Methodology for Quantification of Technological Processes in Passenger Railway Transport Using Alternatively Powered Vehicles

Abstract

Due to the reduction in diesel propulsion on railway networks across the world, it is essential to consider the introduction of an alternative propulsion where electrification would not be feasible. The introduction of alternative propulsions may influence the technological processes of train processing and interrupt its quantification methodology, due to their specific operational requirements. The problem of the quantification of technological processes of train processing is not sufficiently solved even in the field of conventional propulsions; therefore, the aim of this paper is to propose a unique methodological procedure for the quantification of selected processes of train processing operated by multiple units with a conventional or alternative propulsion. The new process quantification methodology enables the duration determination of a specific process, which can be simply determined for multiple units of different length and propulsion under local conditions. The duration determination is based on the final formula or its graphical representation. The function is based on data obtained by analysing the evaluated workflow of a model and multiple units using the PERT network analysis method. The proposed methodological procedure is verified by different types of propulsions through a case study using real values. The application of the methodology can prevent the risks related to non-compliance of the required technological times and at the same time increase the sustainability of the operation stability of railway passenger transport.

1. Introduction

Seemingly environmentally friendly passenger railway transport (PRT) represents a way to reduce society’s dependence on fossil fuels, but usually with the usage of electric vehicles on electrified lines or vehicles with alternative propulsion, which represents a reduction in pollutant emissions and dependence on fossil fuels. These represent a potential reduction in pollutants or emissions and dependence on fossil fuels and can provide a way to sustainable mobility for future generations without the need for the costly electrification of lines or the termination of non-environmentally friendly internal combustion engine (ICE) vehicle operation [1,2].

Alternative propulsions in railway transport are propulsions that are currently not commonly used in the transport industry, and they form an alternative to conventional solutions in order to reduce emissions and the dependence on fossil fuels in the transport sector without a full line electrification of the railways [3]. According to a study carried out by the author of this paper, for the purpose of PRT using alternative propulsions, multiple units (MUs) are the most developed in different types of configurations according to the specific energy source, as detailed in

Table 1. Multiple unit types with alternative propulsion.

Battery			Hydrogen			ICE—Hybrid
MU Config. Type	Energy Source	Number of Modes	MU Config. Type	Energy Source	Number of Modes	MU Config. Type	Energy Source	Number of Modes
Battery (BMU)	ES	1	Fuel-cell (FCMU)	H2, ES	2	Electro-diesel (EDMU)	ICE, LE	2
Battery electric (BEMU)	ES, LE	2	Fuel-cell + BEMU (FCEMU)	H2, ES, LE	3	Hybrid-diesel (HDMU)	ICE, ES	2
						Hybrid electro-diesel (HDMU)	ICE, ES, LE	3

Source: Authors according to [4]. Explanatory notes: ES—energy storage (batteries or SC), H2—hydrogen; LE—line electrification

.

MUs utilising alternative propulsion are characterised by specific properties and limitations with regard to the propulsion they use, e.g., range, required technical base, energy consumption, recharging, special maintenance, etc., which in many cases may be different from conventional propulsion. During the operation of MUs with an alternative propulsion, it is necessary to take these specifications into account while planning the operation, which consists of planning transport diagrams, rolling stock management and creating transport timetables, and also possibly performing economic analysis of the operation of such vehicles [3,5].

There is still not sufficient experience and information in the field of their operation, which are essential in the planning of passenger train processing technology (local processes) that affects the use of the rolling stock and timetables. The issue is focused on the operation of MUs, which is currently the most suitable vehicle variant, especially for regional PRT, which is also claimed by [6,7].

The local processes in the form of conventional propulsion are insufficiently solved, and the transport technologists use a heuristically determined overall normative, which does not represent the real requirements according to environmental conditions, which may cause delays, inefficient use of production resources or other risks [8,9].

The purpose of this paper is to present a new methodological procedure for quantifying the local processes using MUs with an alternative propulsion and to compare the values with the operation of conventional propulsions. The methodology is based on the principles of process mapping in practice, the method of network analysis and the appropriate interpretation of the resulting values that could be used in general. The validation of the methodology proposed by authors is part of a case study on selected railway lines in the Slovak Republic in the Results section. The achieved values can be a suitable basis for passenger transport planners while using conventional or alternatively powered vehicles.

The first part of the paper is the Introduction and Literature Review. In the Introduction, the main purpose of the paper is described. The Literature Review is focused on the current research on alternative propulsions in railway transport and their operation and local process quantification options. A literature review is necessary for discovering research gaps. The second part of the paper is a proposal of the methodological procedure focusing on the local processes quantification divided into three steps, particularly process mapping, CP calculation and application of CP results and process formula. The proposed methodical procedure is verified within the conditions of the case study locality with four various MU propulsions. The brief characterisation of the methodological procedure, its limitations and new research findings are addressed in Section 5 and Section 6. The last part of the paper is the References section.

2. Literature Review

In the present time, researchers have only sporadically or superficially dealt with the processing technology quantification of passenger trains, whether with conventional or alternative propulsions, in their publications and research. However, in order to solve this challenge within the usage of alternative propulsions, it is essential to familiarise ourselves with the trends in railway alternative propulsions, passenger transport technology and its quantification possibilities in research made by other authors, which will serve as an inspiration and data source for the research in this paper.

2.1. Alternative Propulsions in Railway Transport

Authors Mwambeleko, J.J. et al. [10] argues that MUs are suitable vehicles for commuter trains, providing suburban or regional services, while BEMUs or other alternative propulsions should be used instead of diesel multiple units (DMUs) on short routes in order to save fuel costs and demands. In the study [5] have been indicated BEMUs or FC(E)MUs as a suitable alternative to the linear electrification of lines with a larger number of railway substructures (tunnels and bridges), which in the case of linear electrification would need to be rebuilt in order to install the overhead line. Similarly, the study on the Electrification Plan of the Czech Republic [11] argues that alternative propulsion is a way to simplify the electrification of the existing infrastructure, without the need for significant induced investments in modifications of the railway substructure, which would be necessary with full line electrification.

In paper [12] it is argued that a BEMU is an effective way to reduce the carbonisation of regional passenger services on partially electrified lines; however, it depends on the electricity source that is used to charge and power these vehicles. An optimised design of the power infrastructure using on-site green energy sources could reduce the operating costs of BEMUs as well as reduce indirect emissions from the energy production and in many cases, enable faster battery charging.

Dostál, L. [13] investigate the use of the FBS programme to determine the required battery capacity for BEMUs on partially electrified lines. It is shown through simulations between Tabor and Jihlava stations that the programme is usable, although the results should be taken with a grain of salt. The results are being compared between fictitious and real vehicles, and differences in travel time and energy consumption are being found, especially in the upward direction. Although real vehicles are not included in the simulations, a comparison is being made with a real Siemens Mireo Plus B vehicle, emphasising similar parameters.

Ogasa, M. [14] in the paper “Case study of four battery-powered methods to run electric trains on non-electrified lines” evaluates the potential energy supply options of a long-distance passenger train on a partially electrified line as an alternative to a DMU. The options that have been researched by the author are as follows:

• mount enough energy to one-way travel,
• quick charging at every few stations,
• storage battery power supply wagon connection,
• line electrification except tunnels,
• full line electrification.

The study [14] evaluates the requirements for the technical base of vehicles and railway lines for the individual variants and also the cost-effectiveness of the solution with the alternative of full electrification. The author has paid special attention to the usage of a supply wagon, where he considers the solution interesting, but it still requires further research. Fedele, E.; et al. [15] have dealt with the possibility of using supercapacitors (SC) as support for battery energy storage; however, the currently investigated technology does not show any advantage due to the operational characteristics and requirements of SC. The study of SC in railway transport is also studied by [16] with similar results.

Papers [2,17,18] focus on hydrogen railway vehicles and hydrogen distribution, on problems related to the FCMU or FCEMU. Vehicles need to be refuelled with high-quality and clear hydrogen, which is very difficult to produce. A very important part of FC(E)MU operation is the hydrogen distribution problem. FC(E)MUs would be effectively operated at locations with available hydrogen produced by clear energy. Additionally, these vehicles need to have hydrogen refuelling stations located at safe places that are accessible to trains and trucks.

Olmos, J.; et al. [19] in their submission propose the opportunities of increasing the efficiency of the operation of MUs in regional transport through hybridization, i.e., the implementation of electric propulsion elements in the DMU in various forms. In addition, they explore hybridization by using natural gas in engines instead of diesel. A similar field is a study [20], in which scientists found a fuel saving of 24–19% by simulation methods using a hybrid system in DMUs.

2.2. Railway Transport Local Processes Technology and Its Quantification

Bulková, Z. [21] in the paper discusses the possibilities of the implementation of Augmented Reality (AR) for the creation of technologies for processing final freight train sets in three variants in the train station Žilina-Teplička. The technological processes are mapped and quantified via the Gantt chart method in the paper and it is shown that AR can optimise these processes and thus achieve time and personnel savings, which can make their utilisation and the redistribution of labour costs more efficient.

PERT is an extension of the critical path method (CPM) and is used to control complex processes that are stochastic in nature. The duration of each sub-activity is treated as a random variable with a certain probability distribution. Empirically, it has been found that in practice, this is best captured by the so-called β distribution, which better captures the variability of operating conditions and the slope of the estimate of the expected activity duration towards an optimistic rather than a pessimistic value [22].

Authors comparing different PERT methods [23] argue that a combination of the results of different forms of the PERT method is a suitable mathematical method for operational planning and monitoring of work, not only in the construction industry. Tomii, J.; Zhou, L.J [24] are using a combination of the genetic algorithm and Program Evaluation and Review Technique (PERT) methods in a study focused on solving depot shunting problems using several experiments and real environment data. Authors also argue that the problem of shunting planning is similar to the problem of scheduling projects with limited resources. In paper [25] is used PERT to determine the process of air route preparation, which they approximate as a complicated project consisting of serial–parallel activities.

Anodho, B. et al. [26], based on research on duration estimation for construction projects, argue that it is possible to create unified activity items composed of several similar activities, which simplifies the process of calculating the duration of the process. The duration of the simplified activities is defined by a standard deviation.

The paper [27] explores the application of the CPM in process control by using process mining to identify the critical path (CP) in a process model. The aim is to validate the applicability of this method and to investigate its feasibility. A CP determines the shortest possible time to complete a project and requires extra attention in carrying out the activities involved. If any activity on the CP is delayed, it would cause a delay in the overall process completion time and could affect the process schedule.

Abramović, B. et al. [28] in their paper solve the problem of optimising the technology of processing freight trains at the Čierna nad Tisou border crossing station. The bottlenecks of the technological process and the critical activities are identified using the CPM. The paper mentions that the methods of network analysis can also be used for the planning optimisation of technological processes. In the paper [29], the authors use and test a modified CPM in the context of delay management in PRT. According to [30], CPM is the most commonly used network analysis method, but PERT is more advantageous because of its probabilistic approach.

Gašparik, J. et al. [31] in the book Mechanics of Railway Transport determine the shunting time using real values from the recording of the processing time, which are subsequently presented as a linear function in a graph with respect to the number of wagons being shunted, the so-called graph of the dependence of the service time. Similarly, in book [32] is presented the possibility of using a network graph for a critical path search within the process with a larger number of activities to determine the parameters for the service time dependency graph for freight train processing.

In the diploma thesis [33], the author directly deals with the technology of passenger train processing in Žilina station. The thesis aims to determine and quantify the local technological processes (starting, ending, turnarounds) in the form of a MU or a passenger train set. The author has chosen several methods for data processing and the presentation of the results. The individual technological processes are mapped through Gantt charts and quantified through the critical path method (CPM). In the case of trainsets, a linear dependence of the process time is related to the number of trainset wagons.

3. Methodology

Given that the problems mentioned above have to be addressed in a sufficiently professional and, in particular, scientific manner, it is necessary to propose a generally applicable solution that can be achieved through the application of a certain universal methodology. The methodology establishes an overall procedure for the quantification of the local technological processes when using MUs with alternative propulsion systems.

3.1. Technological Process Mapping

Technology is a general engineering discipline concerned with workflows during the production process, the aim of which is to achieve optimisation of the production process and its quantification. An essential part of the quantification of technological processes is their mapping [32] and valuation in a real environment through 4 phases:

• Input parameters focused on the technological processes:

The first phase is the determination of input parameters focused on the technological processes to be studied and the basic characteristics of the implementation environment, i.e., characteristics of the station, vehicles, personnel and so on, which can influence of whole process progression.

2.

Creation of an optimal workflow:

The second phase is the creation of an optimal workflow. In the case of this paper, it is created based on the observation of processes in the real environment being aliased to the corresponding lines and trains. This step involves the creation of a list of activities taking place during the execution of a particular process, i.e., the creation of a detailed and simplified workflow.

3.

Activity duration normalisation:

The third phase is the duration standardisation of the activities, the so-called normalisation. Activities are evaluated by a partial time norm, which represents the time required to carry out a given activity. The following methods can be used to quantify the duration of activities:

• Chronometric method—repeated recordings of activities’ durations performed at one specific workplace (e.g., train cabin);
• Predetermined times method—summary of elements’ durations for which there are objective duration normatives;
• Instantaneous observing method—repeated recordings of the activities’ duration at different times and conditions throughout the workplace, allowing for the capture of parallel activities;
• Compendiums of performance norms and normatives—compendiums that have objectively set durations of elements or activities [33].

4.

Chronological evaluated workflow:

The fourth phase is the compilation of a chronological evaluated workflow of a particular local process composed of specific activities characterised by statistically evaluated duration, continuity with other activities and source of performance. It is a connection of the previous 3 phases, while the result is the basis for the application of the PERT method for quantification of processes.

Table 2. Example of workflow table useful for PERT method.

Outcome of 4th Phase of Process Mapping
Activity ID (ij)	Activity Name	Prede- Cessors	aij	bij	mij	μi	σ2ij	σij
			[min]
i1	Activity i1	-	ai1	bi1	mi1	μi1	σ2i1	σi1
i2	Activity i2	- or ij	ai2	bi2	mi2	μi2	σ2i2	σi2
i3	Activity i3	- or ij	ai3	bi3	mi3	μi3	σ2i3	σi3
...	...	...	...	...	...	...	...	...
nm	Activity im	ij, ij, ij, …	aim	bim	mim	μim	σ2im	σim

Source: Authors.

shows an example of the final form of the workflow table. The table in this form can be a suitable basis for quantifying and calculating the CP of a process through the PERT method.

3.2. The Critical Path Calculation

The CP represents the longest path in the graph, which determines the mean value of the process duration time and outlines its most critical activities [28]. The CP is representative of the typical vehicle and its length in axles n^t_a. The PERT method is used to calculate the CP. The PERT is a method similar to the CPM and it is used to quantify projects or processes by finding a CP while using stochastic variables [22].

The duration of the activities is represented by time-bounded edges, which are modal estimates of the duration m_ij ∈ <a_ij, b_ij> where

• a_ij—optimistic duration, i.e., in the most favourable conditions,
• b_ij—pessimistic duration, i.e., in the most unfavourable conditions,
• m_ij—modal, the most expected duration of the activity,
• where a_ij ≤ m_ij ≤ b_ij [34].

The duration in the interval <a_ij, b_ij> is a continuous function and its probability distribution is not known in advance. However, the distribution can be approximated as a β-distribution, because m_ij used to be estimated closer to the a_ij [22].

The mean duration of activities that depend on the number of axles is calculated according to the relation [22,34]:

$${\mathsf{\mu }}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}+{4\mathrm{m}}_{\mathrm{i}\mathrm{j}}+{\mathrm{b}}_{\mathrm{i}\mathrm{j}}}{6}}$$

(1)

For later calculations, it is convenient to calculate also the variance (σ_ij²) and standard deviation (σ_ij) according to Relation (2):

$${\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}^2={\left({\displaystyle \frac{{\mathrm{b}}_{\mathrm{i}\mathrm{j}}-{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}{6}}\right)}^2;{\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{b}}_{\mathrm{i}\mathrm{j}}-{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}{6}}$$

(2)

The activity duration of local PRT processes is represented in the PERT method by μ_ij, which should represent the most probable activity duration and the sum of μ_ij, belonging to CP, the most probable process duration, from repeatedly recorded activity durations. The CPM is suitable if there are normatives for the duration of activities. PERT also has the advantage of σ_CP of the process, which allows rounding down the time. The calculation of CP is almost similar to CPM and it is possible to divide it into 4 phases [35]:

• Edge-oriented network graph:

The first phase of the CP calculation is the design of an edge-oriented network graph, where edges represent individual activities (their duration) and vertices represent events at the termination of an activity or the start of a follow-up activity. Input variables are data from the table represented by Table 1. The graph has an outgoing and an ending vertex. An example of a graph is in Figure 1a and a graph vertex in Figure 1b.

2.

Forward calculation of CP:

The second phase is the so-called forward calculation from the starting vertex to the ending vertex, composed of the following steps:

2.a.

The earliest start of the whole process, according to the condition:

$$T_{i=1}^E=E_{i=1j}^S=0$$

(3)

where

• T^E_i—mean value of the earliest time of vertex i,
• E^S_ij—mean value of the earliest start time of activity ij.

2.b.

The earliest start of the whole process, according to the condition:

$$E_{ij}^F=E_{ij}^S+{\mu }_{ij}$$

(4)

where

• E^F_ij—median earliest activity end time.

2.c.

The mean value of the earliest possible vertex execution time T^E_j, wherein

$${\mathrm{T}}_{\mathrm{j}}^{\mathrm{E}}=\mathrm{m}\mathrm{a}\mathrm{x}\left\{{\mathrm{E}}_{\mathrm{i}\mathrm{j}}^{\mathrm{F}}\right\}$$

(5)

2.d.

The mean value of the earliest possible start time of other activities, wherein

$${\mathrm{E}}_{\mathrm{i}\mathrm{j}}^{\mathrm{S}}={\mathrm{T}}_{\mathrm{i}}^{\mathrm{E}}$$

(6)

2.e.

By repeating the previous steps, the mean value of the earliest possible times of all activities and nodes is determined, with the last terminal vertex node n representing the mean value of the completion time of the entire T^E_n process, which also corresponds to the duration of the critical path of the M_CP.

3.

Backward calculation of CP:

The third phase is the so-called backward calculation from the end vertex to the starting vertex, composed of the following steps:

3.a.

Mean value of the latest completion time of the whole process T^L_n, conditioned by

$${\mathrm{T}}_{\mathrm{n}}^{\mathrm{L}}={\mathrm{L}}_{\mathrm{ij}=\mathrm{m}}^{\mathrm{F}}={\mathrm{T}}_{\mathrm{n}}^{\mathrm{E}}$$

(7)

where

• L^F_ij—mean value of the latest possible end time of the activity.

3.b.

Mean latest start times of other L^S_ij activities, according to the relation:

$${\mathrm{L}}_{\mathrm{ij}}^{\mathrm{S}}={\mathrm{L}}_{\mathrm{ij}}^{\mathrm{F}}-{\mathsf{\mu }}_{\mathrm{ij}}$$

(8)

3.c.

The mean value of the latest permissible vertex time T^L_i:

$$T_i^L=\min \left\{L_{ij}^S\right\}$$

(9)

where

• L^S_ij—the latest possible start of the activity.

3.d.

Mean value of the latest permissible end of activity L^F_ij, where

$$L_{ij}^F=T_j^L$$

(10)

where

• T^L_j—mean value of the latest permissible vertex time j.

3.e.

Previous calculations must be repeated until the first vertex is met.

4.

Determination of the critical path

The fourth phase is the calculation of the total and interference margin and the determination of the critical path itself, consisting of 3 steps:

4.a.

The mean value of the interference margin R_i for each vertex according to the relation:

$$R_i=T_i^E-T_i^L$$

(11)

4.b.

The CP passes through vertices where R_i = 0 and the definitive duration of the process M_CP is

$$M_{CP}=\sum _{ij}^{nm}{\mu }_{ij}\in \left\{CP\right\}; while M_{CP}=\sum _{ij}^{nm}{\mu }_{ij}^a\in \left\{CP\right\}+\sum _{ij}^{nm}{\mu }_{ij}^0\in \left\{CP\right\}$$

(12)

where

• μ_ij^a—duration agent-dependent activities,
• μ_ij⁰—duration of independent activities.

3.3. Application of Critical Path Outcomes

The overall normative for the investigated technological process of the representative vehicle is valid only for its conditions. Based on the outputs of the PERT method, it is possible to create a process duration curve, from which it is possible to determine the total normative for different vehicle lengths expressed in axles n_a.

• Process duration curve:

The process duration curve, or line, establishes the dependence of the technological process duration concerning the main recording agent for the model train. In the case of MUs, it is the number of MU axles n_a. The initial value for the function and the associated graph is the M_CP at n^t_a from PERT. The process curve can be linear therefore, the line can be written in the form of a linear function:

$$M_{na}=a\times n_a+b; \left(\pm {\sigma }_{CP}\right)={\displaystyle \frac{\sum {\mu }_{ij}^a}{n_a^t}}\times n_a+\sum {\mu }_{ij}^0; (\pm {\sigma }_{CP})$$

(13)

where

• M_na—total process duration normative concerning the number of axles,
• b—duration of independent actions, the sum of μ_ij⁰ from CP,
• a—parameter of the agent-dependent activities, sum of μ_ij^d from CP.

The purpose of the process curve is to graphically represent the dependence of the process duration concerning a factor and thus simplify the determination of the overall normative for different MU lengths. Within the BEMU, it is necessary to compare the M_na with the required static recharging time T_R^S function, which can be calculated as follows:

$$T_R^S={\displaystyle \frac{\left(l_n-R_d\times 2\times T_j^e\right)}{R_S\times n_a^t}}\ast n_a$$

(14)

where

• l_n—length of non-electrified section,
• R_d/R_s—dynamic/static recharging speed, R_d = 2.64 km/min and R_s = 3.3 km/min [3],
• T_j^e—journey time on electrified section.

2.

Total normative rounding

Because the practical application of the overall normative M_na should be rounded up or down by 0.5 min, we receive M_na^R. Rounding down the process duration increases the risk of not completing the process on time while rounding up risks wasting time. As a rule, rounding up is used, but by using the PERT method, it is possible to round down the time if the difference between the σ_CP and the rounded amount is more than 0, i.e., Δ_R > 0, calculated according to (15). Rounding down the can reduce time wasting with almost unchanged delay risk.

$${\Delta }_R={{\sigma }_{CP}-(M}_{na}-M_{na}^d);if {\Delta }_R>0 \to round down;if {\Delta }_R \le 0 \to round up$$

(15)

where

• M_na^d—duration rounded down.

4. Data and Results

The proposed methodological process should be verified via the addition of the values obtained according to the method in Section 3.1. The values will be linked to the specific line section on which the introduction of alternative drives is being considered, specifically Bratislava main station (BA), Dunajská Streda (DS) and Komárno (KN). The line can currently be considered as partially electrified with 25 kV AC voltage with a length of 100 km (126/125 min of travel time), while only short sections of BA, Bratislava-Nové mesto (BANm) (5 km; 7 min of travel time), and KN, Komárno-závody (KNz) (3 km; 4/3 min of travel time) [36], is electrified. It is a case study.

For the introduction of MUs with an alternative propulsion on this line, certain measures would be necessary [7]. In the case of a BEMU, this is the electrification of the BANm—DS section, and the electrification of this section would also be suitable for freight transport purposes due to the intermodal terminal located in DS. In the case of the FCMU operation, it is the location of hydrogen stations. The siding of MU would be within the existing localities with the investments considered according to the standards. The duration values of the alternative propulsion will be compared with the operation of the EMU. The DMU has almost the same features as the FCMU in this concept.

The verification of the methodology relates to the technological procedure for the turnaround, starting and ending train. Due to the limitation of the scope of the paper, the technological procedures and their quantification are valid for both stations, with the exception being the train turnaround where charging has to be counted within the BEMU. Obviously, more accurate data would be if the process for each tariff point is quantified separately.

The type (standard) vehicles used for recording are as follows:

• EMU—Škoda RegioPanter 661, n_a^t = 12 axles,
• BEMU—Škoda RegioPanter BEMU, n_a^t = 8 axles,
• FCMU—Alstom Coradia iLint, n_a^t = 8 axles,
• HDMU—J-TREC Sustina Hybrid, n_a^t = 8 axles [37].

Most of the input data for the evaluated workflow were recorded practically in real conditions using a combination of chronometric and instantaneous observation methods. The authors of this paper and employees of the transport companies in Slovakia and the Czech Republic took part in the measurements after the briefing. The recording tool was a stopwatch and a list of recorded activities, and each activity was recorded repeatedly (about 50 times) under different conditions in winter and late spring. The recorded data were supplemented by data from the scientific literature and existing standards. On the basis of the observations, the sequence of the process activities was determined and discussed with railway operation technologists and experts.

Table 3. Activities of technological processes, their durations μ_ij and standard deviation σ_ij.

Full Activity Name	Abbrevation	EMU 12 Axles		BEMU 8 Axles		HMU 8 Axles		HDMU 8 Axles
		μij	σij	μij	σij	μij	σij	μij	σij
A brake test-complete	BTC	3.083	0.250	3.083	0.250	3.083	0.250	3.083	0.250
A brake test-simple	BTS	0.917	0.017	0.917	0.017	0.917	0.017	0.917	0.017
A departure train path	DTP	1.417	0.583	1.417	0.583	1.417	0.583	1.417	0.583
A stand-by mode (de)activation	SB	0.319	0.038	0.319	0.038	0.000	0.000	0.000	0.000
Activation of the cabin (cockpit)	AOC	1.698	0.048	1.758	0.035	1.702	0.032	1.695	0.018
Activation of the MU	AMU	1.150	0.067	1.113	0.033	1.142	0.025	1.217	0.047
Boarding and unlocking of MU	BU	0.427	0.030	0.427	0.030	0.430	0.030	0.430	0.030
Conductors introduction to traindriver	CI	0.123	0.007	0.123	0.007	0.123	0.007	0.123	0.007
Deactivation of the cabin	DOC	1.430	0.063	1.427	0.047	1.412	0.038	1.350	0.033
Deactivation of the MU	DMU	1.202	0.042	1.217	0.033	1.217	0.033	1.237	0.033
Deferral of personal things	DPT	0.425	0.042	0.425	0.042	0.425	0.042	0.425	0.042
Departing train process	DT	0.500	0.000	0.500	0.000	0.500	0.000	0.500	0.000
Diesel refuelling	DR	0.000	0.000	0.000	0.000	0.000	0.00	14.833	0.833
Electric cable connection (static plug)	ECC	0.000	0.000	0.000	0.000	1.627	0.024	1.491	0.043
Electric cable disconnection	ECD	0.000	0.000	0.000	0.000	1.627	0.024	1.491	0.043
Engine/FC preheating	EFP	0.000	0.000	0.000	0.000	8.167	0.500	9.750	0.917
Faecal maintenance	MF	5.737	0.437	5.737	0.437	5.737	0.437	5.737	0.437
Getting off passengers	GOf	1.083	0.250	1.083	0.250	1.083	0.250	1.083	0.250
Getting on passengers	Gon	2.333	0.667	2.333	0.667	2.333	0.667	2.333	0.667
Hydrogen refuelling	HR	0.000	0.000	0.000	0.000	15.333	1.333	0.000	0.000
Hygienic maintenance	MH	15.840	0.480	10.560	0.320	10.560	0.320	10.560	0.320
Informing of passengers	IP	2.167	0.500	2.167	0.500	2.167	0.500	2.167	0.500
Interior tempering/AC-ing	ITA	7.833	2.500	7.833	2.500	7.833	2.500	7.833	2.500
Leaving of the MU	LM	0.292	0.015	0.292	0.015	0.292	0.015	0.292	0.015
Leaving of the MU with a locking	LML	0.427	0.030	0.427	0.030	0.427	0.030	0.427	0.030
Readiness to shunting report	RRS	0.083	0.003	0.083	0.003	0.083	0.003	0.083	0.003
Shunting to refuelling stations	Sr	3.307	0.116	3.307	0.116	3.307	0.116	3.307	0.116
Shunting to sidling/depot	Ss	2.700	0.067	2.700	0.067	2.700	0.067	2.700	0.067
Shunting to station	Sst	4.885	0.378	4.885	0.378	4.885	0.378	4.885	0.378
Shunting train path	STP	1.133	0.367	1.133	0.367	1.133	0.367	1.133	0.367
Static recharging time	Rs	0.000	0.000	9.855	0.000	0.000	0.000	0.000	0.000
Submission of documentation to driver	SD	0.122	0.005	0.122	0.005	0.122	0.005	0.122	0.005
Take the personal things	TPT	0.425	0.042	0.425	0.042	0.425	0.042	0.425	0.042
Technical inspection-external	TIE	4.396	0.100	2.931	0.067	3.173	0.059	4.067	0.093
Technical inspection-internal	TII	1.822	0.082	1.215	0.055	1.204	0.042	1.209	0.041
The MU interior inspection	MII	2.164	0.088	1.443	0.059	1.443	0.059	1.439	0.049
The MU state familiarisation	MSF	0.745	0.025	0.752	0.018	0.752	0.018	0.752	0.018
Train arrival at the station	TA	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Train documentation (conductor)	TD	0.878	0.038	0.585	0.025	0.585	0.025	0.585	0.025
Train documentation in the cabin (driver)	TDC	0.381	0.037	0.381	0.037	0.390	0.037	0.390	0.037
Unblocking of passengers’ doors	UD	0.080	0.000	0.080	0.000	0.080	0.000	0.080	0.000
Walking between cabins	WBT	1.514	0.022	1.009	0.015	1.026	0.015	1.039	0.020
Water refuelling for the bathroom	WR	12.167	0.833	12.167	0.833	12.167	0.833	12.167	0.833

Source: Authors in cooperation with [3,4,6,33,38,39].

shows the output from the recording of the duration of the individual activities involved in the investigated processes or the duration of existing norms. The table gives the activity name, abbreviation of the name, duration μ_ij and standard deviation σ_ij for a model MU of a particular propulsion system with n_a^t. Agent-dependent activities are highlighted in pink colour.

The process workflows of a particular process and their quantification are tabulated in the following subsections (

Table 4. Technological process of turnaround train.

ID	Name	PR	ID	Name	PR	ID	Name	PR	Value	EMU	BEMU	FCMU	HDMU
11	TA+UD	-	14	WBT	13	17	TDC	16	MCP	7.4920	7.044/TSR	6.999	6.943
31	Gon+Gof	11	15	AOC	14	24	SD	17, 23	Σμa	1.514	1.009	1.026	1.039
21	MII	11	23	IP	22	18	DPT	24	Σμ0 = b	5.978	6.035	5.973	5.904
12	DOC	11	16	BTS	15	42	DT	31, 41, 24, 18	a	0.126	0.126	0.128	0.130
13	DPT	12	41	DTP	11	61	Rs (KN)	-	σCP	0.270	0.196	0.184	0.171
22	TD	21								[min]
CP	EMU	11 → 12 → 13 → 14 → 15 → 16 → 17 → 24 → 18→ 42							Function	EMU	0.126 × ldMU + 5.978; (±0.270)
	BEMU									BEMU	0.126 × ldMU + 6.035; (±0.196) or TSR
	FCMU									FCMU	0.128 × ldMU + 5.973; (±0.184)
	HDMU									HDMU	0.130 × ldMU + 5.904; (±0.171)

Source: Authors.

,

Table 5. Technological process of starting train.

ID	Name	PR	ID	Name	PR	ID	Name	PR	Value	EMU	BEMU	FCMU	HDMU
11	TIE	-	41	STP	11	31	Gon	111	MCP	20.347	20.894	28.552	28.910
12	ECC	11	52	EPH	18	23	TD	22	Σμa	7.732	5.155	7.030	7.805
13	BU	12	19	BTC	18	113	WBT	112	Σμ0 = b	15.615	15.739	21.522	21.105
14	TII	13	42	RRS	19, 52, 41	24	IP	23	a	0.644	0.644	0.879	0.976
15	DPT	14	110	Sst	42	114	AOC	113	σCP	1.142	1.024	1.733	1.714
16	AOC	15	111	AT+UD	110	25	SD	114, 24		[min]
17	MSF	16	21	CI	111	43	DTP	110
51	ITA	15	22	DPT	21	44	DT	51, 31, 25, 43
18	AMU	17	112	DOC	21
CP	EMU	11 → 13 → 14 → 15 → 16 → 17 → 18 → 19 → 42 → 110 → 111 → 21 → 112 → 113 → 114 → 25 → 44							Function	EMU	0.644 × ldMU + 15.615; (±1.142)
	BEMU									BEMU	0.644 × ldMU + 15.739; (±1.024)
	FCMU	11 → 12 → 13 → 14 → 15 → 16 → 17 → 18 → 52 → 42 → 110 → 111 → 21 → 112 → 113 → 114 → 25 → 44								FCMU	0.879 × ldMU + 21.552; (±1.733)
	HDMU									HDMU	0.976× ldMU + 21.105; (±1.714)

Source: Authors.

and

Table 6. Technological process of ending train.

ID	Name	PR	ID	Name	PR	ID	Name	PR	Value	EMU	BEMU	FCMU	HDMU
11	AT+UPD	-	12	Sr	23,42,31	51	MH	15	MCP	38.360	32.066	35.235	33.728
31	Gof	11	13	WR	12	01	MF	15	Σμa	18.882	12.588	12.588	12.584
41	STP	11	14	RD/RH	12	17	TDC	16	Σμ0 = b	19.478	19.478	22.647	21.144
21	MII	11	43	STP	12	18	DMU/SB	17	a	1.574	1.574	1.574	1.573
22	TD	21	44	RTS	13, 14, 43	19	TPT	18	σCP	1.712	1.510	2.010	1.500
42	RTS	41	15	Srs	44	110	ECD	19		[min]
23	TPT	22	16	COD	15	52	LL	110, 51, 01, 19
24	LM	23
CP	EMU	11 → 21 → 22 → 23 → 24 → 12 → 13 → 44 → 15 → 51 → 52							Function	EMU	1.574 × ldMU + 19.478; (±1.712)
	BEMU									BEMU	1.574 × ldMU + 19.478; (±1.510)
	FCMU	11 → 21 → 22 → 23 → 24 → 12 → 14 → 44 → 15 → 51 → 52								FCMU	1.574 × ldMU + 22.647; (±1.574)
	HDMU									HDMU	1.573 × ldMU + 21.144; (±1.500)

Source: Authors.

). The duration values are based on Table 3. Table 4, Table 5 and Table 6 are divided into four parts. The white columns on the left top side of the table represent the technological workflow of a given process (divided into three columns) where the activity identifier (ID), the abbreviated name (“Name”) and the predecessor (“PR”) are given. The green part of the table on the top right shows the process output values for each propulsion under the research achieved by PERT, particularly the total normative M_CP, agent-dependent activities duration Σμ_a, independent activity duration Σμ₀ = b, increment parameter a and standard deviation σ_CP. The blue area on the bottom left of the tables shows the CP that may be shared by several researched propulsions, and the pink area on the bottom right shows the process duration functions for each propulsion. These functions can be illustrated graphically.

4.1. Technological Process of the Turnaround Train

The train turnaround process is a set of activities carried out between two consecutive on-track performances of one MU, while the vehicle is not parked. Usually, it is a return journey. The turnaround consists of only the most necessary technological activities to dispatch a train back to the performance [6]. Table 4 describes and quantifies the technological process of the turnaround train.

The simplified MU turnaround process consists of 16, usually complex, activities. The critical path is the same for each drive and consists of 10 activities. In the case of the BEMU, the values achieved from the linear function need to be compared with the value from the T_R^S (14), determining the static charging time. Figure 2 shows a simplified PERT (CPM) network graph for the HDMU. Due to the limitations of the scope of the paper, this is the only one example graph.

In Figure 3, there is a graphical representation of the function of the dependence of the MU length and the duration of the turnaround train process for each propulsion. The red line represents the battery recharging curve important for BEMU. The red “turning point” represents the value of the length as well as the time since when the static charging in the KN has been longer than the turnaround process itself. The minimum required turnaround time is almost the same for all propulsions, raising according to n_a is minimal (from approx. 5–8 min); however, the exception is the static charging of the BEMU.

4.2. Technological Process of the Starting Train

The starting train technology is a set of prescribed activities to ensure that the vehicle will be ready for on-track performance according to specified safety, qualitative and technical requirements. The methodology quantifies the duration of the originating train from the depot/siding track [6]. Table 5 describes and quantifies the technological process of the starting train.

The simplified technological process of the starting train consists of 26 activities. The shared CP have BEMUs and EMUs within, with similar output values. The FCMU and HDMU also share a similar CP but with more visible temporal differences. The most notable are the activities related to the shunting and preparation of the MU for operation. Figure 4 is a graphical representation of the functions in the form of curves. The increase in duration with respect to vehicle length is steeper than for the turnaround. The process for the HDMU and FCMU takes fundamentally longer and the curves are not very parallel compared to the BEMU and EMU as well.

4.3. Technological Process of the Ending Train

Ending train technology is a set of prescribed activities to ensure the safe siding and locking of a vehicle (MU) after an on-track performance while waiting for an extensive time period for the next on-track performance, most often on the next day [6]. Table 6 describes and quantifies the technological process of ending train.

The simplified technological process of the ending train consists of 22 activities. The CP is shared by BEMUs and EMUs (11 activities), which is different from the CP shared by FCMUs and HDMUs (11 activities). Figure 5 is a graphical representation of the functions in the form of curves that are relatively parallel. The time of the BEMU and EMU is almost identical (20–50 min). The longest duration arises for the HDMU due to the demanding hydrogen refuelling process, which takes more time than water or diesel refuelling (23–54 min).

4.4. Process Duration Rounding

Table 7. Duration time rounding.

Multiple Unit	Turnaround Train Process			Starting Train Process			Ending Train Process
	MCP Round	Mna	MnaR	MCP Round	Mna	MnaR	MCP Round	Mna	MnaR
EMU BA/KN	7.5	7.997	8.0	20.5	25.919	26.0	38.0	44.654	44.5
BEMU—BA	7.0	8.053	8.0	21.0	26.043	26.0	32.0	44.654	44.5
BEMU—KN	9.5	13.582	14.0
FCMU BA/KN	7.0	8.025	8.5	28.5	35.582	35.5	35.0	47.823	47.5
HDMU BA/KN	7.0	7.982	8.0	29.0	36.715	37.0	33.5	46.312	46.0

Source: Authors.

presents the results of applying the process duration function (13/14) at M_na(n_a = 16 axles) and also applying the rounding Formula (15). The input values or the process duration function with the fitted values are included in Table 4, Table 5 and Table 6. By comparing the values of M_CP and M_CP round and M_na and M_na^R, respectiviely, it is possible to see the way of rounding (up or down). For example, within the ending train, due to the large σ_CP, it was possible to round all values down.

5. Discussion

The paper aimed to solve the insufficiently solved problem of the train processing technological times, i.e., local processes, which are necessary for ensuring the operation of PRT, especially in terms of alternative propulsions. The problem is addressed by a unique methodological procedure proposed and validated within the paper. The procedure is developed for the needs of quantification of local technological processes of train processing operated by MU. The proposed methodology is applicable not only for conventional propulsions but also for alternatively powered MUs, taking into account the specific requirements of the BEMU.

The new methodology consists of three main steps, namely, process mapping and valuation, process duration evaluation by using PERT and the application of PERT outputs to achieve the final results. In the case study in chapter 4, it is shown that the methodology is applicable based on the utilisation of real duration values of the turnaround, starting and ending train for EMU, BEMU, FCMU and HDMU.

PERT is preferable to CPM for projects with high uncertainty because it uses three-time estimates (a_ij, m_ij, b_ij) to improve the prediction of the activity duration. This approach allows a more realistic consideration of the risk and variability, which is useful for complex projects or processes where the current deterministic CPM approach may not be sufficiently accurate. It also has the advantage of more accurately interpreting complex activities, parts of which are performed by personnel in different sequences [40]. The effect of using PERT is limited by the incorrect estimation of many activities or incorrect recording [22].

The Gantt chart method is a suitable and simple method for determining the overall normative and interpretation of a process, but not for determining the CP, especially when the process consists of a large number of activities with a large variation in duration [33].

A small or too big value of n_a limits the validity of the function. The CP may be different from that of n_a^S, and thus the function (13) may be different as well. By changing the function to a function other than linear, it might be possible to capture these deficiencies. This solution may be suitable for the establishment of the M_na for several tariff points with relatively similar conditions. In this case, the CP of a given process is calculated repeatedly at different numbers of axles, and a function and curve are constructed based on the values obtained. Future research may also improve the methodology, especially in the context of a function that currently may not provide exact values for very large or small n_a.

Another limitation is the lack of experience with the operation of alternative propulsions and the lack of data sources. With more accurate and up-to-date data, the methodology can provide more accurate and reliable results and its validation would be more unambiguous. A recommendation is the regular recording of activities and actualisation of workflows and data.

The limit of the paper’s scope results in the recorded values being valid for both observed stations (BA and KN), with the exception being the BEMU turnover within KN, where due to charging, the duration is based on the curve according to function. Each M_na duration after rounding should represent the most plausible duration of the process in a particular station with similar conditions.

Looking at the components of the function or its graphical interpretation, it can be seen that the differences between the durations are not very substantial concerning the MU propulsion. The main reason for this is the similarity of the activities performed by modern MUs, which are developed based on international standards, where the specifications related to their propulsion have only a minimal impact on their control. The exceptions are the activities related mainly to the recovery of the range of the vehicles or the achievement of the operating temperature.

Looking at the graphical interpretation of the process duration functions, it can be deduced that the BEMU and EMU processing times are very similar, and in many cases, the FCMU and HDMU durations are also similar to each other. They often have similar CP. By applying the methodology to different MU propulsion, it is proven that the methodology is universally applicable; however, the specifications of the individual propulsion must be taken into account, e.g., BEMU charging, where it is essential to compare the turnaround time consisting of the normal activities with the charging time (14). The HDMU is operationally almost identical to the DMU.

Based on the research, it can be argued that the MU propulsion has a minimal effect on the duration of the sharp turnaround and that the process times are very similar for all propulsions. The exception is the charging of the BEMU, where the duration of which must be compared with the duration of the BEMU turnaround process. All four propulsions share a CP, with most of the activities performed by the train driver.

The duration of starting train processing for the BEMU and EMU couple is almost the same in terms of both the time and operations. The duration rates of the FCMU and HDMU couple are also similar, but they are significantly higher than the previous couple. In addition, from the fo axles, the HDMU starting process takes longer than the FCMU. The most important activities of the starting train are related to vehicle activation, preheating the engine or FC, shunting, cab changing and so on.

The ending train technology lasts the longest of all the drives with the steepest gradient, due to the high value of parameter a. The curve gradient is parallel, with FCMUs and HDMUs achieving the longest M_na. The high duration values are mainly due to activities such as refuelling, hygienic maintenance of the vehicle and repeated shunting. Based on a survey of the MU turnaround times provided by carriers, it can be concluded that the estimation of turnaround times used is not systematically determined and that it is a random value of the duration that minimises the number of vehicle fleet requirements [9]. The quantification of other local processes used to be performed by composing general standards that do not sufficiently cover local conditions and had very inaccurate values [41]. However, the process durations obtained in this paper are similar to the durations in the conditions of the Žilina station studied in the thesis [33].

Due to the stochasticity of the values, there is a standard deviation σ_CP that allows the duration to be rounded down according to Relation (15). Rounding down can save time, reduce resource wastage and increase operational efficiency. By applying the output of the methodology, operational risks associated with the non-acceptance of process times can be avoided, which can have very negative consequences when introducing, in particular, alternative propulsions with a low level of operational experience. The proper usage of M_na will support the sustainability of MU operation with both alternative or conventional propulsion.

6. Conclusions

The paper proposes a unique methodological procedure for the quantification of technological processes of train processing in PRT—local processes in the case of using MUs with conventional or alternative propulsion. The expected benefits of the application of this methodology are as follows:

• a new and simple method for quantification of local processes, suitable for transport carriers or technologists;
• a modifiable method for evaluating local processes;
• the ability to determine reliable technology times concerning various external influences during the operation of MU with various propulsion system;
• seamless planning, preparation and implementation of alternative propulsion in real PRT operations;
• a method for controlling, updating and optimising processes and activities,
• the possibility of creating general valid overall normative for a specific propulsion and process, e.g., one time for several stations;
• reducing operational risks associated with non-compliance with process times and optimal working procedures.

The first step is process mapping, where the methodology for collecting activity data and creating a valuated workflow that is suitably represented for the purposes of the PERT method is established.

The second step is analytical. Through the PERT method, the important values are determined through CP defining the duration of the whole specific process using the model vehicle. The important PERT outputs for the proposed procedure are CP, total normative M_CP, duration of dependent activities Σμ_a and independent activities b and standard deviation σ_CP.

The third step is the application of the process output values, consisting of creating a process-specific duration function for a particular propulsion (13/14). Based on the incremental parameter a and the duration of the independent activities, the function allows us to estimate the duration of the process for MU with the number of axles n_a. The function can also be interpreted as a linear function curve. Each propulsion and process has to be quantified separately.

This paper demonstrates that network analysis methods of project management can be used for process management. It is possible to use a single workflow for all propulsions, but all activities must be included and correctly sequenced. Those that are not executed for a given propulsion result in μ_ij = 0 and σ_ij = 0.

When evaluating the BEMU or FCEMU turnaround at the charging station, the M_na of the sharp turnaround function should be compared with the static recharging time T_R^S, with the longer time being crucial. The static charge time is usually longer, but for short MU or low energy charging, the sharp turnaround time may be longer than T_R^S. In the case study conditions, the reversal occurs from five to six axles at the KN station.

Due to the stochasticity of the input values, the resulting process duration is defined also by σ_CP, which allows M_na to round down according to Relation (15) when Δ_R > 0. The validation of the methodology has shown that for longer processes or processes consisting of high variance activities, such as the ending train, the possibility of M_na rounding down is more likely.

The shortest process duration represents the duration of independent activities belonging to CP at n_a = 0. The longest process duration is at na = 20 (maximum studied length), thus the longer the MU, the longer it takes to execute the processes. The gradient of the curve depends on the number and sum of the duration of agent-dependent critical activities The gradient of the curve depends on the number and sum of the duration of agent-dependent critical activities. In the case of turnaround, the gradient is slight and with a = 0.126 – 0.130; in the case of starting, the gradient is more significant and with a = 0.644 – 0.976. The ending train processing has the most pronounced curve gradient when a = 1.573 – 1.574.

The paper did not demonstrate that the duration of the process depends on the number of its activities. Thus, the duration of the process is mainly influenced by the nature of the activities, the sequence of activities and the length of the vehicle. For example, the starting train FCMU (26 activities) M_na^R (8) = 28.5 min and the ending train FCMU (22 activities) M_na^R (8) = 35 min. The MU propulsion has the greatest impact on the structure and duration of the ending and starting train process, where the differences are most pronounced. The BEMU and EMU show very similar values, with the exception being recharging T_R^S.