP.2016.5.0022
Acta Polytechnica CTU Proceedings 5:22–25, 2016 © Czech Technical University in Prague, 2016

available online at http://ojs.cvut.cz/ojs/index.php/app

INFRASTRUCTURE PARAMETERS AFFECTING CAPACITY
OF RAILWAYS IN TEN-T

Vít Janoš∗, Milan Kříž

Department of Logistics and Management of Transport, Faculty of Transportation Sciences, CTU in Prague,
Czech Republic

∗ corresponding author: janos@fd.cvut.cz

Abstract. The article presents possible solutions of the issue of the lost capacity on a double-track
line. It is shown a solution where an inserted train on the double-track line use the lost capacity of
the opposite line track using active overtaking. The feasibility of such a solution is discussed and the
length of sections suitable for active overtaking is calculated.

Keywords: Capacity, UIC 406, speed ratio .

1. Introduction
The capacity of the railway infrastructure can be con-
sidered as a usable time space for the train paths.
Capacity is thus influenced not only by the parame-
ters of the infrastructure, but also by the character
of the traffic – by the designed train paths and their
heterogeneity. With increasing degree of heterogeneity
the capacity consumption increases too and the num-
ber of possible train paths in a defined time windows
declines.
This phenomenon is also called "capacity bal-

ance" [1]. In the capacity balance there are four
factors on whose interdependencies the capacity is
based: number of trains, average speed, stability and
heterogeneity. Relationships among the individual
factors are shown in Figure 2 [1].
Principle of Figure 2 is explained as follows: "In

this qualitative model, an axis for each parameter
is drawn from a unique origin. A chord links the
points on the axes, corresponding to the value of
each parameter. The length of the chord represents
the capacity. Capacity utilisation is defined by the
positions of the chord on the four axes. Increasing
capacity means increasing the length of the chord".

General effect associated with the modernization of
the Trans-European conventional rail network (typi-
cally the modernization of the transit railway corridors
in the Czech Republic in the original routes to a maxi-
mum speed of 160 km/h) is the rising heterogeneity of
the traffic on some routes in the network. It is caused
by increasing the line speeds. On the one hand re-
gional passenger train paths remains after increasing
the line speed about as fast as before the modern-
ization (journey speed of the regional trains usually
does not exceed 60 km/h due to the higher number
of stops). On the other hand long-distance passenger
trains should logically utilize all characteristics of in-
frastructure for the maximum journey speed (at the
fastest trains the journey speed of 120-140 km/h can
be reached in some line sections). These both cases
are thus usually marginal and between these limits

Figure 1. Possible situation of active overtaking on
a double-track line.

the freight trains paths occur (with journey speeds in
the range of 70-100 km/h).

2. Heterogeneity and its
measuring

Heterogeneity can be measured in different ways. One
way is to compare running speeds of individual train
(or train paths). For this purpose Krueger [2] pro-
posed and used so called Speed Ratio (SR). The Speed
Ratio is the ratio of the fastest train speed to the slow-
est train speed:

SR =
max(v1, v2, ..., vn)
min(v1, v2, ..., vn)

So the SR on the typical line section on some transit
railway corridor in the Czech Republic can reached
value of 3 (the speed of the fastest train about 140
km/h and the speed of the slowest train about 45-50
km/h).

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vol. 5/2016 Infrastructure Parameters Affecting Capacity of Railways in TEN-T

Figure 2. Capacity balance [1].

The very high SR is problematic only when it comes
to the line or line section with a high number of train
paths. But the lines of the Trans-European conven-
tional rail network usually show a high number of
train paths. Line sections with high demand for train
paths and a high SR can usually be solved by segregat-
ing the various types of traffic. This entails increasing
the number of line tracks (e.g. quadruple-track line
sections in urban agglomerations with two tracks for
long-distance passenger trains and fast freight trains
and two tracks for slower regional passenger trains
and slower freight trains) or construction of lines dedi-
cated exclusively for a certain type of traffic (typically
on the one hand high-speed railway lines and, on the
other hand, lines dedicated only for freight train as
e.g. BetuweLijn). This approach, however, is not yet
common in the Czech Republic.

3. Active overtaking
On double-track lines, where high degree of hetero-
geneity is because of the mixed traffic and high re-
quirements for the number of the train paths, so called
lost capacity arises. Lost capacity is unusable time
space between train paths with different train speeds,
where any additional train path cannot be inserted
(e.g. because there is no other station). Lost capac-
ity can be limited by reducing heterogeneity of train
paths. Either the slowest trains can be accelerated
(e.g. these trains can pass some stops), or vice versa
the fastest trains can be slowed. Lost capacity may
be also used for active overtaking1. An example of
this solution is shown in the Figure 1.
Active overtaking is a very interesting possibility

of using a part of the lost capacity. This idea can be
very helpful in cases, when the number of stations
on a line section is reducing within modernization of
infrastructure. In the former stations there are only
crossovers for crossing between the line tracks for cases
of interruptions. In such cases there is no possibility to
insert one more train path into a sequence of differently

1Active overtaking can be defined as an overtaking of slower
train by faster train, when the slower train does not have to
stop [3].

fast train paths, but they can also be used for crossing
between line tracks and in regular operation.
The actual possibility of using these crossovers for

regular traffic, however, depends on the diverging
speed that affects the train speed (and thus journey
time) of the overtaking or the overtaken train and
thus affects the length of the section required for over-
taking. Furthermore, it is obvious that the greater
the heterogeneity of the train paths in the reference
section is (i.e. the larger the difference of the jour-
ney speeds between the overtaken and the overtaking
train), the shorter the section required for overtaking
is. With regard to the above mentioned borderline
cases it is evident that the overtaken slower train is
always a regional passenger train.
There are generally two cases possible:

(1.) The slower train crosses over to the other line
track and runs against the right direction, the faster
train runs in the right direction.

(2.) The faster train crosses over to the other line track
and runs against the right direction, the slower train
runs in the right direction.

The cases from the first group are suitable for situ-
ations, in which the platforms of stations and stops in
the line section are situated between the line tracks,
or in which only stations equipped with a good vi-
sual and audible information system are. This system
should provide clear information about platforms and
tracks of arriving and departing trains.
The cases from the second group are suitable, if

the speed limit over the crossovers between the line
tracks corresponds or is close to the line speed or the
maximum train speed.

4. Case study: the first transit
railway corridor between
Prague and Děčín

The part of the first transit railway corridor between
Prague and Děčín links the Prague Metropolitan Area
[4] with the Ústí Metropolitan Area and with the
north part of Germany. The most typical situation
for the active overtaking is an interaction of a fast
freight train (maximum train speed about 100 km/h)
and a regional passenger train (journey speed about
50 km/h).

The active overtaking of the first type can be used
in the line sections:

• Hněvice – Hněvice seř.n.
• Roudnice nad Labem – Hrobce
• Lovosice jih – Lovosice
• Prackovice nad Labem – Ústí nad Labem jih – Ústí
nad Labem hl.n.

Now we have to analyse these line section, whether
the active overtaking leads to time saving in compar-
ison with overtaking of the regional passenger train

23



Vít Janoš, Milan Kříž Acta Polytechnica CTU Proceedings

Figure 3. Relationship between speed ration and
Length of section for overtaking.

by the fast freight train, when the regional passenger
train is dwelling in some station.

Sections Hněvice – Hněvice seř.n. and Lovosice jih
– Lovosice can be excluded immediately, because the
result time savings will be negative. In both cases
the regional passenger train is stopping only once in
the line section and in both cases the speed limit
over crossovers in the stations which bounds the line
section is lower than the speed limit on passing sidings
in these stations.

Sections Roudnice nad Labem – Hrobce and Prack-
ovice nad Labem – Ústí nad Labem jih – Ústí nad
Labem hl.n. show always positive time savings. In
both cases the regional passenger train is stopping
twice in the line section2. In these cases, the parallel
run is generally about 2 minutes more effective then
overtaking of the slower train in the station. It is
very important that the overtaking train is guided
precisely to the desired time position. The accuracy
of this guidance may have a significant effect on the
resulting time savings.

By the active overtaking of the second type the jour-
ney time of the overtaking train is extended because
of the diverging speed of the crossovers in the bound-
ing stations. In Table 1 values for typical situation
on the first transit railway corridor are shown. The
values were calculated with linear margin 9%. Value
are graphically illustrated in Figure 3.

From Table 1 it is possible to determine the length
of the line section which is needed for active overtaking.
If the actual line section is shorter, then the dwell
times of the slower train have to be extended.

5. Conclusions
The Verification of heterogeneity in relation to the
partial use of the lost capacity by active overtaking of
differently fast trains showed clearly that in the case of
the interaction of regional passenger trains and freight
trains there are solutions which can be divided into

2Also the stops in bounding stations of the line section are
counted, if the regional passenger is being already overtaken
during the stay in the station.

Sum of operating
intervals and time
reserves [min]

5

Journey speed of
slower train [km/h]

50

Speed
Ratio [1]

Speed
of faster
train
[km/h]

Length
of section
for over-
taking
[km]

1,1 55 45,83
1,2 60 25,00
1,3 65 18,06
1,4 70 14,58
1,5 75 12,50
1,6 80 11,11
1,7 85 10,12
1,8 90 9,38
1,9 95 8,80
2 100 8,33
2,1 105 7,95
2,2 110 7,64
2,3 115 7,37
2,4 120 7,14
2,5 125 6,94
2,6 130 6,77
2,7 135 6,62
2,8 140 6,48
2,9 145 6,36
3 150 6,25

Table 1. Length of section for overtaking.

two situations. Either if the diverging speed over the
crossovers in the bounding station of the line section
is clearly lower than the running speed of the fast
freight train, then the regional passenger train should
run against the right direction on the other line track.
Or if the diverging speed over the crossovers in the
bounding station of the line section is high enough
(minimum is 80 km/h), then then the fast freight train
should run against the right direction on the other line
track. It is important to mention that by modernizing
the infrastructure, which should also allow such use of
the lost capacity, platforms should be mostly located
between the main line tracks.

With regard to the actual length of the line sections
for active overtaking and with regard to demand for
the train paths it is necessary to mention that on

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vol. 5/2016 Infrastructure Parameters Affecting Capacity of Railways in TEN-T

Trans-European conventional rail network this solu-
tion will be usually marginal. Furthermore, it is likely
that the heterogeneity of demanded train paths will
not decline. Authorities ordering the long distance
passenger trains and open access operators do not
want to, on the one hand, slow down artificially their
trains. On the other hand, local authorities ordering
the regional passenger trains do not want to reduce
the number of operated railway stops, which is a very
problematical political topic.

In the Czech Republic the construction of quadruple-
track line sections remains as a permanent challenge in
cases where a high degree of heterogeneity connected
with high demand for train paths occurs. Only such a
solution leading to the segregation of various types of

traffic allows homogenization of the train paths and
effective elimination of the lost capacity.

References
[1] UIC Leaflet 406 - Capacity. Paris: International Union
of Railways (UIC).

[2] H. Krueger. Parametric modeling in rail capacity
planning. Simulation Conference Proceedings. AZ,
Phoenix, 1999.

[3] M. Drábek. Periodic Freight Train Path in Network.
ČVUT, Praha, 2014.

[4] T. Kostelecký, D. Čermák. Metropolitan Areas in the
Czech Republic - Definitions, Basic Characteristic,
Patterns of Suburbanisation and Their Impact on
Political Behaviour. Sociologický ústav AV ČR, 2004.

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	Acta Polytechnica CTU Proceedings 5:22–25, 2016
	1 Introduction
	2 Heterogeneity and its measuring
	3 Active overtaking
	4 Case study: the first transit railway corridor between Prague and Decín
	5 Conclusions
	References