The Management of Railway Operations during the Planned Interruption of Railway Infrastructure

Abstract

A planned interruption of railway infrastructure is a situation where the operation of the track line or the operation of railway transport is limited. If there is also a restriction on the railway infrastructure, it means there will be complications not only for passengers but, above all, for railway undertakings operating freight transport. However, because of the planned railway infrastructure interruption, the quality of services provided not only to passengers but also to freight transport is decreasing. The aim of this paper is to propose effective planned maintenance works based on the analysis and evaluation of the processes performed during the planned railway infrastructure interruption or restriction. The research describes the process of affected railway infrastructure from technical, cost, and safety points of view. A methodological procedure is proposed under the condition of the Czech infrastructure manager. The main method is the calculation of the costs for the railway infrastructure manager and railway operator during the infrastructure interruption. The application part is undertaken using two interrupted lines according to the established alternative timetable in the area of České Budějovice.

Full text

Citation: Bulková, Z.; Gašparík, J.;
Zitrický, V. The Management of
Railway Operations during the
Planned Interruption of Railway
Infrastructure. Infrastructures 2024,9,
119. https://doi.org/10.3390/
infrastructures9070119
Academic Editors: Benedetto
Barabino, Giulio Maternini and
Roberto Ventura
Received: 14 June 2024
Revised: 18 July 2024
Accepted: 19 July 2024
Published: 22 July 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
infrastructures
Article
The Management of Railway Operations during the Planned
Interruption of Railway Infrastructure
Zdenka Bulková* , Jozef Gašparík and Vladislav Zitrický
Department of Railway Transport, Faculty of Operation and Economics of Transport and Communication,
University of Žilina, Univerzitná8215/1, 01026 Žilina, Slovakia; jozef.gasparik@uniza.sk (J.G.);
vladislav.zitricky@uniza.sk (V.Z.)
*Correspondence: zdenka.bulkova@uniza.sk; Tel.: +421-41-513-34-11
Abstract: A planned interruption of railway infrastructure is a situation where the operation of the
track line or the operation of railway transport is limited. If there is also a restriction on the railway
infrastructure, it means there will be complications not only for passengers but, above all, for railway
undertakings operating freight transport. However, because of the planned railway infrastructure
interruption, the quality of services provided not only to passengers but also to freight transport
is decreasing. The aim of this paper is to propose effective planned maintenance works based on
the analysis and evaluation of the processes performed during the planned railway infrastructure
interruption or restriction. The research describes the process of affected railway infrastructure
from technical, cost, and safety points of view. A methodological procedure is proposed under the
condition of the Czech infrastructure manager. The main method is the calculation of the costs for
the railway infrastructure manager and railway operator during the infrastructure interruption. The
application part is undertaken using two interrupted lines according to the established alternative
timetable in the area of ˇ
CeskéBudˇejovice.
Keywords: railway infrastructure; railway transport; planned railway interruption; railway operation;
infrastructure manager costs; operator costs
1. Introduction
Railway infrastructure plays a key role in modern transport systems, which require
constant innovation and precise management and maintenance [
1
]. The basic goals of the
infrastructure manager are to ensure regular, reliable, and safe railway infrastructure and to
provide it to operators of railway passenger and freight transport in a non-discriminatory
manner [
2
]. Since the property components of rail transport, especially rail infrastructure,
are capital-intensive and have a long life cycle, their operation and maintenance require
a long-term and sustainable strategy. Strategic planning involves gathering information,
setting goals, translating goals into specific goals, and taking action to achieve those
goals [
3
]. In the transport policy of the European Union, the ownership model of the
railway infrastructure is preferred to the vertically controlled model. In this system, one
entity manages and takes care of the infrastructure, while transport services on this network
are then provided by one or more operators (rail operators) who compete (unbundling) [
4
].
It focuses on increasing competitiveness in rail transport and making investments in rail
and road infrastructure at a uniform level.
Infrastructure managers (hereafter IMs) are either the owners of the railway infrastruc-
ture or companies that have obtained concession contracts. They are responsible for the
safety and maintenance of railway lines but mainly for enabling the various train operators
to access the line. According to [
5
], in all European Union countries, IMs are national
monopolies, most of which are publicly owned. They mention a few exceptions, such as
some German railway lines or the Perpignan–Figuears line. IMs have far-reaching effects
Infrastructures 2024,9, 119. https://doi.org/10.3390/infrastructures9070119 https://www.mdpi.com/journal/infrastructures

Infrastructures 2024,9, 119 2 of 32
on the business models of railways and industry players, resulting in them being highly
regulated.
It is similar in the Czech Republic, where the state is the owner of the national railway
and most of the regional railways. They manage this state property, and the function of
the railway owner on it is in accordance with Act 266/1994 Coll. about railways, which
is carried out by the Czech infrastructure manager. According to the Act on Railways,
the owner of the railway is obliged to ensure the maintenance and repair of the railway
to the extent necessary for its operability. As far as the national or regional railways are
concerned, the owner is also obliged to take care of the development and modernization
of the railway to the extent necessary to ensure the transport needs of the state and the
transport services of the regional territory [
6
,
7
]. To fulfill the letter of the law regarding
infrastructure maintenance and, at the same time, maintain safety in the organization
and operation of rail transport, planned interruptions of railway traffic are held. For
the activities of the transport process to proceed safely and undisturbed (smoothly), it is
necessary to interrupt a part of the infrastructure for a certain period. That means that there
will be restrictions, which, to a lesser or greater extent, manifest themselves in the delay of
passenger and freight transport [
8
]. Interrupting railway traffic is a method of transport and
operational use of transport road equipment requiring the adoption of special technological
and technical measures, during which there is a restriction on the operation of the track
and possibly also on the restriction of the operation of rail transport [
9
]. The interruption
of railway traffic is carried out by the railway operator as part of regular maintenance,
repair, or reconstruction of the railway transport route, safety equipment, traction line, or
preservation of a clear crossing. All this is to maintain the safety of train operations. The
interruption of railway traffic is carried out due to modernization or reconstruction or due
to repair or maintenance, and it must be planned in such a way that the negative impacts on
railway transport are as small as possible [
10
]. Therefore, it is necessary to pay attention to
the proper preparation and organization of rail traffic interruption and to use the necessary
technologies or applications for this [
11
]. During repairs, reconstruction, or construction of
new tracks, the normal operation of railway or station tracks, switches, and fixed electric
traction equipment may be interrupted, or the safety equipment may be completely or
partially switched off. The interaction between pantographs and catenaries in ensuring the
uninterrupted supply of electricity to trains is described in the papers [12–14].
This paper deals with the analysis and evaluation of the processes that are carried out
during the planned interruption or limitation of railway traffic. The aim of this research is to
propose a new methodical procedure for evaluating variants of work organization during
the interruption of railway traffic, considering the technical, cost, and safety aspects based
on knowledge of the processes of the affected railway operation during the infrastructure
interruption. The proposed methodological procedure is verified using the example of the
infrastructure of the Czech infrastructure manager, which is currently the Správa železnic.
The proposal uses four types of methods that relate to the planned interruption of railway
traffic. The methodology also focuses on the determination of technological procedures
and safety in the implementation of the interruption of railway traffic. The ambition of
the proposed solution is to expand the hitherto applied approaches to the solution of
the mentioned issue and provide a global view to all actors implementing rail transport,
i.e., to the managers of the railway infrastructure and operators, especially in passenger
transport. The goal is to determine, in an objective manner, the most advantageous option
for interrupting railway operations during maintenance. The application part of this
research is carried out on two interrupted lines according to the established alternative
timetable.
2. Literature Overview
The rail industry is currently investigating viable measures to strengthen the track
and reduce the need for frequent maintenance. These remedial measures should not
only be cost-effective but should also be consistent with the sustainability of the railway

Infrastructures 2024,9, 119 3 of 32
infrastructure, considering growing environmental concerns. The rail system is undeniably
vital for the transport of passengers and goods along the main rail corridors. To meet the
growing demand for freight and public transport, the railway industry is constantly using
advanced technologies to model infrastructure capacity [
15
]. This led to the development of
faster passenger trains and increased capacity for freight trains. Increased train speed and
higher tonnage in recent years have escalated the deterioration of the railway infrastructure.
As a result, frequent maintenance or even reconstruction became necessary [16].
The issue of the interruption of railway traffic is very extensive, from planning through
the correct process to the economic and technological consequences. The authors of [
17
]
describe the distribution, technology, and specific examples of the interruption of railway
traffic on railway lines in the Czech Republic. The authors solve the problem of optimizing
the technology and organization of the interruption of railway traffic and the consequences
for passengers. Passenger transfers are very problematic (at stations from/to connecting
trains). General transportation costs are rising. A complication is also the occurrence of
several parallel interruptions of railway traffic in one specific region (for example, two
railway lines next to each other). The implementation of freight transport is also very
important because the diversion of trains is not always possible.
Increasing supply in railway networks comes at the cost of an increased need for
infrastructure maintenance. It also means adjusting the schedule due to the long mainte-
nance or property of the building. In the research of [
18
], the train timetable adjustment
problem (TTAP) was solved for a given station and free track, which led to an alterna-
tive timetable that minimized the deviation from the original timetable. To solve TTAP,
the authors propose a mixed-integer linear programming (MILP) model and apply re-
timing, reordering, truncation, and cancelation to generate alternative timetables. The
model presents an extended periodic event scheduling problem (PESP) formulation and
introduces new constraints for the cancelation and rescheduling of train lines, while short
detours are applied in the preprocessing step. In addition, with some modifications, it can
be used for interrupted management. Operators and infrastructure managers could use it
to automatically generate optimal alternative timetables at a macroscopic level in case of
maintenance or construction work, thus coordinating transport for the entire network.
The author of [
19
] presented a survey on possible maintenance activities, associated
planning problems, and mathematical models developed for these problems. Planning
infrastructure maintenance activities is important at all levels of planning—strategic, tac-
tical, and operational. Depending on the time of planning, assets can be categorized as
preventive or corrective. The author focuses on preventive measures, which are defined as
maintenance that can be planned long in advance, such as the renewal and replacement of
existing tracks. The author also distinguished two types of maintenance: the main ones,
which cause conflicts with planned train routes, and smaller ones that do not interfere with
train operation. Additionally, a train route involves the infrastructure capacity required to
run a train between two locations during a given period [20].
Maintenance can be scheduled for a different time of day or even on other days.
In another paper [
21
], these cases were divided into three main categories: overnight
asset component maintenance, weekend asset component maintenance, and daytime asset
component maintenance. From a traffic point of view, night maintenance is the most
desirable because it would cause the least disturbance to the operation or not disturb the
operation at all. However, night maintenance is often not favorable for employees, or
the given time is insufficient. Longer maintenance will obviously interfere with traffic
during the day. Examples of such ownership are renovation works on a station platform
that can cause the occupation of adjacent tracks for up to several weeks or the repair
of signals along a track between two stations lasting a full working day. As the author
considers major maintenance, adjustments to the timetable are necessary. Three approaches
to solving the major maintenance problem are distinguished: (a) planning maintenance
windows independently of the timetable, which can also be considered a strategic problem;

Infrastructures 2024,9, 119 4 of 32
(b) adjusting timetables for a given asset component maintenance; and (c) planning train
traffic and simultaneously monitoring the maintenance of the asset component.
The authors of [
22
] assessed and dimensioned the maintenance windows before
creating a timetable for the interruption of railway traffic. Providing a certain pattern of
maintenance windows without trains would have an impact on overall maintenance costs
and would also affect subsequent timetable development. The authors tried to distribute
the departures evenly, but due to predetermined maintenance intervals, the model had to
cancel train routes, adjust event times (retiming), or extend journey times. A cost model
was compiled to establish dimensions for the time windows and assess their resulting
maintenance costs as well as passenger and freight transport costs. In the paper of [
23
],
the authors focused on the interruption of railway traffic to the existing timetable by
adjusting train traffic and interruption simultaneously. For this purpose, they proposed an
expert rule-based local search heuristic that uses the Problem Search Space approach. As a
benchmark, they simulated the practice of manual planning. Their heuristics reduced total
and maximum train delays by 17–34%. No comparison with the optimal solution is given.
In the case of conventional railway lines, when breakdowns occur, dispatchers have the
difficult task of quickly finding feasible rescheduling solutions to restore normal conditions
as soon as possible. Such management of disturbances in railway passenger transport
was dealt with by [
24
]. The authors of [
25
] propose a model system for railway system
management that combines a microscopic simulation model with a matching tool capable
of considering passenger flows on the network. An application on a real regional track
in Campania (Italy) shows the benefits of the proposed approach for performing offline
analyses of intervention solutions and helping dispatchers make decisions during critical
events to improve service quality. The authors of [
26
] present a model that optimizes the
production schedule for both trains and preventive maintenance. Scheduled maintenance
activities cannot be canceled but can be moved within pre-defined time windows. Trains
can be shifted in time, diverted to other parts of the geography, or even canceled. The
goal of optimization is to find the best possible traffic flow, given a fixed set of planned
maintenance activities. The authors of [
27
–
29
] researched the modeling of train routes and
the modification of timetables for given maintenance. From the user’s point of view, one
of the main strengths of rail transport systems is reliability, that is, the ability to respect
timetables and travel times. However, interruptions to scheduled services can occur for
several reasons (stochastic fluctuations in travel demand, infrastructure damage, convoy
breakdowns, etc.), causing a significant reduction in service levels. One of the objectives of
the railway network operator is, therefore, to minimize the duration of such interruptions
and their negative effects. This issue, from the point of view of passenger satisfaction, was
dealt with by [30–33].
3. Theoretical Backgrounds
In the EU, in the vertically separated model of the railway market, the railway is
usually owned by the state, which is most often represented by the Ministry of Transport.
The owner of the railway is obliged to permanently maintain the railway in operable
condition, to restore the operation of the railway after an accident or after an extraordinary
event, and to take care of the maintenance and development of the railway in accordance
with the safety and flow of traffic. The duties of the railway infrastructure manager (IM)
primarily include the fair and non-discriminatory allocation of railway infrastructure
capacity to licensed railway undertakings [
34
]. In cases of operational emergencies, the
infrastructure manager is obliged to find out the cause of the accident or extraordinary
event on the track and report it to the investigating body. In the research, the IM in the
Czech Republic was selected, which is the entity Správa železnic. The Czech infrastructure
manager issues and constantly updates the internal regulations by which the employees
are guided both during normal operation and, above all, during various emergencies to
which the interruption of railway traffic belongs. These regulations are also binding for
operators that operate rail transport on railways, as well as foreign legal entities working

Infrastructures 2024,9, 119 5 of 32
on railway facilities. The interruption of railway traffic on national and regional railways is
supported by Act No. 266/1994 Coll. on Railways [
6
], and its organization is dealt with by
internal regulation D7/2 [
35
]. It is also necessary to follow the regulations on the traffic and
signaling system D1 [
36
], the regulation on simplified traffic control D3 [
37
], the regulation
on traffic control on tracks equipped with radio blocks D4 [
38
], the regulation on works
on railway superstructure S3/1 [
39
], and, last but not least, safety and health protection
at work, which are addressed by regulation Bp1 [
40
]. There are 9349 km of railway lines
in the Czech Republic, of which 7279 km are single-track, 2070 km are double-track and
multi-track, and 3258 km are electrified lines of alternating current and one-way traction
systems. One hundred twenty-six operators operate rail transport on these lines [41]. The
number of train paths in the timetables in 2022 and 2023 by category in the Czech Republic
is shown in Table 1. The recalculation of allocated train paths per 100 km of lines, which on
one of the densest networks in the EU reaches an average of 176, is supplemented.
Table 1. Number of train paths in timetables in 2022 and 2023 (authors, according to [41]).
Indicator 2022 2023
Regional trains (Reg) 8842 10,574
Fast trains (F) 1098 1473
Higher quality trains (EC, EN, Ex, IC, LE, SC, Railjet) 264 347
Freight express (Fex) 471 703
Freight running trains (Fr) 766 899
Freight commuter trains (Fc) 1278 926
Locomotive trains (Loc) 626 557
The number of allocated train routes on the network 15,479 17,560
The length of the tracks of the Czech infrastructure
manager network 9358 9355
Transport performance in train kilometers is affected by the interruption of railway
traffic. During the continuous interruption of railway traffic due to the diversion routes,
transport performance is increased in railway freight transport and, in some cases, also in
railway passenger transport. In railway passenger transport, there may be a decrease in
transport performance if alternative bus transport is used instead of a train on the railway
transport route. Figure 1shows an overview of the transport performance of operators in
passenger and freight transport on the railway network in the Czech Republic in the years
2019–2023, which is expressed in millions of train kilometers.
Infrastructures 2024, 9, 119 6 of 34
Figure 1. Performance of operators on the Czech infrastructure manager network in 2019–2023 in
millions of train kilometers (authors, according to [41]).
Table 2 shows selected indicators associated with the interruption of railway
operations in the Czech Republic and the number of repaired kilometers, tracks, switches,
and other components for the years 2022 and 2023 that are necessary to ensure operability.
Based on the authors’ calculation, maintenance and, therefore, closures affected an
average of 25% of the length of the railway network per year (considering that some
maintenance activities were carried out simultaneously on the same section of
infrastructure).
Table 2. Selected activities related to railway traffic interruption in the period 2022–2023 (authors,
according to [41]).
Indicator Measureme
nt Unit
Quantity
2022 2023
Adjustment of the geometric position of switches pcs 717 1294
Cleaning—switches pcs 137 205
Routine inspection and welding—switches pcs 305 359
Exchange of sleepers pcs 172,121 315,446
Adjusting the geometric position of the tracks km 1256 1658
Cleaning—tracks km 82 206
Routine inspection and welding—rails km 221 662
Rail replacement km 293 512
According to [42,43], there are two types of such interruptions within the planned
interruption of railway traffic: planned interruption of railway traffic (as part of at least a
weekly plan) and unplanned interruption of railway traffic (not included in the weekly
plan). The interruption of railway traffic is carried out on different timelines. Operative
interruption of railway traffic takes place within a predetermined time range, number,
and duration of interruption of the traffic. Operative interruption of traffic can only be
used in exceptional cases. Infrastructure interruptions take place in different timelines.
According to the duration of the infrastructure interruption and the time in which they
take place, infrastructure interruptions are divided into day, night, and continuous. Table
3 shows the types of infrastructure interruptions according to their duration and the time
in which they take place.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
2019 2020 2021 2022 2023
Transport performance (mil. train
kilometres)
Year
Total Passenger transport Freight transport
Figure 1. Performance of operators on the Czech infrastructure manager network in 2019–2023 in
millions of train kilometers (authors, according to [41]).

Infrastructures 2024,9, 119 6 of 32
Table 2shows selected indicators associated with the interruption of railway operations
in the Czech Republic and the number of repaired kilometers, tracks, switches, and other
components for the years 2022 and 2023 that are necessary to ensure operability. Based on
the authors’ calculation, maintenance and, therefore, closures affected an average of 25% of
the length of the railway network per year (considering that some maintenance activities
were carried out simultaneously on the same section of infrastructure).
Table 2. Selected activities related to railway traffic interruption in the period 2022–2023 (authors,
according to [41]).
Indicator Measurement
Unit
Quantity
2022 2023
Adjustment of the geometric position of switches
pcs 717 1294
Cleaning—switches pcs 137 205
Routine inspection and welding—switches pcs 305 359
Exchange of sleepers pcs 172,121 315,446
Adjusting the geometric position of the tracks km 1256 1658
Cleaning—tracks km 82 206
Routine inspection and welding—rails km 221 662
Rail replacement km 293 512
According to [
42
,
43
], there are two types of such interruptions within the planned
interruption of railway traffic: planned interruption of railway traffic (as part of at least
a weekly plan) and unplanned interruption of railway traffic (not included in the weekly
plan). The interruption of railway traffic is carried out on different timelines. Operative
interruption of railway traffic takes place within a predetermined time range, number, and
duration of interruption of the traffic. Operative interruption of traffic can only be used in
exceptional cases. Infrastructure interruptions take place in different timelines. According
to the duration of the infrastructure interruption and the time in which they take place,
infrastructure interruptions are divided into day, night, and continuous. Table 3shows the
types of infrastructure interruptions according to their duration and the time in which they
take place.
Table 3. Types of railway infrastructure interruptions.
Type of Interruption of Railway Traffic
According to its duration
Per day—day of infrastructure interruption
Per night (6.00 P.M.–6.00 A.M.)
Continuously—continuous mode, which exceeds the parameters
of night infrastructure interruption
According to the range of
interrupted devices
Complete interruption of service (alternative bus transport or
diversion required)
Partial restriction of the railway traffic
Railway operations may be interrupted due to the maintenance of the track, traction
line, or safety equipment. Considering the slope ratios and the highest permitted speed in
the given section, it is possible to cross the so-called road by driving with the pantographs
retracted. If the slope conditions are not favorable, the operator must implement measures.
One of them is that it will replace dependent traction-drive vehicles with independent
traction-drive vehicles. With this measure, however, it depends on the number of trains
for which the compensation should take place and whether the operator is able to make
the compensation in such a quantity [
44
]. Within railway stations, operations may be
interrupted in the entire station or only in some of its parts. It is possible to interrupt
operation on individual traffic tracks or a group of traffic tracks. An example of such an

Infrastructures 2024,9, 119 7 of 32
interruption is shown in Figure 2. In these cases, it is possible to operate railway traffic on
the remaining traffic tracks.
Infrastructures 2024, 9, 119 7 of 34
Table 3. Types of railway infrastructure interruptions.
Type of Interruption of Railway Traffic
According to its duration
Per day—day of infrastructure interruption
Per night (6.00 P.M.–6.00 A.M.)
Continuously—continuous mode, which exceeds the parameters of night
infrastructure interruption
According to the range of
interrupted devices
Complete interruption of service (alternative bus transport or diversion required)
Partial restriction of the railway traffic
Railway operations may be interrupted due to the maintenance of the track, traction
line, or safety equipment. Considering the slope ratios and the highest permied speed in
the given section, it is possible to cross the so-called road by driving with the pantographs
retracted. If the slope conditions are not favorable, the operator must implement
measures. One of them is that it will replace dependent traction-drive vehicles with
independent traction-drive vehicles. With this measure, however, it depends on the
number of trains for which the compensation should take place and whether the operator
is able to make the compensation in such a quantity [44]. Within railway stations,
operations may be interrupted in the entire station or only in some of its parts. It is possible
to interrupt operation on individual traffic tracks or a group of traffic tracks. An example
of such an interruption is shown in Figure 2. In these cases, it is possible to operate railway
traffic on the remaining traffic tracks.
Figure 2. Example of interruption of one transport track and a group of station transport tracks [45].
Another interruption in the station may be the switch, which is shown in Figure 3.
Maintenance work in these parts of the station is not directly concerned with the complete
interruption of the station tracks. But it is always related to their partial limitations and
use. It is not possible to carry out departures or arrivals of trains in all directions, and in
the case of an interruption at the switch, it is not possible to carry out the circulation of
sets by locomotives.
Figure 3. Interruption of the traffic of the station switch [45].
In the case of multi-track sections, the rule is to maintain single-track operation. To
maintain the flow of rail traffic, Figure 4 shows the interruption of the track on a single-
track line and a double-track line.
Figure 2. Example of interruption of one transport track and a group of station transport tracks [
45
].
Another interruption in the station may be the switch, which is shown in Figure 3.
Maintenance work in these parts of the station is not directly concerned with the complete
interruption of the station tracks. But it is always related to their partial limitations and use.
It is not possible to carry out departures or arrivals of trains in all directions, and in the
case of an interruption at the switch, it is not possible to carry out the circulation of sets by
locomotives.
Infrastructures 2024, 9, 119 7 of 34
Table 3. Types of railway infrastructure interruptions.
Type of Interruption of Railway Traffic
According to its duration
Per day—day of infrastructure interruption
Per night (6.00 P.M.–6.00 A.M.)
Continuously—continuous mode, which exceeds the parameters of night
infrastructure interruption
According to the range of
interrupted devices
Complete interruption of service (alternative bus transport or diversion required)
Partial restriction of the railway traffic
Railway operations may be interrupted due to the maintenance of the track, traction
line, or safety equipment. Considering the slope ratios and the highest permied speed in
the given section, it is possible to cross the so-called road by driving with the pantographs
retracted. If the slope conditions are not favorable, the operator must implement
measures. One of them is that it will replace dependent traction-drive vehicles with
independent traction-drive vehicles. With this measure, however, it depends on the
number of trains for which the compensation should take place and whether the operator
is able to make the compensation in such a quantity [44]. Within railway stations,
operations may be interrupted in the entire station or only in some of its parts. It is possible
to interrupt operation on individual traffic tracks or a group of traffic tracks. An example
of such an interruption is shown in Figure 2. In these cases, it is possible to operate railway
traffic on the remaining traffic tracks.
Figure 2. Example of interruption of one transport track and a group of station transport tracks [45].
Another interruption in the station may be the switch, which is shown in Figure 3.
Maintenance work in these parts of the station is not directly concerned with the complete
interruption of the station tracks. But it is always related to their partial limitations and
use. It is not possible to carry out departures or arrivals of trains in all directions, and in
the case of an interruption at the switch, it is not possible to carry out the circulation of
sets by locomotives.
Figure 3. Interruption of the traffic of the station switch [45].
In the case of multi-track sections, the rule is to maintain single-track operation. To
maintain the flow of rail traffic, Figure 4 shows the interruption of the track on a single-
track line and a double-track line.
Figure 3. Interruption of the traffic of the station switch [45].
In the case of multi-track sections, the rule is to maintain single-track operation. To
maintain the flow of rail traffic, Figure 4shows the interruption of the track on a single-track
line and a double-track line.
Infrastructures 2024, 9, 119 8 of 34
Figure 4. Interruption of track on single-track and double-track lines [45].
Such an interruption of traffic on a single-track line is classified as an interruption
with a complete stop of railway traffic. However, there are sections where there is a line
without detour that can be used for running trains as part of the traffic measure. This
situation is shown in Figure 5.
Figure 5. Interrupted track on a single-track line without the possibility of a detour route [45].
However, there are sections where there is a detour route that can be used for running
trains as part of the traffic measure. The track with a detour route is shown in Figure 6.
Figure 6. An example of a single-track line with an interrupted track with a detour route [45].
3.1. Planned Railway Infrastructure Interruption
Before the start of the planned interruption of railway traffic, an application must be
submied to the locally relevant customer for the interruption of railway traffic. The
request is submied by the applicant for the railway infrastructure interruption.
Professional units responsible for the safe operation of parts of the railway infrastructure
will draw up a plan for the railway infrastructure interruption for repair and
modernization actions according to the current technical status of a specific infrastructure
device. Maintenance works have a set maintenance schedule as a basis, which considers,
e.g., vegetative rest. Such documents can also be simulations, for example, for modeling
the throughput performance of railway traffic on a track where maintenance is taking
place [46]. The railway undertaking operating passenger transport shall ensure that in the
railway stations affected by the interruption of traffic, passengers are informed about
alternative bus transport, train queues, and the location and marking of stations intended
for boarding or output passengers [47].
There is much research on planned infrastructure interruptions that addresses the
issue through operational, tactical, strategic, and simulation models. As part of our
research, we focused on the intersection between tactical and strategic models (area
Figure 4. Interruption of track on single-track and double-track lines [45].
Such an interruption of traffic on a single-track line is classified as an interruption with
a complete stop of railway traffic. However, there are sections where there is a line without
detour that can be used for running trains as part of the traffic measure. This situation is
shown in Figure 5.
However, there are sections where there is a detour route that can be used for running
trains as part of the traffic measure. The track with a detour route is shown in Figure 6.

Infrastructures 2024,9, 119 8 of 32
Infrastructures 2024, 9, 119 8 of 34
Figure 4. Interruption of track on single-track and double-track lines [45].
Such an interruption of traffic on a single-track line is classified as an interruption
with a complete stop of railway traffic. However, there are sections where there is a line
without detour that can be used for running trains as part of the traffic measure. This
situation is shown in Figure 5.
Figure 5. Interrupted track on a single-track line without the possibility of a detour route [45].
However, there are sections where there is a detour route that can be used for running
trains as part of the traffic measure. The track with a detour route is shown in Figure 6.
Figure 6. An example of a single-track line with an interrupted track with a detour route [45].
3.1. Planned Railway Infrastructure Interruption
Before the start of the planned interruption of railway traffic, an application must be
submied to the locally relevant customer for the interruption of railway traffic. The
request is submied by the applicant for the railway infrastructure interruption.
Professional units responsible for the safe operation of parts of the railway infrastructure
will draw up a plan for the railway infrastructure interruption for repair and
modernization actions according to the current technical status of a specific infrastructure
device. Maintenance works have a set maintenance schedule as a basis, which considers,
e.g., vegetative rest. Such documents can also be simulations, for example, for modeling
the throughput performance of railway traffic on a track where maintenance is taking
place [46]. The railway undertaking operating passenger transport shall ensure that in the
railway stations affected by the interruption of traffic, passengers are informed about
alternative bus transport, train queues, and the location and marking of stations intended
for boarding or output passengers [47].
There is much research on planned infrastructure interruptions that addresses the
issue through operational, tactical, strategic, and simulation models. As part of our
research, we focused on the intersection between tactical and strategic models (area
Figure 5. Interrupted track on a single-track line without the possibility of a detour route [45].
Infrastructures 2024, 9, 119 8 of 34
Figure 4. Interruption of track on single-track and double-track lines [45].
Such an interruption of traffic on a single-track line is classified as an interruption
with a complete stop of railway traffic. However, there are sections where there is a line
without detour that can be used for running trains as part of the traffic measure. This
situation is shown in Figure 5.
Figure 5. Interrupted track on a single-track line without the possibility of a detour route [45].
However, there are sections where there is a detour route that can be used for running
trains as part of the traffic measure. The track with a detour route is shown in Figure 6.
Figure 6. An example of a single-track line with an interrupted track with a detour route [45].
3.1. Planned Railway Infrastructure Interruption
Before the start of the planned interruption of railway traffic, an application must be
submied to the locally relevant customer for the interruption of railway traffic. The
request is submied by the applicant for the railway infrastructure interruption.
Professional units responsible for the safe operation of parts of the railway infrastructure
will draw up a plan for the railway infrastructure interruption for repair and
modernization actions according to the current technical status of a specific infrastructure
device. Maintenance works have a set maintenance schedule as a basis, which considers,
e.g., vegetative rest. Such documents can also be simulations, for example, for modeling
the throughput performance of railway traffic on a track where maintenance is taking
place [46]. The railway undertaking operating passenger transport shall ensure that in the
railway stations affected by the interruption of traffic, passengers are informed about
alternative bus transport, train queues, and the location and marking of stations intended
for boarding or output passengers [47].
There is much research on planned infrastructure interruptions that addresses the
issue through operational, tactical, strategic, and simulation models. As part of our
research, we focused on the intersection between tactical and strategic models (area
Figure 6. An example of a single-track line with an interrupted track with a detour route [45].
3.1. Planned Railway Infrastructure Interruption
Before the start of the planned interruption of railway traffic, an application must be
submitted to the locally relevant customer for the interruption of railway traffic. The request
is submitted by the applicant for the railway infrastructure interruption. Professional units
responsible for the safe operation of parts of the railway infrastructure will draw up a plan
for the railway infrastructure interruption for repair and modernization actions according
to the current technical status of a specific infrastructure device. Maintenance works have a
set maintenance schedule as a basis, which considers, e.g., vegetative rest. Such documents
can also be simulations, for example, for modeling the throughput performance of railway
traffic on a track where maintenance is taking place [
46
]. The railway undertaking operating
passenger transport shall ensure that in the railway stations affected by the interruption
of traffic, passengers are informed about alternative bus transport, train queues, and the
location and marking of stations intended for boarding or output passengers [47].
There is much research on planned infrastructure interruptions that addresses the
issue through operational, tactical, strategic, and simulation models. As part of our research,
we focused on the intersection between tactical and strategic models (area marked in red),
which includes a plan of operation from the point of view of cost, technology, and safety.
Figure 7shows the models of planned infrastructure interruption.
Infrastructures 2024, 9, 119 9 of 34
marked in red), which includes a plan of operation from the point of view of cost,
technology, and safety. Figure 7 shows the models of planned infrastructure interruption.
Figure 7. Types of models during infrastructure interruption.
The practical application of the proposed methodology will be demonstrated in the
case of a planned interruption of traffic on two selected interrupted lines: České
Budějovice–České Velenice (number 705) and České Budějovice–Horní Dvořiště
(number 706).
The planned suspension of operations on the České Budějovice–České Velenice line
(705) was intended for repair and maintenance work on the České Velenice–České
Budějovice track section. The maintenance was divided into five stages, A–E (Table 4),
which took place every two working days. In each stage, the interstation section between
two neighboring stations was interrupted by track, and at the same time, the voltage was
interrupted in the same section with a continuation up to the České Velenice railway
station. As part of the operation of railway transport on both lines, all passenger trains
were replaced by alternative bus transport for the duration of the infrastructure
interruption, and diversion routes were not used. Freight trains were waiting for the end
of the infrastructure interruption, and, subsequently, after the resumption of operations
on these lines, passenger and freight trains were again put into normal operation. As this
was a planned infrastructure interruption, freight trains did not use diversion routes and
waited in stations. The locations of railway lines for the infrastructure interruption on lines
705 and 706 are shown in Figure 8, and the locations of railway lines for the stages of
infrastructure interruption are shown in Figure 9.
Figure 7. Types of models during infrastructure interruption.

Infrastructures 2024,9, 119 9 of 32
The practical application of the proposed methodology will be demonstrated in the
case of a planned interruption of traffic on two selected interrupted lines: ˇ
CeskéBudˇejovice–
ˇ
CeskéVelenice (number 705) and ˇ
CeskéBudˇejovice–HorníDvoˇrištˇe (number 706).
The planned suspension of operations on the ˇ
CeskéBudˇejovice– ˇ
CeskéVelenice line
(705) was intended for repair and maintenance work on the ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice
track section. The maintenance was divided into five stages, A–E (Table 4), which took place
every two working days. In each stage, the interstation section between two neighboring
stations was interrupted by track, and at the same time, the voltage was interrupted in the
same section with a continuation up to the ˇ
CeskéVelenice railway station. As part of the op-
eration of railway transport on both lines, all passenger trains were replaced by alternative
bus transport for the duration of the infrastructure interruption, and diversion routes were
not used. Freight trains were waiting for the end of the infrastructure interruption, and,
subsequently, after the resumption of operations on these lines, passenger and freight trains
were again put into normal operation. As this was a planned infrastructure interruption,
freight trains did not use diversion routes and waited in stations. The locations of railway
lines for the infrastructure interruption on lines 705 and 706 are shown in Figure 8, and the
locations of railway lines for the stages of infrastructure interruption are shown in Figure 9.
Infrastructures 2024, 9, 119 10 of 34
Figure 8. Locations of railway lines 705 and 706 within infrastructure interruption in the Czech
Republic (authors, according to [48]).
Figure 9. Railway lines with the stages of infrastructure interruption.
Table 4. Stages of maintenance activities on the České Budějovice–České Velenice line (authors,
according to [49]).
Stage Description
Stage A
Determined range of days (date), which was always from 7:30 A.M. to 3:35 P.M.
The 13 km long České Velenice–Nové Hrady (Jakule) track section, which was
interrupted by tracks.
Figure 8. Locations of railway lines 705 and 706 within infrastructure interruption in the Czech
Republic (authors, according to [48]).

Infrastructures 2024,9, 119 10 of 32
Infrastructures 2024, 9, 119 10 of 34
Figure 8. Locations of railway lines 705 and 706 within infrastructure interruption in the Czech
Republic (authors, according to [48]).
Figure 9. Railway lines with the stages of infrastructure interruption.
Table 4. Stages of maintenance activities on the České Budějovice–České Velenice line (authors,
according to [49]).
Stage Description
Stage A
Determined range of days (date), which was always from 7:30 A.M. to 3:35 P.M.
The 13 km long České Velenice–Nové Hrady (Jakule) track section, which was
interrupted by tracks.
Figure 9. Railway lines with the stages of infrastructure interruption.
Table 4. Stages of maintenance activities on the ˇ
CeskéBudˇejovice– ˇ
CeskéVelenice line (authors,
according to [49]).
Stage Description
Stage A
Determined range of days (date), which was always from 7:30 A.M. to 3:35 P.M.
The 13 km long ˇ
CeskéVelenice–NovéHrady (Jakule) track section, which was interrupted by tracks.
The distance for alternative bus transport from the ˇ
CeskéVelenice station to the NovéHrady station via the Vyšné
railway stop, with the route being determined by the infrastructure interruption traffic order, was 14.7 km.
During maintenance, the train consists of two Regio Panter electric units. In the NovéHrady (Jakule)– ˇ
CeskéVelenice
and ˇ
CeskéVelenice–NovéHrady (Jakule) track section, 8 regional trains were replaced by alternative bus transport.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 3:45 P.M.
Stage B
Determined range of days (date), which was always from 7:20 A.M. to 3:30 P.M.
The NovéHrady (Jakule)–Jílovice track section that has been interrupted by tracks.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 3:40 P.M.
Stage C
Determined range of days (date), which was always from 7:10 A.M. to 3:20 P.M.
The Jílovice–Borovany track section was interrupted from the track.
For stages B and C, 8 regional trains in the NovéHrady (Jakule)–Jílovice–Borovany and Borovany–Jílovice–NovéHrady
(Jakule) track section were replaced by alternative bus transport. It is a 16.4 km long track section. The distance for
alternative bus transport from NovéHrady station to Borovany station via Petˇríkov railway stop, Jílovice railway stop,
Jílovice station, and Hlubokáu Borovan railway stop, with the route being determined by infrastructure interruption
traffic order, was 28.1 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 3:30 P.M.
Stage D
Determined range of days (date), which was always from 7:15 A.M. to 2:10 P.M.
The Borovany–NováVes track section was interrupted.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 2:20 P.M.
Stage E
Determined range of days (date), which was always from 7:20 A.M. to 2:00 P.M.
The NováVes– ˇ
CeskéBudˇejovice track section was interrupted.
For stages D and E, 6 regional trains in the ˇ
CeskéBudˇejovice–NovéHrady–Borovany and Borovany–Nové
Hrady– ˇ
CeskéBudˇejovice track section were replaced by alternative bus transport. It is a track section 19.9 km long. The
distance for alternative bus transport from Borovany station to ˇ
CeskéBudˇejovice station going through the railway
stops Radostice and Trocnov, station NováVes, and the railway stop StaréHodˇejovice, with the route being determined
by the infrastructure interruption traffic order, was 24.9 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 2:10 P.M.

Infrastructures 2024,9, 119 11 of 32
The ˇ
CeskéBudˇejovice–HorníDvoˇrištˇe line (706) is a single-track electrified line in-
cluded in the TEN-T system. Following the European division, the routes of railway
corridors were established in the Czech Republic, which is an IV. transit corridor [
50
],
and this is the national designation of this corridor, which is the main long-distance
railway connecting Stockholm–Dresden–Deˇcín–Prague–Tábor–Veselíand Lužnicí–ˇ
Ceské
Budˇejovice–HorníDvoˇrištˇe–Linz–Salzburg–Ljubljana–Rijeka–Zagreb [
51
,
52
]. The planned
infrastructure interruption on this line was intended for repair and maintenance work in
the HorníDvoˇrištˇe track section of the state border in ˇ
CeskéBudˇejovice. Maintenance was
divided into six stages, A–F (Table 5), which always took place on working days.
Table 5. Stages of maintenance activities on the ˇ
CeskéBudˇejovice–HorníDvoˇrištˇe line (authors,
according to [49]).
Stage Description
Stage A
Determined range of days (date), which was always from 9:10 A.M. to 4:45 P.M.
The HorníDvoˇrištˇe–Rybník track section, including HorníDvoˇrištˇe station, was 7.3 km long.
The distance for alternative bus transport from HorníDvoˇrištˇe station to Rybník station, with the route being
determined by infrastructure interruption traffic order, was 8.4 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 4:55 P.M.
Stage B
Determined range of days (date), which was always from 9:00 A.M. to 4:25 P.M.
The Rybník–Kaplice track section, including the entire Omlenice station.
The distance for regional trains from Louˇcovice station to Kaplice station (Rybník–Lipno nad Vltavou line) is a railway
transport route that is 35.8 km; alternative bus transport was 44.6 km.
The distance for alternative bus transport of fast trains from the Rybník station to the Kaplice station is a railway
transport route that is 16.7 km; alternative bus transport was 20.9 km.
The distance for alternative bus transport of fast trains from the HorníDvoˇrištˇe station to the Kaplice station is a railway
transport route that is 24 km; alternative bus transport was 25 km.
Freight trains were waiting for the infrastructure interruption to end. Their running began at 4:35 P.M.
Stages C
and F
Determined range of days (date), which was always from 8:45 A.M. to 4:15 P.M.
The Kaplice–Holkov track section, including the entire Velešín station.
The distance for regional trains from the Kaplice station to the Holkov station is a railway transport route of 12.3 km,
while the alternative bus transport is 11.4 km
The distance for alternative bus transport of fast trains from the Omlenice station to the Kaplice station is a railway
transport route that is 6.6 km; alternative bus transport was 20.1 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 4:25 P.M.
Stage D
Determined range of days (date), which was always from 8:50 A.M. to 4:10 P.M.
The Holkov–Vˇcelnátrack section, including the entire station Kamenný Újezd.
The distance for regional trains from Holkov station to Vˇcelnástation is a railway transport route that is 12.8 km;
alternative bus transport was 11 km.
The distance for alternative bus transport of fast trains from HorníDvoˇrištˇe station to ˇ
CeskéBudˇejovice station is a
railway transport route that is 56.8 km; alternative bus transport was 51 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 4:20 P.M.
Stage E
Determined range of days (date), which was always from 8:55 A.M. to 4:00 P.M.
The Vˇcelná–ˇ
CeskéBudˇejovice track section with a length of 8.1 km.
The distance for regional trains from the Vˇcelnástation to the ˇ
CeskéBudˇejovice station is a railway transport route that
is 8.1 km; alternative bus transport was 8 km.
The distance for alternative bus transport of fast trains from HorníDvoˇrištˇe station to ˇ
CeskéBudˇejovice station is a
railway transport route that is 56.8 km; alternative bus transport was 51 km.
Freight trains were waiting for the infrastructure interruption to end. Their operation started at 4:10 P.M.
Stage F
Determined range of days (date), which was always from 8:45 A.M. to 4:15 P.M.
The train heading toward Velešín was interrupted, along with switch no. 12 in Kaplice station.
Freight trains were waiting for the infrastructure interruption to end. Their operation began at 4:25 P.M.

Infrastructures 2024,9, 119 12 of 32
3.2. Analysis of Costs for Activities Related to the Railway Infrastructure Interruption
The costs incurred by the Czech infrastructure manager in the years 2010–2019 to
ensure the operability of the railway as part of repairs and maintenance on the entire
network are shown in Figure 10 and are calculated per one kilometer of track.
Infrastructures 2024, 9, 119 13 of 34
Figure 10. Unit costs spent on the operability of the infrastructure of the Czech infrastructure
manager [EUR/km] (authors, according to [49]).
The highest-cost item is repair and maintenance work. Figure 11 shows the unit sales
for the sale of services converted to EUR 1/km. The line graph shows how much of the
total revenue is made from the use of the railway infrastructure for passenger and freight
transport and the allocated capacity converted to EUR 1/km.
Figure 11. Revenues from the sale of products and services of the Czech infrastructure manager
[EUR/km] (authors, according to [49]).
The total price for the use of a track by a train operated by the Czech infrastructure
manager depends on the length and parameters of the track traveled, the train parameters,
the basic price, and the application of the product factor and specific factors. The price is
determined by a calculation that is based on the actual scope of performance of the
operators and the train kilometers traveled in the given billing period on the railway
network of the Czech infrastructure manager.
3.3. Safety during the Interruption of Railway Traffic
Ensuring safe and smooth operation is a priority in the operation of railways and
railway transport. In the case of an emergency, the risk of injury or accident is higher. The
number of all accidents in the years 2013–2022, as well as injuries that occurred as part of
maintenance work during the interruption of traffic, is shown in Figure 12.
0
10
20
30
40
50
60
70
80
90
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Costs per 1 €/km
Year
0
5
10
15
20
25
30
35
40
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Revenues per 1 €/km
Year
Revenues Use of railway infrastructure
Figure 10. Unit costs spent on the operability of the infrastructure of the Czech infrastructure manager
[EUR/km] (authors, according to [49]).
The highest-cost item is repair and maintenance work. Figure 11 shows the unit sales
for the sale of services converted to EUR 1/km. The line graph shows how much of the
total revenue is made from the use of the railway infrastructure for passenger and freight
transport and the allocated capacity converted to EUR 1/km.
Infrastructures 2024, 9, 119 13 of 34
Figure 10. Unit costs spent on the operability of the infrastructure of the Czech infrastructure
manager [EUR/km] (authors, according to [49]).
The highest-cost item is repair and maintenance work. Figure 11 shows the unit sales
for the sale of services converted to EUR 1/km. The line graph shows how much of the
total revenue is made from the use of the railway infrastructure for passenger and freight
transport and the allocated capacity converted to EUR 1/km.
Figure 11. Revenues from the sale of products and services of the Czech infrastructure manager
[EUR/km] (authors, according to [49]).
The total price for the use of a track by a train operated by the Czech infrastructure
manager depends on the length and parameters of the track traveled, the train parameters,
the basic price, and the application of the product factor and specific factors. The price is
determined by a calculation that is based on the actual scope of performance of the
operators and the train kilometers traveled in the given billing period on the railway
network of the Czech infrastructure manager.
3.3. Safety during the Interruption of Railway Traffic
Ensuring safe and smooth operation is a priority in the operation of railways and
railway transport. In the case of an emergency, the risk of injury or accident is higher. The
number of all accidents in the years 2013–2022, as well as injuries that occurred as part of
maintenance work during the interruption of traffic, is shown in Figure 12.
0
10
20
30
40
50
60
70
80
90
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Costs per 1 €/km
Year
0
5
10
15
20
25
30
35
40
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Revenues per 1 €/km
Year
Revenues Use of railway infrastructure
Figure 11. Revenues from the sale of products and services of the Czech infrastructure manager
[EUR/km] (authors, according to [49]).
The total price for the use of a track by a train operated by the Czech infrastructure
manager depends on the length and parameters of the track traveled, the train parameters,
the basic price, and the application of the product factor and specific factors. The price
is determined by a calculation that is based on the actual scope of performance of the
operators and the train kilometers traveled in the given billing period on the railway
network of the Czech infrastructure manager.

Infrastructures 2024,9, 119 13 of 32
3.3. Safety during the Interruption of Railway Traffic
Ensuring safe and smooth operation is a priority in the operation of railways and
railway transport. In the case of an emergency, the risk of injury or accident is higher. The
number of all accidents in the years 2013–2022, as well as injuries that occurred as part of
maintenance work during the interruption of traffic, is shown in Figure 12.
Infrastructures 2024, 9, 119 14 of 34
Figure 12. The number of injuries to employees of the Czech infrastructure manager in 2013-2022.
(authors, according to [49]).
4. Methodology
The proposal for the methodology of the management of works during the
interruption of railway traffic is intended to evaluate variants of the organization of these
works, which considers the technical, cost, and safety aspects. Basic scientific methods of
induction, deduction, abstraction, concretization, classification, and visualization were
used. Qualitative and quantitative research, brainstorming, and consultations with
opponents from practice were carried out. A key step in the proposed procedures is the
use of procedures in the modeling of traffic processes, where simulation tools and
operational analysis tools can be used. It is about determining the optimal algorithm or
simulation model to facilitate the solution of procedures in cases of partial or complete
blocking of the designated route. The essence is in the use of a mathematical apparatus,
which has the task of analyzing the impact of interruptions, identifying affected train
paths, quickly rescheduling train paths in real time after traffic interruptions, optimizing
costs, and minimizing delays by adjusting timetables or routes. The models optimize the
planning of train paths in the timetable, including heuristic algorithms, data analysis, and
simulations, to minimize the impact of restrictions on rail traffic and ensure the safety and
quality of railway services.
There are many tools, methods, and mathematical models that can be used to
optimize railway operations during infrastructure interruption. The RailSys software 3.0
[53] is a planning system for railway transport, but at the same time, it provides a very
flexible use of integration and functionality to consider all requirements and needs. It is
suitable for infrastructure management, capacity management, timetable simulation,
operational simulation, and others. Models such as [54,55] also serve to optimize and
propose the train traffic diagram during emergency situations, such as infrastructure
interruption. The authors of [54] describe models for the optimization of railway
timetables and their applicability in practice. The authors of [55] describe a heuristic
approach to the integration of train timetable planning, platform planning, and
maintenance planning of the railway network. The authors of [56] describe a model for
determining the price for the allocation of railway infrastructure capacity in the Czech
Republic. There are still many more models for railway timetable optimization and
planning [57–62].
We can also think of a railway network as a directed graph with nodes and edges
with different weights, taking the nodes as branching railway stations and the edges as
inter-station sections. Such a network can include simple requests but also inputs from
advanced logistics systems. Connected transport operations are entering the system,
increasing the complexity of transport networks. More inputs equal a more demanding
possibility of predicting the occurrence of a fault [63]. This is addressed as a simulation
model exploring logistics networks. The output of the model is the determination of faults
in the given network and the recommendation of their solution. The model works with
0
100
200
300
400
500
600
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Number of injuries
Year
Total during the interruption
Figure 12. The number of injuries to employees of the Czech infrastructure manager in 2013–2022.
(authors, according to [49]).
4. Methodology
The proposal for the methodology of the management of works during the interrup-
tion of railway traffic is intended to evaluate variants of the organization of these works,
which considers the technical, cost, and safety aspects. Basic scientific methods of induction,
deduction, abstraction, concretization, classification, and visualization were used. Quali-
tative and quantitative research, brainstorming, and consultations with opponents from
practice were carried out. A key step in the proposed procedures is the use of procedures
in the modeling of traffic processes, where simulation tools and operational analysis tools
can be used. It is about determining the optimal algorithm or simulation model to facilitate
the solution of procedures in cases of partial or complete blocking of the designated route.
The essence is in the use of a mathematical apparatus, which has the task of analyzing the
impact of interruptions, identifying affected train paths, quickly rescheduling train paths in
real time after traffic interruptions, optimizing costs, and minimizing delays by adjusting
timetables or routes. The models optimize the planning of train paths in the timetable,
including heuristic algorithms, data analysis, and simulations, to minimize the impact of
restrictions on rail traffic and ensure the safety and quality of railway services.
There are many tools, methods, and mathematical models that can be used to optimize
railway operations during infrastructure interruption. The RailSys software 3.0 [
53
] is a
planning system for railway transport, but at the same time, it provides a very flexible
use of integration and functionality to consider all requirements and needs. It is suitable
for infrastructure management, capacity management, timetable simulation, operational
simulation, and others. Models such as [
54
,
55
] also serve to optimize and propose the
train traffic diagram during emergency situations, such as infrastructure interruption.
The authors of [
54
] describe models for the optimization of railway timetables and their
applicability in practice. The authors of [
55
] describe a heuristic approach to the integration
of train timetable planning, platform planning, and maintenance planning of the railway
network. The authors of [56] describe a model for determining the price for the allocation
of railway infrastructure capacity in the Czech Republic. There are still many more models
for railway timetable optimization and planning [57–62].
We can also think of a railway network as a directed graph with nodes and edges with
different weights, taking the nodes as branching railway stations and the edges as inter-
station sections. Such a network can include simple requests but also inputs from advanced
logistics systems. Connected transport operations are entering the system, increasing the

Infrastructures 2024,9, 119 14 of 32
complexity of transport networks. More inputs equal a more demanding possibility of
predicting the occurrence of a fault [
63
]. This is addressed as a simulation model exploring
logistics networks. The output of the model is the determination of faults in the given
network and the recommendation of their solution. The model works with three basic
scenarios and allows for changes in requirements: first, if there is an increased demand
during a certain period for a certain area; second, if there is an increased network-wide
demand during a period; and third, if there is a permanent change in demand to find
a new route with sufficient transport capacity. The creation of timetables is a complex
process based on the experience and expertise of their creators and, at present, the great
support of software tools. Creators face challenges to ensure that the constructed timetables
are sufficiently robust (durable) and the accuracy of operation is maintained despite high
demand and minimal capacity consumption.
The methodological procedure is verified using the example of the infrastructure of
the Czech infrastructure manager. Railway infrastructure interruption is governed by
internal regulations [
35
–
41
,
64
]. The methodology is established based on four types of
proposed methods related to the railway infrastructure interruption, the determination of
technological procedures for the interruption, and safety during the railway infrastructure
interruption (Figure 13) as a tool for better management of the railway infrastructure
interruption on the railway network. Subsequently, the individual procedures in the
methodology are characterized.
Quantitative research was focused on measuring and testing data from real railway in-
frastructure interruptions on the solved railway lines and transport performance in railway
transport. Tests of causal relationships between variables were performed, predictions were
made, and results were generalized to passengers, operators, and the infrastructure man-
ager. The literature review includes academic literature searches (peer-reviewed journal
articles only) conducted on the Scopus and Google Scholar platforms, as well as scholarly
article searches. The keyword combinations used to search the academic and grey literature
were as follows:
(A)
“railway interruption” OR “interruption” OR “railway operation” OR “response to
interruption”;
(B)
“maintenance” OR “maintenance of railway infrastructure” OR “repair of railway
infrastructure” OR “renewal” OR “strategy” OR “strategies”;
(C)
(“modernization” OR “modernization of railway infrastructure” OR “response to
modernization”;
(D)
“planned interruption of railway traffic” OR “interruption of railway traffic strategy”
OR “unplanned interruption of railway traffic”;
(E)
“railway infrastructure” OR “railway transport route” OR “railway line”;
(F)
“rail transport” OR “railway transport” OR “mobility”;
(G) “Impact” OR “consequences” OR “conduct” OR “travel” OR “perception” OR “traffic”.
The issue of railway infrastructure interruption is at a certain level in the academic
literature, but the methodology and management of railway traffic during the infrastructure
interruption are only a small scope of published research.
An important research procedure was the discussion of practitioners, where the
impacts of planned and unplanned railway infrastructure interruptions were determined.
The main brainstorming format was panel discussions with these experts, where it was
determined what needed to be solved from the perspective of operators, infrastructure
managers, and also passengers. Quantitative research was carried out using brainstorming
methods, the aim of which was to propose methods for the management methodology
during the railway infrastructure interruption. As part of the qualitative research step, we
investigated the opinions, behaviors, and experiences of railway transport experts. They
collected and analyzed data and findings in research papers. In this contribution, the results
and findings for the railway lines ˇ
CeskéBudˇejovice– ˇ
CeskéVelenice and ˇ
CeskéBudˇejovice–
HorníDvoˇrištˇe are used. A mixed-methods research methodology is used to confirm the
findings and explain any results obtained to verify that the results observed using both

Infrastructures 2024,9, 119 15 of 32
methods are complementary. Based on the mentioned methods, the authors proposed a
universal methodology for the railway operation management system during the planned
infrastructure interruption. There have been several useful scientific methods that are
general and universal but are particularly applicable to a given issue. The methodology
consists of several steps, which are shown in Figure 10.
Infrastructures 2024, 9, 119 16 of 34
management system during the planned infrastructure interruption. There have been
several useful scientific methods that are general and universal but are particularly
applicable to a given issue. The methodology consists of several steps, which are shown
in Figure 10.
Figure 13. Work management methodology during the railway infrastructure interruption.
Figure 13. Work management methodology during the railway infrastructure interruption.

Infrastructures 2024,9, 119 16 of 32
Defining the conditions and requirements of the planned interruption of traffic on the
infrastructure. This concerns both the infrastructure manager and the railway undertakings
(operators) and end customers (passengers, forwarders). The railway operator in passenger
transport will ensure that passengers are informed about alternative bus transport, train
queues, and the locations and marking of stations intended for boarding or disembarking
passengers at the railway stations affected by the interruption of traffic. The railway
operator in freight transport informs their customers about the restriction of loading and
unloading at the affected transport points and the interruption of railway tracks.
Define the individual stages of the planned infrastructure interruption. For each stage
of the planned infrastructure interruption, it is necessary to determine the range of days
and the time range when the planned interruption will be implemented, define the specific
sections that the planned interruption will affect within each stage, and determine the
distances for rail transport and substitute bus transport for the subsequent calculation of
prices within the methodology.
Submitting the work schedule during the planned interruption. The schedule of the
planned interruption of the railway traffic of temporarily limited capacity consists of four
levels of impacts on the time course of planning (low impact, medium impact, high impact,
and significant impact). It is a system of coordination and consultation over the course of
planning.
Knowledge of methods related to planned infrastructure interruption. These methods
include the price for the use of the infrastructure, the price for alternative bus transport,
the assessment of risks by the infrastructure manager, the determination of technological
work procedures, and safety. In freight transport, it is necessary to determine diversion
routes or stations where trains will wait for the interruption to end.
The calculation of the price for the use of the infrastructure. This is determined based
on the established procedures of each railway infrastructure manager, which, in principle,
differ very little. In terms of the Czech infrastructure manager, it is determined according
to Formula (1), considering the track category, product factor, and specific factors.
The calculation of the price for alternative bus transport. The amount of this price is
determined by RU based on the product of the relevant unit prices, the transport services
performed, and the necessary waiting periods according to Formula (2). In case of using
alternative bus transport, the railway operator saves the price for the use of railway
infrastructure.
An evaluation of possible risks by the infrastructure manager and the calculation of
risk using the simple point method—three components (probability, consequence, and
evaluator weights) are evaluated according to Formula (3).
Determination of technological work procedures during the planned infrastructure
interruption. This is a technological procedure of work that is divided into three categories
and must be firmly established and observed regarding the timetable of the interruption of
traffic. The idea is to ensure that the work on the track is done safely and in the shortest
possible time.
Selection of a variant for the implementation of infrastructure interruption. In this step,
based on the several variants presented for the implementation of the planned infrastructure
interruption, the optimal variant will be selected. The decisive factor is the global view of
the optimization criterion, which is the minimization of costs caused by works during the
infrastructure interruption as the total costs of all actors, i.e., the manager of the railway
infrastructure and the affected operators.
Ensuring safety during the implementation of the planned infrastructure interrup-
tion. All persons who participate in the implementation of the works will, in the process,
implement the movement of railway vehicles and mechanisms along the track operated
by IM. Also, all employees who participate in the operation of the railway and railway
transport in connection with the implementation of maintenance. Safety must also be
ensured for passengers (all construction measures necessary for the safe exit and boarding
of passengers).

Infrastructures 2024,9, 119 17 of 32
4.1. Price for Using the Infrastructure by Train
To determine the price for the use of railway infrastructure, each IM has established
procedures that are very similar in principle. In terms of the Czech infrastructure manager,
a calculation formula is used [65,66]:
Ctrain =L×Z×K×Px×S1×S2(1)
where
Ctrain denotes the price for using the infrastructure by running a train.
L denotes the length of the train route.
Z denotes the basic price.
K denotes the track category coefficient (Table 4).
Pxdenotes the product factor (Table 5).
S1and S2denote specific factors (Tables 6and 7).
Table 6. Coefficient of line category K (authors, according to [64]).
Line Category Value K
1 1.15
2 1.12
3 1.00
4 0.88
5 0.71
Table 7. Product factor P (authors, according to [64]).
Product Factor Value P
P1—passenger transport 1.00
P2—unspecified freight transport 1.00
P3—freight transport within the collection and delivery system of individual wagon shipments 0.30
P4—combined freight transport 0.65
P5—freight transport—non-standard trains 2.00
The categorization of individual lines depends on the result of the evaluation of the
technical condition of the line, the type of security equipment, and the inclusion of the line
in the TEN-T network. The line category coefficients are shown in Table 6.
The product factor is a factor that considers market segmentation into services with
different price levels. Individual types of product factors are listed in Table 7.
The specific factor S
1
indicates the level of track wear depending on the total weight
of the train. These factors are listed in Table 8.
Table 8. Rate of track wear depending on the total gross weight of the train (authors, according
to [64]).
Weight Range Brutto (t) Value S1Weight Range Brutto (t) Value S2
to 49 0.42 1000–1199 2.77
50–99 0.49 1200–1399 3.36
100–199 0.59 1400–1599 3.88
200–299 0.76 1600–1799 4.36
300–399 0.94 1800–1999 4.89
400–499 1.14 2000–2199 5.37
500–599 1.34 2200–2399 5.92
600–699 1.50 2400–2599 6.39
700–799 1.76 2600–2799 6.88
800–899 2.03 2800–2999 7.30
900–999 2.31 over 3000 8.35

Infrastructures 2024,9, 119 18 of 32
The specific factor S
2
depends on the equipment of the active locomotive with the
train safety system ETCS Level 2 or higher security equipment. The values for the specific
factor S2are shown in Table 9.
Table 9. Specific factor S2(authors, according to [64]).
Equipment of the Driving Vehicle ECTS Level 2 and Above Value S2
Non-equipped drive vehicle 1.00
Equipped drive vehicle 0.95
4.2. Price for Alternative Bus Transport for Canceled Trains
The total price is formed by the product of the respective unit prices, the transport
services performed, and the necessary waiting times. A calculation formula is used to
determine the price for the use of the track by the train [67]:
Cbus =Cp+Co+L×Ckm (2)
where
Cbus denotes the price for alternative bus transport.
Cpdenotes the rate for bringing the bus.
Codenotes the rate for stopping the bus.
Ckm denotes the rate per kilometer traveled by the bus.
L denotes the length of the alternative bus transport route.
4.3. Simple Point Method for Risk Calculation
The simple point method for risk calculation of IM consists of the evaluation of three
components: probability, consequence, and weight of evaluators. The probability estimate
consists of the considered danger that may occur, and the probability estimate is determined
by numbers 1–15, where the degree of danger is simply included. The probability (P) is
shown in Table 10.
Table 10. Probabilities of danger occurrence (authors, according to [68]).
Degree Frequency of Occurrence Severity of Consequences
1 Unlikely A very small threat
2 Likely Small threat
3 Very likely Frequent threats
4 Highly probable Continuous threat
5 Permanent Critical threat
Like probability, the category of consequences is also determined. For each situation,
the most serious possible damage will be determined using five degrees, which indicate the
severity of the possible injury. The severity of the consequences (N) is shown in Table 11.
The product of the relevant values of severity and probability yields the final value of
the risk of health damage (R), which is a risk.
Evaluation:
1. Negligible impact on the degree of danger and threat;
2. Little impact on the level of danger and threat;
3. Greater, non-negligible impact on the degree of danger and threat;
4. A large and significant impact on the degree of danger and threat;
5.
More significant and adverse impacts on the severity and consequences of threats and
hazards.

Infrastructures 2024,9, 119 19 of 32
Table 11. Degrees of consequences (authors, according to [68]).
Degree Consequence Example
1 Insignificant
Injury without incapacity for work, negligible system failure, incurred damage up to
EUR 395.77, outage less than 1 day.
2 Small impact Injury with incapacity for work, without permanent consequences, amount of
damage (EUR 395.77–EUR 19,788.66), production outage of 1 day–2 weeks.
3 Bigger, not insignificant
Injury with permanent consequences (serious injury) that require long-term
treatment, occupational disease, significant damage to the system, loss in
production, large financial losses, damage ranges from EUR 19,788.66 to EUR
98,943.29, production outage of 2 weeks to 1 month.
4 Large and important
Large and significant influence on the degree of danger and threat (severe
occupational accident). Extensive damage to the system, loss of production, large
financial losses, damage is in the range of EUR 98,943.29–EUR 197,886.57,
production outage lasts 1 month–4 months.
5 Catastrophic
Fatal injury, complete destruction of the system, irreplaceable losses, significant
damage, the amount of damage is more than EUR 197,886.57, production outage
lasts longer than 4 months.
Risk calculation using a simple point method
R=N×P×H (3)
where
R = risk.
N = consequence of the threat.
P = probability.
H = evaluation.
Based on the above calculation, we obtain the resulting risk. The resulting risk is
divided into five categories and is shown in Table 12.
Table 12. Result matrix for risk assessment (authors, according to [68]).
Category Level of Risk Risk Assessment
I. Insignificant
R is less than 5 No action is required.
II. Acceptable
R is in the range of 6–10
No additional management is required. Attention should be paid to improving
solutions that would be more effective in terms of the resources spent and do not
carry the burden of additional costs. Monitoring is required for procedural
compliance.
III. A slight risk
R is in the range of 11–50
It is necessary to minimize the risks that have arisen, and the costs of prevention
need to be considered and defined. Risk minimization measures are to be
implemented within the specified time. If a moderate risk is associated with very
harmful consequences, further estimation and a more precise determination of the
probability may be needed as a basis for determining the need to improve the
management system.
IV.
Unwanted risk
R is in range of
51–100
Work should not be started until the risk has been reduced. Considerable resources
can be allocated to risk reduction. If the risk-related work has already started, the
necessary steps must be taken.
V.
Unacceptable risk
R is greater than
101–125
Work must not be started or continued until the risk has been reduced. If it is not
possible to reduce the risk even by using unlimited resources, the work must be
prohibited.

Infrastructures 2024,9, 119 20 of 32
4.4. Technological Procedures during the Railway Infrastructure Interruption
It is a technological procedure of work that is divided into three categories and must
be firmly set and followed due to the time schedule of traffic interruptions. The point is
that the work on the track is safe and carried out in the shortest possible time.
Determination of the technological procedure before the railway infrastructure inter-
ruption
•
Measurements of vehicle runs are made on the tracks at regular intervals. The measure-
ments’ outcomes form the foundation for commissioning rail equipment maintenance
and repairs, such as kilometer position specification;
•
We carry out preparatory work before commencing the maintenance. It goes, for
example, to the timely arrival of mechanization and delivery of material and necessary
portable signs to a railway station to which the maintenance works are concerned. All
employees participating in these projects must be informed about their technological
progress. And that is in accordance with all applicable regulations. At the same time,
they must be instructed about work safety and confirm their acknowledgment by
signing;
•
If mechanization is to be worked on during the maintenance work, which will have
to be shut down at a certain station during this work, the contractor must request
the allocation of tracks for these mechanisms through the operational application (in
the case of the Czech infrastructure manager, it is the KAZAS application) well in
advance.
Determination of the technological procedure during the railway infrastructure inter-
ruption
•
Notification of the responsible representative of the maintenance work order to the
transport employee that the conditions for starting the maintenance work are met, the
preparatory work is completed, and the maintenance can be started;
•
Beginning of maintenance—according to the interrupted type of equipment on the
track, safety equipment, or voltage equipment;
•
In the case of electrified lines and voltage interruption of traffic, switching off the
current of the traction line;
•Possible switching off the crossing security device;
•
Taking over the station, determining and marking the section with interrupted opera-
tion with portable signs;
•The arrival of mechanization in the workplace;
•
Performing preparatory work for a specific activity stipulated by the relevant IM
regulation (SŽ S3/1), the contractor is responsible for the timely and high-quality
performance of preparatory work unless otherwise stipulated by the contract;
•
Performing work according to the technological procedures specified in the IM regula-
tion (SŽ S3/1);
•Completion of work;
•The return of mechanization from the workplace;
•Clearance of portable signs;
•Turning on and testing the correct function of the crossing security device;
•Switching on the current and testing the traction line;
•
The responsible representative of the maintenance customer shall keep a record of the
track availability and operability of affected track parts;
•Ending of maintenance.
Determination of the technological procedure after the end of the railway infrastructure
interruption
•
After the maintenance is completed, the traffic employee must check all indications of
the security device and remove the temporary signs.

Infrastructures 2024,9, 119 21 of 32
4.5. Selection of the Variant of Implementation of Railway Infrastructure Interruption
In this step, based on the several variants presented for the implementation of the
planned infrastructure interruption, the optimal variant will be selected. The decisive
factor is the global view of the optimization criterion, which is the minimization of costs
caused by works during infrastructure interruption as the total costs of all actors, i.e., the
manager of the railway infrastructure and the affected operators. On the IM side, these are
additional costs due to the implementation of these works, including the costs of modifying
the security equipment. On the part of the operators, these are additional costs for running
trains on diversion routes and waiting for the end of planned interruptions or moods for
alternative bus transport minus the costs of unrealized train routes and compensation from
IM, according to Formula (4). The variant that shows the lowest costs will be implemented.
CIM ∓CRU =min (4)
where
∆CIM denotes the additional costs of IM.
∆CRU denotes the additional costs of RU.
The infrastructure manager’s additional costs are, therefore, all the costs that need to be
incurred in connection with the interruption compared to the null option (no interruption).
These are the costs of securing the work according to the chosen variant of technological
procedures regarding risk. The carrier’s additional costs are made up of the costs of
alternative bus transport minus the costs of unrealized train paths. In the case of a freight
operator, these are additional costs of diversion routes or incurred costs of trains waiting to
end the interruption (energy consumption, train crews, etc.).
The detailed range of types of costs that need to be included in the calculation is
presented in Table 13.
Table 13. Additional structure costs for calculation.
Additional costs of
IM ∆CIM
+
Total costs for securing the selected variant of exclusion
Discounts on the price of using the infrastructure on diversion
routes for passenger trains
Discounts on the price of using the infrastructure on diversion
routes for freight transport
Costs related to alternative bus transport (informing passengers in
stations, information systems)
−
Additional costs for extending the infrastructure interruption (labor
costs)
Risk of injuries and accidents (costs for accidents during working
hours)
Additional costs of
RU ∆CRU
+
Costs of alternative bus transport
The cost of the diversion routing
Costs of waiting for trains to end the interruption (train staff,
energy, etc.)
Reimbursed fare costs due to interruption (passenger transport)
Costs of unrealized transports due to interruption (freight
transport)
−The price for using the infrastructure for unrealized train paths
4.6. Safety during the Implementation of Railway Infrastructure Interruption
All persons who participate in the implementation of the works and will, in the process,
implement the movement of railway vehicles and mechanisms on the track operated by
IM must have a contract with IM on the operation of railway transport. All employees
who participate in the operation of the railway and railway transport in connection with
the implementation of maintenance are required to have valid professional and medical

Infrastructures 2024,9, 119 22 of 32
qualifications. Even in the maintenance planning phase, the contractor must provide the
customer with a detailed work schedule, including a list of mechanizations that, during the
performance of the work, restrict the operation of rail traffic on the adjacent track (slow
runs, prohibition of trains with exceeded loading width, interruption of the adjacent track,
etc.), including the deadline for when operation will be restricted.
Safety must also be ensured for passengers. All construction measures necessary for
the safe exit and boarding of passengers (preserving the prescribed length of the platform,
building access roads, maintaining crossings over the interrupted track, etc.), which are
determined by valid documents and regulations, must be implemented in a timely manner
and completely.
5. Results
As part of the application part of this research, the railway infrastructure interruption
on the Czech infrastructure manager network, specifically in the region of ˇ
CeskéBudˇejovice,
on the HorníDvoˇrištˇe– ˇ
CeskéBudˇejovice (706) and ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice (705)
lines are addressed. These lines are single-track, electrified with an AC traction system of
25 kW, and are included in the TEN-T system. Table 14 shows an overview of the individual
stages of infrastructure interruption on line 705 and the number of affected trains operating
on this line.
Table 14. Overview of the stages of infrastructure interruption on line 705 and the number of affected
trains.
705 Stage A Stage B Stage C Stage D Stage E
Infrastructure interruption duration (time) 7:30 A.M.–
3:35 P.M. 7:20 A.M.–
3:30 P.M. 7:10 A.M.–
3:20 P.M. 7:15 A.M.–
2:10 P.M. 7:20 A.M.–
2:00 P.M.
Duration of stages (days) 2 2 2 2 2
Operated
regional trains
workday even direction 14 14 14 14 14
odd direction 13 13 13 13 13
weekend even direction 11 11 11 11 11
odd direction 10 10 10 10 10
Replaced trains
workday even direction 4 4 4 4 3
odd direction 4 4 4 4 3
Freight trains even direction 1 1 1 1 1
odd direction 1 1 1 1 1
Table 15 shows an overview of the individual stages of infrastructure interruption on
line 706 and the number of affected trains.
Table 15. Overview of the stages of infrastructure interruption on line 706 and the number of affected
trains.
706 Stage A Stage B Stage C+F Stage D Stage E Stage F
Infrastructure interruption duration (time) 9:10 A.M.–
4:45 P.M. 9:00 A.M.–
4:25 P.M. 8:45 A.M.–
4:15 P.M. 8:50 A.M.–
4:10 P.M. 8:55 A.M.–
4:00 P.M. 8:45 A.M.–
4:15 P.M.
Duration of stages (days) 232211
Operated
regional trains
workday even direction 10 10 10 10 10 10
odd direction 11 11 11 11 11 11
weekend even direction 888888
odd direction 999999
Operated fast
trains
workday even direction 444444
odd direction 444444
weekend even direction 444444
odd direction 444444
Replaced
trains weekend even direction 444444
odd direction 444444
Freight trains even direction 111111
odd direction 222222
Figure 14 shows the schedule of planned infrastructure interruption on lines 705 and
706.

Infrastructures 2024,9, 119 23 of 32
Infrastructures 2024, 9, 119 24 of 34
Operated
regional
trains
odd direction 11 11 11 11 11 11
weekend even direction 8 8 8 8 8 8
odd direction 9 9 9 9 9 9
Operated
fast trains
workday even direction 4 4 4 4 4 4
odd direction 4 4 4 4 4 4
weekend even direction 4 4 4 4 4 4
odd direction 4 4 4 4 4 4
Replaced
trains weekend even direction 4 4 4 4 4 4
odd direction 4 4 4 4 4 4
Freight trains even direction 1 1 1 1 1 1
odd direction 2 2 2 2 2 2
Figure 14 shows the schedule of planned infrastructure interruption on lines 705 and
706.
Figure 14. Time schedule of planned infrastructure interruption.
The individual stages are arranged according to the day of their implementation and
not according to the designation. This designation is only formal. Maintenance activities
were carried out gradually and were assigned to individual stages according to the
importance of its implementation. The green color shows the normal operation of railway
transport without restrictions, and the red color shows the duration of the infrastructure
interruption (these times are shown in Tables 14 and 15). After the end of the maintenance
activity, the operation was resumed until the next day, when the operation was carried
out again at the specific time of the planned maintenance. On line 705, the planned
infrastructure interruption lasted 14 days (including two weekends when the operation
was in normal mode—they are marked with an X). On line 706, the planned interruption
lasted 12 days (including one weekend—operation in normal mode). The total time of
railway infrastructure interruption during the entire period was 38 h for line 705 and 44 h
and 25 min for line 706.
5.1. Operator Costs during Infrastructure Interruptions
The necessary parameters of abandoned passenger trains on railway line 705 and the
parameters of canceled regional trains (Reg) and fast trains (F) on railway line 706 were
obtained from the operational application train track position. Table 16 shows the prices
for the use of the track by the train for all stages of infrastructure interruption, which are
calculated according to Formula (1).
Table 16. Price for using the track by train.
Stage A B, C D, E
Infrastructure
Interruption Operation
Order
Train
category 705 706 705 706 705 706 705 706
Figure 14. Time schedule of planned infrastructure interruption.
The individual stages are arranged according to the day of their implementation
and not according to the designation. This designation is only formal. Maintenance
activities were carried out gradually and were assigned to individual stages according
to the importance of its implementation. The green color shows the normal operation
of railway transport without restrictions, and the red color shows the duration of the
infrastructure interruption (these times are shown in Tables 14 and 15). After the end of the
maintenance activity, the operation was resumed until the next day, when the operation
was carried out again at the specific time of the planned maintenance. On line 705, the
planned infrastructure interruption lasted 14 days (including two weekends when the
operation was in normal mode—they are marked with an X). On line 706, the planned
interruption lasted 12 days (including one weekend—operation in normal mode). The total
time of railway infrastructure interruption during the entire period was 38 h for line 705
and 44 h and 25 min for line 706.
5.1. Operator Costs during Infrastructure Interruptions
The necessary parameters of abandoned passenger trains on railway line 705 and the
parameters of canceled regional trains (Reg) and fast trains (F) on railway line 706 were
obtained from the operational application train track position. Table 16 shows the prices
for the use of the track by the train for all stages of infrastructure interruption, which are
calculated according to Formula (1).
Table 16. Price for using the track by train.
Stage A B, C D, E
Infrastructure
Interruption Operation
Order
Train
category 705 706 705 706 705 706 705 706
L
[kilometer]
Reg
13
7.3
16.4
35.8
19.9
8.1
F - 16.7 8.1
Ex - 24 56.8
Z [EUR] 0.85 0.85 0.85 0.85 0.85 0.85
K 1 1 1 1 1 1
P1 1 1 1 1 1 1
S1
Reg 0.76 0.59 0.76 0.59 0.76 0.59
F - 0.76 - 0.76 - 0.76
Ex - 0.94 - 0.94 - 0.94
S2
Reg 1 1 1 1 1 1
F - 1 - 1 - 1
Ex - 1 - 1 - 1
C/train
[EUR]
Reg 8.41 3.66 10.61 17.97 12.87 4.07
F - 4.72 - 10.80 - 5.24
Ex - 5.84 - 18.13 - 45.43
C/stage
[EUR] 134.51 791.03 169.69 259.47 154.43 288.25 458.63 579.03

Infrastructures 2024,9, 119 24 of 32
For trains that are replaced by alternative bus transport due to maintenance, the
operator would pay the sum of EUR 458.63 for railway line 705 and EUR 579.03 for railway
line 706 when using the railway transport route. However, the operator thus incurred costs
associated with the provision of alternative bus transport.
5.2. Price for Alternative Transport for Canceled Trains
The calculation of the price, according to Formula (2), for the operator of alternative
bus transport for one bus is made up of the price for bringing in and stopping the bus; the
product of the relevant unit price, which is EUR 2.77/train kilometer; and the performed
transport services. The assumption is that each train is replaced by two buses. Table 17
shows the price for alternative bus transport and the increase compared to train travel.
Table 17. Price for alternative bus transport for canceled trains on railway line 705.
Stage L [km] C/BUS [EUR] C/Stage [EUR] Increase [EUR]
A 14.7 46.27 740.25
B, C 28.1 83.39 1334.23
D, E 24.9 74.52 1192.39
Infrastructure interruption operation order 3266.87 2808.23
The railway operator will pay EUR 3266.87 for alternative bus transport, which is an
increase of EUR 2808.23. Figure 10 shows a comparison of the prices for the transportation
route traveled by trains and buses, as well as alternative bus transport, in individual stages.
The resulting price is calculated according to the calculation in Formula (2). Table 18 shows
the price for alternative bus transport and the increase compared to train travel.
Table 18. Price for canceled trains on railway line 706.
Stage Rail
Infrastructure
Alternative Bus
Transport Increase [EUR]
A 31.31 806.74
B 172.20 3457.47
C 87.27 2637.99
D 156.10 2770.41
E 132.15 2537.70
Infrastructure interruption
operation order [EUR] 579.03 12,210.27 11,631.28
The price for the railway journey covered by trains would be EUR 579.03. Since
many buses were used, the costs for alternative bus transport reached EUR 12,210.27. The
operator’s costs were increased by EUR 11,631.28. The comparison of the price for the
traveled transport path of railway lines 705 and 706 is shown in Figure 15.
It is obvious that the railway transport operator will pay several times more than for
normal operation when trains are running in the given section. The increase in these costs
is EUR 2808.23 during the infrastructure interruption. However, this price is not final. The
railway operator pays the railway transport operator compensation for this interruption.
From a logistical and cost point of view, it is more advantageous for operators to have
infrastructure interruptions that do not result in a complete stoppage of operations or the
use of alternative bus transport.

Infrastructures 2024,9, 119 25 of 32
Infrastructures 2024, 9, 119 26 of 34
Infrastructure interruption operation order
[EUR] 579.03 12,210.27 11,631.28
The price for the railway journey covered by trains would be EUR 579.03. Since many
buses were used, the costs for alternative bus transport reached EUR 12,210.27. The
operator’s costs were increased by EUR 11,631.28. The comparison of the price for the
traveled transport path of railway lines 705 and 706 is shown in Figure 15.
Figure 15. Price for the traveled transport path of railway lines 705 and 706.
It is obvious that the railway transport operator will pay several times more than for
normal operation when trains are running in the given section. The increase in these costs
is EUR 2808.23 during the infrastructure interruption. However, this price is not final. The
railway operator pays the railway transport operator compensation for this interruption.
From a logistical and cost point of view, it is more advantageous for operators to have
infrastructure interruptions that do not result in a complete stoppage of operations or the
use of alternative bus transport.
5.3. Simple Point Method
This method is applied to all activities and causes of risk. As an example, the situation
of the movement of workers in the rail yard is given. During the movement of workers on
the track, the worker may be hit by railway vehicles, slip, fall, or be injured by falling
objects.
According to the interviewing experts, the probability that this risk may occur is set
to 2 because it is a probable phenomenon that can occur. The consequence of this risk is
assessed as level 3 because an injury with permanent consequences (a more severe injury)
may occur, which requires long-term treatment. Extensive damage may even occur. The
economic evaluation in the amount of EUR 98,943.29– EUR 197,886.57 may include the
treatment of the employee and the damage to property that will be caused by this risk.
The weight for the evaluators was set to 4—a large and significant impact on the degree
of danger and threat. Assessors set this value because these injuries happen. The resulting
risk is calculated using a simple point method according to Formula (3). The resulting risk
will, therefore, be calculated as follows:
R = 2 × 3 × 4 = 24
The resulting risk rate is 24, which belongs to category 3—moderate risk. As a
measure to reduce this risk, the following will be established:
• Use prescribed and assigned protective equipment in proper condition (reflective
protective equipment);
0
500
1000
1500
2000
2500
3000
3500
4000
0
20
40
60
80
100
120
140
160
180
200
Stage A Stage B Stage C Stage D Stage E
Price for travelled distance by
alternative transport (€)
Price for travelled distance by rail
transport (E)
Stage of planned infrastructure interruption
705 706 705 706
Figure 15. Price for the traveled transport path of railway lines 705 and 706.
5.3. Simple Point Method
This method is applied to all activities and causes of risk. As an example, the situation
of the movement of workers in the rail yard is given. During the movement of workers
on the track, the worker may be hit by railway vehicles, slip, fall, or be injured by falling
objects.
According to the interviewing experts, the probability that this risk may occur is set
to 2 because it is a probable phenomenon that can occur. The consequence of this risk is
assessed as level 3 because an injury with permanent consequences (a more severe injury)
may occur, which requires long-term treatment. Extensive damage may even occur. The
economic evaluation in the amount of EUR 98,943.29– EUR 197,886.57 may include the
treatment of the employee and the damage to property that will be caused by this risk.
The weight for the evaluators was set to 4—a large and significant impact on the degree of
danger and threat. Assessors set this value because these injuries happen. The resulting
risk is calculated using a simple point method according to Formula (3). The resulting risk
will, therefore, be calculated as follows:
R=2×3×4 = 24
The resulting risk rate is 24, which belongs to category 3—moderate risk. As a measure
to reduce this risk, the following will be established:
•
Use prescribed and assigned protective equipment in proper condition (reflective
protective equipment);
•Enter the track concentratedly and only for the performance of work;
•
Move with increased caution, always anticipate the movement of rolling stock, and
look around in all directions;
•Use designated paths;
•
Cross the tracks only in places reserved for this (crossings, footbridges, underpasses);
•
Increase attention when passing railway vehicles; step away from moving railway
vehicles;
•Use the assigned lights in reduced visibility;
•Adjust the walking speed about the possibility of the terrain, considering the current
state of the weather and the possibility of an injury;
•
Prohibition of the movement of persons in places marked with safety signs “Prohibi-
tion of entry and movement of persons”;
•Securing dangerous openings and depressions;
•Ensuring sufficient free space for the movement of people along the tracks;
•Professional and medical qualifications of employees;

Infrastructures 2024,9, 119 26 of 32
•Qualified staff;
•Ban on the consumption of alcohol and narcotic substances.
5.4. Costs of the Railway Operator during the Railway Infrastructure Interruption and
Technological Procedures of Works
If the operator must provide alternative bus transport due to maintenance on the
transport route, the railway operator pays compensation, which is one of the cost items.
The amount of compensation is non-public information. The costs of the railway operator
include, among other things, the wages of employees.
The usual working hours of the organizational units ensuring maintenance are
6 A.M.–2 P.M. In the case of resolved maintenance, which always took place outside
working hours, the employees are entitled to an hourly wage increased by additional
payments according to the collective agreement. Namely, a 25% surcharge for overtime and
EUR 0.28 for each hour. Wages up to 2 P.M. cannot be included in the costs because, at this
time, regular IM employees are paid even if there is no infrastructure interruption. Table 19
shows the labor costs incurred within the individual stages of infrastructure interruption.
Table 19. Additional labor costs for IM employees within the individual stages of work during
infrastructure interruptions.
Tariff Level/
Number
Rail
Line
Stage A
[EUR]
Stage B
[EUR]
Stage C, F
[EUR]
Stage D
[EUR]
Stage E
[EUR]
Infrastructure
Interruption
Operation Order
5/2 705 52.08 48.98 44.74 14.46 10.47
706 82.36 109.17 68.79 66.55 31.28
6/4 705 113.19 106.62 97.38 31.54 22.84
706 179.03 237.49 149.63 144.73 68.02
9/3 705 105.61 99.86 91.16 29.66 21.48
706 167.11 222.09 139.88 135.28 63.55
10/2 705 75.32 71.28 65.07 21.20 15.35
706 3011.50 158.48 99.80 96.51 45.33
12/1 705 119.19 40.37 36.85 12.03 8.71
706 67.40 89.70 56.48 54.61 51.30
Total [EUR] 705 388.79 367.12 335.20 108.89 78.85 1278.85
706 615.10 816.92 514.58 497.68 259.47 2703.75
The amount of labor costs in case of interruption on railway line 706 is EUR 2703.75,
and on railway line 705 it is EUR 1278.85.
5.5. Work Safety during the Infrastructure Interruption
Maintenance works are activities performed on or near the track. The work is governed
by safety regulations, where the risks are determined. There were three occupational
accidents during the interruption on railway line 705. One was classified as a serious work
injury, and the other was classified as a minor work injury. The cause of the accident was an
unforeseeable occupational risk. During the interruption on railway line 706, there was one
occupational accident, which was evaluated as a serious occupational accident. A worker
was injured by a work machine.
6. Discussion
Currently, maintenance activity is increasing, and certain risks are associated with it.
Based on the analysis performed, deficiencies were identified, especially in the observance
of occupational safety and related risks. During the maintenance of the treated track
sections, there was an increase in the number of occupational accidents. In connection with
this, costs have increased, but it also affects the course of maintenance activities.

Infrastructures 2024,9, 119 27 of 32
In the application part, two track sections were selected. The infrastructure inter-
ruption took place on the ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice (railway line 705) and on the
HorníDvoˇrištˇe– ˇ
CeskéBudˇejovice (railway line 706) lines. On both track sections, repair
and maintenance work was carried out on the top and bottom of the railway in the track
sections. During both maintenance operations on these track sections, according to the defi-
nition in the individual stages, the operation on the railway transport route was completely
stopped. To preserve the public service, the operator had to introduce measures in the form
of alternative bus transport for passenger transport.
The economic point of view of the investigated maintenance activities showed the
possibility of reducing costs. One possibility is to move maintenance activities to night
hours. During normal operation, the operator paid EUR 458.63 for trains running on the
ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice line. As part of the maintenance, the operator must pay
EUR 2808.23 for alternative bus transport. However, if the maintenance was shifted to
night hours, only three trains would be affected by this maintenance. The operator would
pay EUR 1225.08 for alternative bus transport. Savings would also occur in wage costs
for employees of the infrastructure manager working on maintenance. The employer will
pay additional fees in the amount of EUR 1278.85 to the employees for maintenance at the
specified time. The time shift would also be suitable from an economic point of view for the
maintenance of the 706 HorníDvoˇrištˇe– ˇ
CeskéBudˇejovice line. On this line, the operator
will pay EUR 579.03 for the canceled train paths on the railway infrastructure. Since it is
a line where fast trains also run, in case of stopped operation and use of alternative bus
transport, the operator will pay EUR 12,210.31. With the time shift, there would also be
a reduction in the number of trains that are replaced. The operator will pay EUR 369.14
for trains running on the railway infrastructure. The operator will pay EUR 8156.09 for
alternative bus transport, replacing these trains. Considering the time frame of maintenance
in individual stages and the work of employees beyond working hours, the wage costs are
EUR 2703.74.
In terms of safety, there were a total of four occupational accidents in the analyzed
maintenance activities. Two accidents were classified as minor occupational accidents; the
other two accidents were classified as severe occupational accidents. Based on the analysis,
it was found that the biggest problems are outdated work risks and non-compliance with
established regulations. Subsequently, it is recommended that the date of training in safety
and health protection at work be set at an interval of once a year. Currently, training takes
place once every two years.
Infrastructure interruption during the night hours was not addressed and calculated in
detail in this article. As part of the comparison of possible solutions for the introduction of
night interruptions on the infrastructure, the operator would pay EUR 1225.08 on railway
line 705 and EUR 8156.09 on railway line 706. The railway infrastructure manager would
pay EUR 1143.74 on railway line 706 as part of night-time infrastructure interruptions on
railway line 705. As part of the economic benefits, shifting the time of implementation of
infrastructure interruptions to the night hours would lead to financial savings, both for the
infrastructure manager and for the operators. Table 20 presents the costs for alternative
bus transport for operators and wage costs for employees of the infrastructure manager for
individual maintenance activities in the current time frame, in case of a possible time shift,
and the amount of savings.
Table 20. Costs and savings for alternative bus transport and labor costs.
Interrupted
Railway Line
Operator—Costs for Alternative Bus Transport
[EUR] IM’s Additional Labor Costs [EUR]
Existing Night Time Savings Existing Night Time Savings
705 3266.87 1225.08 2041.79 1278.85 1143.74 135.11
706 12,210.31 8156.09 4054.22 2703.75 1143.74 1560.00

Infrastructures 2024,9, 119 28 of 32
The operator’s savings for maintenance on the ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice line
amount to EUR 2041.79, and on the HorníDvoˇrištˇe– ˇ
CeskéBudˇejovice line, they amount to
EUR 4054.22. The infrastructure manager’s savings for maintenance on the ˇ
CeskéVelenice–
ˇ
CeskéBudˇejovice line amount to EUR 135.11, and on the HorníDvoˇrištˇe– ˇ
CeskéBudˇejovice
line, they amount to EUR 1560.00. Operator costs for line 705 are
EUR 326.67 per day
,
and for line 706, they are EUR 1221.03 per day. The infrastructure manager’s costs for
line 705 are EUR 127.88 per day for maintenance activities, and for line 706, they are
EUR 270.37 per day.
Trouble-free operation on the railway requires regular maintenance of the infrastruc-
ture, while according to the findings, up to 25% of the length of the infrastructure is subject
to some activities aimed at maintenance every year and, with it, planned interruption of
traffic on the infrastructure. Maintenance interventions interfere with normal operation
and limit the fulfillment of the established timetable. The proposed methodology and
its individual procedures (calculations, technological procedures, and others) represent a
suitable tool for the infrastructure manager to properly manage the interruption of railway
traffic on the infrastructure. The application part of this research is proposed based on
real infrastructure interruptions on the network of the Czech infrastructure manager. It
follows from the proposed methodology that the economic point of view of the investigated
maintenance activities showed the possibility of reducing costs, proposing the possibility
of implementing infrastructure interruption during night hours and stricter compliance
with safety at work to reduce the risks of accidents as a tool for reducing costs, which
also affects the course of maintenance activities. Since the operation and maintenance of
railway infrastructure require a long-term and sustainable strategy, it is important to set
up infrastructure interruption management to ensure regular, reliable, and safe railway
infrastructure for all operators.
The emphasis in the research was placed on the economic side of this issue and a
global view of the railway market and the provision of the resulting service at the required
quality level. Another key moment in the methodology is the precise planning of the travel
schedule during infrastructure interruptions using modeling and simulation. There may
be situations where such a timetable is not able to handle existing requests, e.g., due to
the delay of the trains concerned and other circumstances. The situation created in this
way must be treated as an unplanned interruption. These newly created interruptions
cause deviations in timetables during infrastructure interruptions and cause delays at
destination stations. The aim is for the timetable during the infrastructure interruption
to be closer to the original timetable and to cover, as much as possible, all existing rail
traffic requirements. A correct understanding of the technological aspects of the planning
of operational activities has a decisive influence on the economic efficiency of the evaluated
measures during infrastructure interruption.
Passenger transport also incurs increased costs for passengers in terms of increased
waiting time, longer transport time, or discomfort. The presented methodology does not
calculate the cost of lost passenger time. This approach would be possible if we were
to calculate the societal (economic) costs of different variants of railway operation. In
that methodology, returned tickets are counted as giving up the intended trip due to the
interruption. Similarly, in freight transport, the costs of foregone transports due to road
closures or the reduced transport capacity of the train are included (reduced standard
weight of the set due to the deviation along a more inclined track) or additional costs
for maintaining the transport capacity of the train (for example, the addition of a spur
locomotive or an independent locomotive traction).
Compared to the research of [
18
], where the authors dealt with the proposal of an
alternative timetable in case of interruption of the railway infrastructure due to mainte-
nance activities, our paper does not deal with a specific proposal of the timetable in the
case of infrastructure interruption but proposes a management system of infrastructure
interruption from the point of view of the infrastructure manager and the operator and
costs incurred for this infrastructure interruption. Our research should be understood

Infrastructures 2024,9, 119 29 of 32
from the point of view of saving costs, ensuring safety during maintenance activities, and
ensuring the transportation of passengers during the duration of the infrastructure inter-
ruption. Compared to the research of [
25
], where the authors dealt with the management
of the interruption of railway operations, we can state that this research mainly focused on
passengers and their transportation options. This research dealt with a strategy focused
on travelers. Compared to this research, our paper mainly focused on the infrastructure
managers and operators who are directly affected by the infrastructure interruption. In
the case of further research, it would be appropriate to link our research together with
the proposal of a strategy focused on passengers and their transport during infrastructure
interruptions and link these two strategies into a suitable model.
The originality of this research comes in solving the problem of planned infrastructure
interruption from the point of view of the infrastructure manager, as well as the costs
and safety measures spent on employees who perform maintenance activities. This pa-
per also deals with the cost activity of railway operators, which are directly affected by
the infrastructure interruption by the fact that their performance is transformed into the
performance of alternative bus transport. In the case of freight transport, the carrier’s risk
of shipment delays increased, as diversion routes were not used, and all freight trains
(line 705—two freight trains; line 706—three freight trains) waited at stations until the end
of the infrastructure interruption. Also, the originality of this research is focused on the
safety of employees of infrastructure managers at work in the framework of reducing the
risk of possible accidents and injuries.
7. Conclusions
Ensuring the operability, maintenance, and care of the transport infrastructure is the
duty of the IM in terms of the EU transport policy. The fulfillment of this requirement is
determined precisely by works on the transport infrastructure, which can be carried out
in two ways. The first method is the restriction of operation, and the second method is
the interruption of traffic on the infrastructure. In any case, it is very important that the
maintenance activity is carried out in an optimized manner with a global view towards all
actors in the railway market, minimizing the costs caused by this activity.
The goal of the research was, based on the analysis of the current state, to evaluate
the works during the infrastructure interruption and to determine the most advantageous
variant of the implementation of these measures. The evaluation was carried out in terms
of the economic and safety impacts of maintenance activities. The proposal consists of the
processing of methodological procedures that lead to the efficiency of work during the
infrastructure interruption from a global perspective. The methodology can contribute
to determining the amount of compensation to operators operating passenger transport
for complications in the introduction of substitute bus transport. This paper deals with
the activities during the infrastructure interruption of the Czech infrastructure manager,
other activities, and the risks associated with them. In the application part, an analysis of
maintenance activities on the lines ˇ
CeskéVelenice– ˇ
CeskéBudˇejovice and HorníDvoˇrištˇe–
ˇ
CeskéBudˇejovice was carried out. As part of both maintenance activities, a calculation was
made according to calculation formulas for the timing of maintenance activities, as well
as subsequently if maintenance is shifted to night hours. It was found that the amounts
paid by the operator for the railway route traveled and the amounts paid for alternative
bus transport were subsequently compared. In the case of the infrastructure manager, the
calculation was based on the wage costs of employees working on maintenance with the
current time allocation and shift to evening and night hours. From an economic point of
view, a time shift is clearly appropriate for both maintenances. And that is both from the
point of view of the operator and from the point of view of the infrastructure manager. In
terms of time, the shift would also increase the quality of transport services, as fewer trains
would be affected by maintenance. In this way, inconvenience to passengers associated
with alternative bus transport would be eliminated to a minimum.

Infrastructures 2024,9, 119 30 of 32
Author Contributions: Conceptualization, Z.B. and J.G.; methodology, Z.B. and J.G; validation, J.G.;
formal analysis, Z.B.; investigation, J.G.; resources, Z.B.; data curation, V.Z.; writing—original draft
preparation, Z.B. and J.G.; writing—review and editing, Z.B.; visualization, V.Z.; supervision, J.G.
and V.Z.; project administration, J.G.; funding acquisition, J.G. All authors have read and agreed to
the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: This study did not report any specific data.
Acknowledgments: This paper is supported by the VEGA Agency through Project 1/0640/23,
“Elements of quality in competitive public tendering in railway passenger transport”, through the
Faculty of Operations and Economics of Transport and Communication, University of Žilina.
Conflicts of Interest: The authors declare no conflicts of interest.
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