Structure of Public Passenger Transport Lines in the Region of Prešov in Slovakia to Support the Development of an Integrated Transport System

Abstract

In the framework of sustainable development, the most important goal in the transport sector is sustainable mobility. It is necessary to improve the quality of the means of transport and the organisation of their operation in transport systems in addition to the management systems, coordination, and integration of individual types of transport. The aim of this paper is to propose a complex system of public transport lines in the region to achieve an effective transport service, in accordance with the principles of sustainable mobility, supporting the development of an integrated transport system. This research presents a proposal for the public transport lines of the region of Prešov in Slovakia, which is currently connected to an integrated transport system (IDS Východ). The proposal is defined by the tracing and functions of the lines, the mode of transport and headways on individual lines, the necessary number of vehicles for the operation of individual lines, transfer times at relevant points and directions, and the border of the radius of attractive daily commuting to the centre of the region, as well as a rough timetable for each line. Using an analytical hierarchical process (AHP method), we determine the two most suitable variants of traffic services. The results indicate that based on the multicriteria evaluation of these variants using descriptors, it is possible to determine the optimal variant of the transport service of the region, which will be introduced into a functional integrated transport system.

1. Introduction

Public transport is considered an important backbone of sustainable urban development, as it enables more efficient movement around cities. However, public transportation systems often struggle to provide a good level of service at an affordable price for public administration and users. These systems must provide a high quality of service that is attractive to users. They must also be affordable for low-income segments of the population. To achieve this objective, public systems inevitably require subsidies, which society is increasingly questioning [1].

Public passenger transport is an important area of public service that affects the standard of living and lifestyle of a population. As a mediator of transport relations in a territory, it influences the formation and development of settlements, economies, and landscape structures [2]. The efficiency of a transport system depends on several elements, such as the available technology, government policies, planning processes, and control strategies. The interaction between these elements is quite complex, which results in intractable decision-making problems [3].

The development of sustainable transportation is a priority in cities. Its objective is to increase the number of trips using public transport while minimising social costs and negative impacts on the environment [4]. However, operators often do not change the existing lines, stops, or timetables, which they justify based on passenger habits. This approach can create a mismatch between the availability and demand for public transport services. Therefore, planning and improving a public transport system should be based on a thorough analysis [5].

It is necessary to ensure the preference for public passenger transport over individual automobile transportation. The organisation and support of integrated transport systems is a trend in the public passenger transport sector [6]. The goal of integrated transport systems is to combine the advantages of individual types of transport and create a common, complex system of transport services in a defined region [7].

Regional public passenger transport is implemented within a larger territorial unit (e.g., a self-governing region) while ensuring connections between individual settlements in the region, especially between larger cities and between each municipality and its catchment city [8]. Regional transportation has become increasingly important. Current urbanisation processes place great demands on regional transport, as many people consider it more advantageous to live in smaller settlements in a region. This trend was made possible by automobile transport and rising living standards. In the case of passenger transport, it is therefore necessary to create mass transport systems capable of competing with individual automobile transport.

Line-planning models differ in terms of the decisions involved (determining train routes, setting frequency of trains, or both) and take into consideration infrastructural and operational aspects, objective functions, and the way passenger decisions are considered in the decision-making process. The goal of route planning is to determine routes that are regularly served by a vehicle (trains, buses, trams, etc.) and the frequency of these connections. Route planning is a strategic public transport problem that was addressed early in the development of conventional public transport. The result, the so-called line concept, is then used as a basis for further decisions such as scheduling and vehicle planning. A condition for the design of public passenger transport lines is knowledge of the transport behaviour of the region’s inhabitants, its causes, and development forecasts [9].

The proposal of a public transport system is a two-level optimisation problem. At the higher level, the system is designed by the operator, and at the lower level, passengers in the system choose travel that optimises their individual goal function. The general transportation trend in recent years has been that the performance of public passenger transport has decreased at the expense of individual motoring, which is much more popular among residents than mass transport. As public transport service providers are limited by the constraints of already developed networks, their strategic actions are limited.

This contribution is focused on the design of the structure of public passenger transport lines to support the development of an integrated transport system. For the de-sign of public passenger transport lines in the region, scientific methods are used, such as the method of collecting and processing information, analysis, synthesis, visualisation of processes, and abstraction (when determining the specific quality factors of a new system of public transport lines, induction; when creating a general model of an effective system of lines, benchmarking; when comparing the approach to the creation of public passenger transport systems in different regions, benchmarking; when comparing the approach to the creation of public passenger transport systems in different regions, brainstorming; during consultations regarding the methodology of the proposal of public passenger transport lines with researchers and people from professional practice, graph theory), when modelling the transport network and external influences of public passenger transport, and the main method used in this research is the AHP method (analytical hierarchical process) for the evaluation of the proposal for practical purposes—the selection of the optimal transport service system for the region. This proposal is applied to the case of the region of Prešov in Slovakia, which is currently involved in an integrated transport system (IDS Východ). The proposal is aimed at building a comprehensive transport service system in addition to the proposal of new regional lines in the region and a new timetable. The determination of optimal traffic serviceability with the proposal of complex changes in traffic serviceability based on the original traffic serviceability on a specific route is a direct application of the proposal together with the resulting multicriteria evaluation of the variants within the framework of the AHP evaluation method. The methodology focuses on four main criteria, which are the accessibility of transport, the quality of transport from the passenger’s point of view, the costs of the public sector, and the impact of transport on the external environment, which covers environmental factors. The methodological procedure consists of two main steps: the proposal of routing functional layers of public passenger transport and determining the optimal traffic service of the line being addressed. In the framework of the proposal for the functional routing of the layers of public passenger transport, it belongs to the design of regional lines in the addressed area, the proposal of a timetable for the functional integrated transport system, and determining transfer points in the area. It belongs here as part of determining the optimal traffic service by determining the criteria of individual variants, determining the weights of criteria and subcriteria, calculating the utilisation of variants, and selecting the optimal variant.

The proposed methodology is applicable to any region, considering its traffic and geographic, economic, social, cultural, and historical specificities, as well as the development potential of the region in the case of a suitable setting for the traffic service system. The main goal of this research is to develop a methodological procedure for the design phase of planning a public passenger transport system that assumes continuity with the already completed analytical phase. At the end of this research, the procedure is demonstrated on the example of a real integrated functional territory (Prešov Region) and is solved on the basis of the simultaneously solved problems of transport services in the Prešov Region, optimisation of public transport lines, and optimisation of the timetables of railway passenger transport carriers, suburban bus transport, and urban public transport, which will be part of the newly built integrated system IDS Východ.

Currently, the integrated transport system IDS Východ operates only in the region of Košice, but in the coming days, the region of Prešov will also be involved in this integrated transport system. The critical aspects of the current infrastructure system are poorly set timetables that cannot be coordinated within the integrated transport system. Therefore, there is a need to optimise the infrastructure system. As part of the coordination of timetables, it is necessary to adjust the arrivals and departures of trains and buses into the functional system, considering the usual habits of passengers in this region and the requirements of carriers and customers of transport services. The aim of this research is to connect the needs of passengers, carriers, and customers of transport services and transform them into a complex and high-quality model of transport service for the territory, which is defined by the routing and functions of lines, the type of transport and the intervals of connections on individual lines, the number of vehicles (sets) required for the service of individual lines, transfer times at relevant points and directions, the limit of the radius of an attractive daily commute to the centre of the region, as well as the general timetable on each line.

An innovative part of our research is the creation of a new form of multicriteria evaluation in the form of determining descriptors on an evaluation scale that always compares the paired importance of the criteria and their weights and respects the current traffic, socioeconomic, and natural specifics of the territory served by the proposed line, as well as its potential, especially in terms of labour mobility strength, time losses, and the health risks of residents resulting from the unproductive and stressful spending of time in transport, or from the point of view of the development of tourism. The limitations of our research result from the usual habits of the travelling public, since when creating or optimising traffic services in a region that is to be part of an integrated transport system, it is necessary to start from the original traffic services, knowledge of the area being addressed, and the usual habits of the travelling public, adapting the proposal to the requirements of the interested parties (operators, contractors of public passenger services, and passengers) and the needs of the travelling public. All these aspects must be connected to create a high-quality traffic service in the territory and an effective integrated transport system.

This article is divided into several sections. The Introduction section provides a general view of public transport, with a primary focus on regional transport and its line formation. Also described here is the methodology creation process and approach to the design of traffic services with a connection to an integrated transport system.

The Literature Review section provides an overview of the research with a similar focus on this issue, which points to the differences and innovativeness of individual research.

The Research Background section contains the background of solving the theoretical transport service problems of the territory and a description of the currently solved problems of the transport service of the Prešov Region in Slovakia.

The Methodology section is focused on the basic procedures of the design of the transport services of the territory, supported by the development diagram of these routes and the multicriteria evaluation of the variants of the transport services.

The Results section represents the application of the proposed methodology to a case study focused on the region of Prešov. This section contains a proposal of regional lines and a fragment of the proposed timetable, the determination of the optimal transport service for a specific line, the determination of the weights of criteria and subcriteria, the determination of the variants for multicriteria evaluation, and the resulting multicriteria evaluation of variants.

The Discussion section evaluates the individual procedures for the design of the transport services of the territory, as well as the advantages and disadvantages of the chosen evaluation method.

The Conclusion section approximates the complexity of this research and refers to the definition of existing limitations and possibilities for further research.

2. Literature Review

Trip planning is a key process in public transport, wherein passengers are informed how to best use a given public transport system for their individual travel needs. A common feature of most available journey planners is that they assume deterministic travel times; however, public transport vehicles often deviate from their schedules. In a previous study [10], the problem of finding path plans in a stochastic environment was investigated. To take full advantage of the flexibility inherent in multiservice public transport systems, the authors suggest using a routing concept instead of a linear route plan.

One of the basic problems in the strategic planning of public and railway transportation is the line-planning problem [11] for determining the system of lines and related frequencies. The goals of the planning process are typically multiple and often conflicting. The operator wants to minimise costs, while passengers want to have the smallest possible fares, without any or with only small transfers between different lines. Previous research [12] has combined route-planning models and a transport assignment model to overcome this problem. Public transport planning at the strategic level refers to the design of a public transport network, which includes the determination of public transport stations and the development of public transport routes [13]. The modelling and solution planning of public transport lines have been described in [14]. Network designs can respond to slight fluctuations in passenger demand if designed robustly [15]. In previous research [16], the authors showed that, instead of further optimising each individual step, it would be more beneficial to consider the entire process in an integrated manner. The authors proposed a custom model that they applied to three planning phases and showed how it can be used to design iterative algorithms as heuristics for an integrated problem.

The planning process for public transport is the first step of the route design, and schedule calculation is the second step. Finally, the vehicle and crew schedules are planned. The authors proposed a change in the order of the classic sequence of the planning steps. In their new approach, they first designed vehicle routes, divided them into lines, and finally calculated a (periodic) timetable [17]. A more detailed overview of line-planning concepts and models is described in [18]. In [19], the challenges of network design, operational planning, and control of intelligent public transport systems were discussed.

Defining suitable lines in a public transport system (bus, rail, tram, or metro) is an important real-world problem. The authors in [20] investigated the problem of designing lines in a public transport system, wherein they included the user’s optimal choice of route [21].

There have been many studies aimed at optimising the network of public passenger transport lines using linear programming models and optimisation algorithms [22]. The authors in [23] presented a mixed-integer linear programming model that they developed to design tools for finding solutions for planning lines and timetables in automated urban metro networks. Despite the recent progress in the field of automatic public transport route optimisation, there is a clear gap between the development of optimisation algorithms and their applications in real planning processes [24]. For each planning area, the approach in [25] uses a network reduction process that requires relatively few network evaluations. The network reduction process begins with a network of the shortest lines. The lines are then gradually deleted, merged, or shortened using an optimisation algorithm. Nonlinear integer formulations for power lines that connect main lines and minimise transfer times were investigated in [26]. Further research [27] resolves the public transport network model based on layer operations; Ref. [28] solves the network route design of a public transport system with network evolution; Ref. [29] solves metro network expansion using deterministic and robust optimisation models; Ref. [30] deals with real-time optimisation of urban rail transit train scheduling via advantage actor-critic deep reinforcement learning; and Ref. [31] deals with collaborative optimisation of passenger flow control and bus-bridging services in commuting metro lines.

Line planning determines the critical service contents of a passenger railway schedule. In real-world scenarios, passengers’ travel expectations or preferences of service quality tend to be heterogeneous among different origin–destination (in short O-D) pairs or even in the same O-D pair, which requires railway operators to schedule train services catering to those diverse passenger demands. However, previous line-planning approaches either treated passengers homogeneously or roughly divided simple passenger groups by travel purposes or service types. In [32], the authors focused on each passenger O-D pair as an individual O-D market and proposed a line-planning approach where they concluded train lines can deliver matched service levels of trains for each O-D market. Based on the set-covering problem (in short SCP), we establish a novel bi-objective mixed-integer linear programming (in short MILP) model that considers the benefits of both railway operators and passengers. Multiple service qualities for each passenger O-D pair, such as travel speed, direct or transfer connection, frequency, price, etc., are seen as the objects to be “covered” by train lines to achieve a more accurate supply–demand match.

Today, the planning of metropolitan areas considers improving the quality of life of their inhabitants, and urban mobility is one of the main concerns. Studies point out that investments in public transportation and other modes are aimed at the overall improvement of mobility. However, there is a gap in the proper tools for optimising public transport networks. In fact, network optimisation is an NP-hard problem (in short a nondeterministic polynomial time problem), and there are usually many conflicting objectives that need to be optimised simultaneously. The authors in [33] proposed the use of many objective evolutionary algorithms to address the problem of public transport network optimisation, focusing on metropolitan bus lines. The proposal consists of optimising the position of bus stops and consequently obtaining new routes that pass through these stops to minimise the average travel time, the time spent between the origin and destination, and the variance of distance between the stops.

Integrating emerging shared mobility with traditional fixed-line public transport is a promising solution to the mismatch between supply and demand in urban transportation systems. In [34], the authors studied the problem of jointly optimising the timetable and the vehicle schedule within an intermodal urban transit network utilising modular vehicles (in short MVs) within the context of distributionally robust optimisation (in short DRO), which allows MVs to dynamically (de)couple at each stop and permits flexible circulations of modular units (in short MUs) across different transportation modes. The authors in [35] deal with the issue of the organisational structure of integrated transport systems. It addresses the issue of the responsibility, powers, and competences of the so-called participants in integrated transport systems. Finally, it also covers an important area, which is the transport service control system. Other research focusing on integrated transport systems deals with the methods of combining edges into transport lines within the framework of line formation for integrated timetables [36], the development stages of the creation of integrated transport systems [37], and information tools for integrated public passenger transport [38].

3. Research Background

The nature of transport is influenced by the dispersion of settlement. This has an impact on the transport service of a territory, the dispersion of investments, the costs of maintenance and operation, and thus the overall efficiency of public passenger transport. In accordance with European transport policy and national concepts of the development of transport networks, a process is underway towards the concentration of transport services in selected axes or corridors, both in extra-urban and built-up areas (intra-urban areas). When solving the issue of transport services, it is necessary to start with the natural characteristics of the region [39]:

• From the viewpoint of geographical location, which mainly affects the investment and operating costs of transport infrastructure, as well as the costs of operating transport on this infrastructure;
• From the perspective of population density, which affects the load on individual roads, density and intensity of transport, and number of connections;
• From the perspective of the territorial area of the region we want to serve;
• From the viewpoint of the economic structure (this creates conditions and possibilities for the economic and social development of the region);
• Access to transport routes (locations on main transport routes, locations in the centre of the state or region, and locations in peripheral zones and border areas).

One of the indicators of the quality of life in the region is the so-called work–life balance. The spatial relationship between work and housing characterises the potential demands for the transport process. Housing, work, and education are among the basic functions of the spatial organisation of the territory. The spatial distribution of population and jobs is equal only in exceptional cases of territorial planning. In most cases, the spatial discrepancy between residence and workplace is overcome by commuting to work. When commuting becomes unbearable in terms of transportation costs and time loss (combined with income), residents often change jobs, move to a new residence, or become unemployed.

Transport ensures operational links between the four functional components of the territory, namely, housing, workplace, civic amenities, and recreational/green areas. These components create surface zones in the territory with the predominant character of the function of a residential zone (urban or rural), production zones (industrial or agricultural), civic amenity zones (service centres, schools, hospitals, offices, or cultural events), and recreational zones (sports fields, swimming pools, parks, forest parks, cottage areas, etc.) [40]. Figure 1 shows the basic links between activities within the addressed territory.

The variant distribution of urban elements in the territory has an impact on the type and size of transport demand and supply. This is related to the issue of the placement of transport sources and destinations (whose weight is different). The interrelationships of functional elements generally change over time and in terms of their spatial inclusion. Among the main functional elements, i.e., residence, workplace, civic facilities, and recreation, they exist in specific conditions with mutual ties that can be evaluated both qualitatively and quantitatively. Trips tied to residence (as source or destination) make up 80–85% of all trips on personal transport.

In Slovakia, self-governing regions and municipalities, according to Act No. 56/2012 Coll. [41] on road transport, established an obligation to develop a transport service plan for a given territory through public transport. It precisely specifies the routes and frequencies of connections or the overall quality of transport services provided to the population. In contrast to Slovakia, in other countries, such documents represent real strategic materials, according to which individual municipalities are governed. These plans include not only the method of transport service but also specific goals for the future, such as increasing the number of transported passengers [42].

The customer of public passenger transport services on the railway is a public administration body or another person obliged to ensure the transport service of the territory. To ensure this, the customers of services conclude contracts for transport services in the public interest with the operators. Transport service refers to the provision of an adequate range of transport services in the territory defined in such a contract to ensure transport to work, schools, medical facilities, and offices and to satisfy cultural, recreational, and social needs. The reasonable scope refers to the number of connections per day, the accuracy and regularity of connections, and the capacity of vehicles on individual tracks and lines, which are determined by the customers to satisfy public demand on individual days of the week [43]. To ensure the availability of transport services, those ordering transport services draw up transport service plans. When drawing up a transport service plan, the legitimate demands of the public, capacity of the railway infrastructure, operational possibilities of the operators, possibilities of simultaneous transport, economy of public passenger transport, and possibilities of the public budget to compensate for operator losses are considered. The transport service plan primarily comprises the following [43]:

• Defining the territory of the transport service;
• Requirements for an adequate range of transport services;
• A method of solving parallel transport and ensuring continuity with transport services provided by other types of transport, especially bus transport;
• A method of compensating operators for the loss of transport services, payments from the budget, adjustments to fare tariffs, or granting exclusive rights to transport services;
• The goals and objectives of solving the disproportion between demand and supply in a certain area, including the need for investments in infrastructure;
• Measures to ensure coordination with other types of transport in the territory, particularly with bus transport.

Transport services refer to the creation of adequate transport services to ensure regular transportation. A reasonable scope refers to the number of connections per day and the accuracy and regularity of connections on individual bus lines to satisfy public demand on individual days of the week, while considering the possibilities of simultaneous transport and transfers, distances to stops, road capacity during the day, safety of transport, equipment, and the capacity of vehicles and fares for selected groups of passengers [41].

To ensure the transport service of the territory, the customer draws up a transport service plan and concludes service contracts with the operators. When drawing up the transport service plan, the customer takes into consideration the legitimate demands of the public, the operating railway and bus lines and their transport capacity or other capacity options of the operators, the technical condition of the roads on the route of the bus lines, the capacity options of the parallel rail transport, the economy of providing transport, and the financial possibilities of the public budget for payment of services in the public interest. When drawing up the plan, the customer cooperates with the rail transport customer to harmonise the capacity and operational options for rail and bus transport. The transport service plan primarily comprises the following [41]:

• A list of the planned bus transport lines in the public interest;
• The requirements for an adequate range of transport services;
• The method for dealing with parallel transport, measures to ensure coordination, and continuity with rail transport or urban rail transport;
• Method of calculation and provision of contributions to operators from the public budget;
• Options for adjusting the basic fare or granting exclusive rights to transport services on a certain bus line or certain stops;
• Solutions to the disproportions of demand and supply in the territory, including investments in the vehicle fleet, the technical base, and the organisation and routing of bus lines.

Providing public passenger transport services in areas with low population density is significantly economically inefficient. Sparsely populated areas are difficult to adequately cover with public passenger transport stops. If the distances between stops are adapted to dispersed demand, they will be too far from home for a large part of the population. If they are at the same distance as in the zones of compact development, too few people will board them. In addition, in this case, the journey by public transport will take significantly longer than when using individual automobile transport. Furthermore, if the buses are running half-empty, public passenger transport operators often try to reduce the cost per passenger by reducing the frequency of services. However, if the frequency of connections drops below a level that still allows users to choose travel times as needed, they will start using individual automobile transport, although it is perhaps too financially and time-consuming, and they would like to use public passenger transport. The potential for the use of demand-responsive public passenger transport connections is primarily in the service of sparsely populated rural estates in cases where regular transport is not used, so to speak, or would not be attractive to users due to the low transport offer. The concept of demand-responsive service could also be widely used in Slovak regions, whose topography is often characterised by a “main valley” with a concentrated concentration of settlements and “side valleys” with small settlements, where it is very problematic to operate public passenger transport in an efficient manner. Research [44,45,46] has identified demand-responsive transport (DRT) to meet the challenges and effectively improve mobility through the carpooling concept. Nevertheless, most of these DRT services are being explored in urban environments with high mobility demand and population density. Research in low-demand regions is rarely considered. In addition, applied DRT services bring several restrictions regarding stops, target groups of customers, or space restrictions. This paper therefore fills this gap through a spatial and temporal analysis of a real, fully flexible, and real door-to-door DRT experiment. Road analysis shows that unrestricted DRT service between major centres (or cities) results in major travel axes between these cities, while more remote areas lose mobility to these centres of public service provision. Consequently, a feeder system should be prioritised for future DRT services in low-demand areas to sustainably improve mobility in remote regions. Complementary expansion of existing public transport through such a DRT service should then meet the mobility needs of rural areas to offset car dependency and improve mobility for all population groups. The region of Prešov can be considered demand-orientated even in the more distant areas of this region. All areas of the region of Prešov were considered within the concept of the transport service proposal, i.e., those with strong demand (larger cities or villages) and those with weak demand. That is why the proposal for transport services for this region was also orientated towards the needs of passengers, where mutual links between individual modes of transport are logically and gradually created so that every part of the addressed region is secured by public transport together with transport links to other districts of the region within the integrated transport system. As an example, we can cite the operation of RadioBUS in the Czech Republic. The connections are operated as part of the regular timetable but with the difference that the trip will only be made if a passenger orders it by phone. The passenger must make the request no later than 30 min before the scheduled departure of the train from the stop. Such on-call connections are usually operated during peak traffic times or during days with minimal transport demand. The rest of the connections are operated in a conventional, regular mode. In Slovakia, this method of additional service is not established.

The modern system of integrated public transport is characterised by lines with an interval (clock) operation with short intervals, well-designed transfers and connections, a clear and user-friendly tariff, high-quality operational information, and developed conditions for intermodal travel (such as park and ride (P + R) or bike and ride (B + R)). A customer- and passenger-orientated integrated public transport system is an effective competitor to individual automobile transport and a path to sustainable mobility. As part of the integration, the advantages and disadvantages of individual modes of transport are maximised; this increases the attractiveness of public transport for the passenger and, at the same time, increases efficiency for the customer. The passenger does not travel with specific operators; they use comprehensive services. In this sense, integrated transport systems are the first phase of the mobility-as-a-service concept. The principle of the integration of public transport is the connection of its individual modes (railways, metro, trams, trolleybuses, buses, etc.) and operators into one logical unit. Before integration, both individual modes of transport and urban and regional transport are separated. Holders of public transport tickets cannot use regional lines for which a different tariff applies; the capacity of individual (even parallel) connections is not used evenly or optimally. On city lines, demand peaks in the city centre, while on regional lines, it is mostly on the outskirts of the city. For integrated transport systems, the hierarchisation of lines into backbone lines with short or very short intervals and lines providing general service to the territory, which are connected to the backbone lines at transfer points, is typical [47].

Prešov has a large network of nearby municipalities that are either directly connected to public transport or have a network of suburban bus lines. Prešov has a large attendance (12,871 daily commuters for work in 2018) but also a lot of people leave it daily for work (4607 in 2018)—usually to Košice. The city is continuously losing part of its population to its satellites. It can be concluded that the disproportion between places of residence and places of work can be solved with the existing system, which can be improved and thus increase the attractiveness of many places in the region for life. As for the districts covered within the radius of daily commuting to Prešov, according to data from the last population census of the Slovak Republic in 2018, 7214 people (20.0% of the economically active population) went to work from the Bardejov district daily, and from the Svidník district, 3162 people (20.2% of the economically active population), 1821 people from the Stropkov district (18.6% of the economically active population), and 8094 people from the Vranov nad Topľou district (22.1% of the economically active population). The data do not say where exactly the residents who left the district for work went, but it is reasonable to assume that in most cases, the destination was Prešov, as the only point of significant concentration of economic activity in the region [48]. In 2018, due to significant attendance, the number of people present daily in the Prešov district increased by 3% (or 4257 people) compared to the number of residents of the district, even though, e.g., 20.7% of economically active residents (or 16,172 persons) left it daily for work, mainly to Košice. In Prešov, the number of people present daily increased by up to 25% (or 22,946 people) compared to the number of city residents, even though, e.g., 10.6% of economically active residents (or 9728 persons) left it daily for work, mainly to Košice. At the same time, the number of people present daily in the Bardejov district was lower by 13% (resp. 10,122 people), in the Svidník district also lower by 13% (resp. 4321 people), in the Stropkov district by 14% (resp. 2930 persons), and in the district of Vranov nad Topľou lower by 12% (or 9564 persons) compared to the number of inhabitants of the given district. The active population in this region travels regularly to schools, work, civic amenities, and healthcare. The data are valid as of November 2018 [48].

The target state of the integrated transport system in eastern Slovakia is a modern, attractive public transport system consisting of all types of public transport (trains, buses, and public transport), covering the entire territory of the Prešov and Košice self-governing regions and enabling travel on one travel document (one-time or time-based subscription), regardless of transfers or used modes of transport, with uniform transport and tariff conditions and mutually agreed travel schedules. The name or brand of this system is IDS Východ. The benefits for passengers with the gradual construction of the integrated transport system will mainly be as follows [49]:

• Uniform transport and tariff conditions in trains, buses, and public transport;
• New types of fares: transfer tickets, timed subscription tickets (monthly, quarterly, etc.), and so on;
• Technological news: mobile application, near-field communication payments (NFC payments, etc.);
• More regular, faster, and more comfortable connections within the region and within cities;
• Harmonised system of public transport (regular guaranteed continuity of connections and lines);
• A simple and clear transport system (schemes of routes, timetables, etc.);
• Timely information about transport emergencies (delays, detours, etc.);
• Generally higher quality of services provided in transport.

The benefits for operators and those ordering transport services will be mainly as follows [49]:

• Growing demand for transport (more passengers);
• Greater efficiency of vehicle circulation;
• Stabilisation of transport performance.

The Transport Infrastructure Network in the Examined Region

As part of the design of the public passenger transport lines in the region, a compact area was selected in the north-eastern quarter of the Prešov catchment area. The territory is defined by the current lines of public passenger transport starting from Prešov in the direction of the village of Kapušany (and continuing in all directions), while to the north and east, it is bordered by the cities of Bardejov, Giraltovce, and Hanušovce nad Topľou.

This territory is not an isolated transport unit, and for the effective design of public passenger transport lines, it must necessarily be extended by the routes of the four skeleton transport lines crossing its borders. This is the railway line Prešov–Hanušovce nad Topľou–Vranov nad Topľou–Humenné and the road communications Prešov–Giraltovce–Svidník, Prešov–Giraltovce–Stropkov, and Prešov–Hanušovce nad Topľou–Vranov nad Topľou, which connect the regional city with the district city in its catchment area (see dashed line in Figure 2).

Figure 3 schematically shows the complete transport infrastructure network of the selected area, consisting of railway lines and roads with a continuous paved surface, extended by the roads Giraltovce–Svidník, Giraltovce–Stropkov, and Hanušovce nad Topľou–Vranov nad Topľou–Humenné, used by direct lines of public passenger transport from Prešov to Svidník, Stropkov, Vranov nad Topľou, and Humenné.

The individual points in Figure 3 represent residential units in the area under consideration and are divided into four categories: 1st category (regional city), 2nd category (district towns), 3rd category (other cities and important resort villages), and 4th category (other municipalities and other relevant residential units). Figure 3 shows the settlement formations relevant from the point of view of the transport service of the territory. The category of a specific residential unit is determined by the numbers 1 to 4 and is also distinguished by colour. The scheme also includes the names of residential units. Part of the area covered are 86 towns and villages that are part of four different districts.

Of the settlements marked in Figure 3, the following do not have the character of municipal self-government: Bardejovská Nová Ves (part of the town of Bardejov), Kľušovská Zábava (part of the village of Kľušov), Podstavenec (part of the village of Bartošovce), Dubie (part of the village of Koprivnica), Tarbaj (part of the village Mičakovce), Podhrabina (part of the Lipníky village and part of the Chmeľov village), Podlipníky (part of the Pavlovce village), Zimná Studňa (part of the Nemcovce village) and Šiba intersection (it is not a residential unit—the point shows the Šiba railway station, which is located on the crossroads, outside the village itself). As for the towns depicted in Figure 3 but located outside the area covered, their population numbers are as follows: Svidník: 10,938; Stropkov: 10,617; Vranov nad Topľou: 22,490; Strážske: 4298; and Humenné: 33,295. The data are valid as of November 2018 [48].

4. Methodology

The aim of modern public transport planning is primarily the mutual coordination of line management and the operational parameters of the lines (interval, capacity of vehicles or sets, timetables, interchanges, and connections) in each area (typically the entire area served by an integrated public transport system), thereby increasing the “logic”, attractiveness, and, at the same time, economic efficiency of public transport.

The demand for transportation by public transport is directly influenced by its quality. The quality criteria for public passenger transport include the following:

• Network density depends on the population structure of the territory;
• Availability of stops: walking distances and attractive areas of stops;
• Density of connections: greater density means a greater probability of connection-to-connection lines in transfer nodes;
• Transport speed is determined by the speed of connections, transfer times, and the length of the interval between connections on the line;
• Relocation time—the time required to move “from house to house” using one line of public passenger transport—is expressed by the equation:

$$T_{O-D}=t_a+t_w+T_1+t_e$$

(1)

where

T_O−D—total travel time from the starting point to the destination point (origin—destination);

t_a—access time;

t_w—waiting time;

T₁—in-vehicle travel time;

t_e—egress time;

• Transportation distance: the distance between the boarding and destination stops;
• The price of transportation plays an important role in the customer’s decision;
• Simplicity of transport clearance: unification of travel documents;
• Regularity: introduction of transport tactics;
• Reliability: maximum possible adherence to the travel schedule;
• Safety: in the vehicle, at stops, as well as in terms of crime;
• Information: in the vehicle, on the Internet, at stops and stations, and orientation at stops and stations (pictograms);
• Comfort and culture of transport.

Modern transport planning is based on the backbone function of electrified rail transport, which is the most advantageous mode of public transport in terms of transport capacity, energy, and economic efficiency. In practice, this means that the backbone role in the public transport system is typically played by modern railways (S lines) in suburban and regional transport and metro or tram lines in urban transport. These rail transport lines ensure strong radial and diametrical transport relations, in which they ideally apply their strengths (high travel speed and reliability, high transport performance).

Following the stations and stops of these backbone modes, transfer points for subsequent (typically bus) transport and P + R and B + R parking lots are created to ensure conditions for multimodal travel. The bus network (in the centres of large cities as well as tram lines) provides general service to the territory; however, trolleybuses or buses can also provide some important (for example, tangential) transport connections in the territory.

There are many approaches to optimisation models, such as in [51,52,53]. If mass passenger transport is to fulfil its purpose and not degenerate to the extreme where it will only fulfil the legal obligation to provide transport services, it must maximise customer satisfaction so that the demand for transport is as high as possible, and thus the price is as low as possible, or as much profit is made as possible. The role constructed in this way must first respect the interests of the passenger.

The basic requirements of the passenger, which can be influenced by the solution to this task, are the speed and comfort of driving without transfers (each transfer means an extension of the travel time by at least a time shift between the arrival of one connection and the departure of another and the associated discomfort). Therefore, if the journey for the largest number of passengers is to be as fast as possible and without transfers, it is necessary to find out where and how many passengers are going.

By monitoring the maximum flow of passengers, it is possible to construct a line route that will satisfy the maximum number of transport requirements as quickly as possible and without transfers. Thus, if we select a set of local centres and from them the centre to which the maximum flow of transport requests flows, we can say that there is a route leading to the given centre that will satisfy the largest number of transport requests for the entire addressed area by the shortest route and without transfers. To be able to create additional routes based on this principle, the situation can be changed simply by subtracting the smallest number of transport requests from the edges of the selected route from all the values of the edges of the selected route. In this way, the edge leading to the end village of the selected route is reset. When repeating the application of this principle, another route will be created, which, in the new situation, after subtracting the flow from the previous route, will serve the maximum number of transport requests by the shortest route and without transfers. The generation of routes should therefore create routes that will offer transport along the shortest or fastest route without transfers for the maximum number of transport requests. Based on these principles, an algorithm can be formulated [51].

Inputs for the algorithm:

-

a vector map of the infrastructure, which can be represented by a graph defined by a set of edges H and vertices V: G = (V, H), where the vertices represent intersections and villages (network nodes), and the edges represent sections of the infrastructure;

-

Q—set of ordered pairs (r, s), where r ∈ V, s ∈ V are municipalities between which there is a request for transportation;

-

O-D (origin–destination) matrix—matrix of transport relations between all pairs of municipalities in the given region O = {p^rs}, where (r, s) ∈ Q;

-

the set of incidence centres C;

-

the maximum permitted increase in the length of the line d_e with respect to the length of the shortest path;

-

maximum permitted length of walk d_d.

Variables and quantities that are used in the description of the algorithm [51]:

c_i—evaluation of the edge h_i, which indicates the number of transport requests transported along the given edge;

R_r,s = {h₁, h₂, …, h_n} shortest path from vertex r to vertex s consisting of edges h₁, h₂, … h_n;

p(v)—evaluation of the peak v, which indicates the number of inhabitants of the village represented by the given peak. If the peak does not represent a village, then p(v) = 0.

Outputs of the algorithm:

l = {h₁, h₂, …, h_m}—a line defined by a sequence of connected edges;

L—set of all lines.

Multicriteria evaluation methods have the same objective: to assess several variants of solving a problem according to the selected criteria and determine their order. The procedure for solving tasks using a multicriteria evaluation is as follows:

• Defining the criteria by which individual variants will be evaluated;
• Determination of weights for individual criteria (normative or non-normative);
• Calculation of the total utility of individual variants;
• Selection or determination of the optimal variant.

A prerequisite for the proposal of public passenger transport lines is knowledge of the transport behaviour of the region’s inhabitants, its causes, and development forecasts. The proposed methodology is not devoted to the investigation of the existing transport behaviour; it considers its description as the input data of the process. The methodology should be applicable both in terms of the proposal of completely new transport service structure lines as well as in the process of the reorganisation of existing public transport lines’ structures, including rail and bus transport.

The basic input in the planning process of regional public passenger transport lines is the knowledge of mutual transport dependencies between individual sources and destinations on the network within a predefined region. These dependencies are displayed using the so-called matrix source–target or graphically through a network graph, where individual vertices (nodes) represent resources and goals in the territory, while rated and directional edges show the direction and intensity of passenger transport flows. Nodes on the network need to be divided based on the hierarchy, ideally into 3–4 categories. The node in the first category is the natural centre of gravity of the solved region. Nodes in the 2nd to 3rd category are local catchment centres (district towns, resort villages, etc.), while nodes in the last (3rd or 4th) category are all other settlements, usually of a small rural nature. The number of categories depends on the size as well as the transport and settlement structures of the region. Figure 4 shows the methodological routing procedure and functional layers of public passenger transport lines. The extended procedure for the routing and functional layers of public passenger transport lines is presented in the Supplementary Materials of this article.

The transport service system in the study area comprises two essential and interrelated steps. The first step is to determine the direction of the functional layers of public passenger transport in the selected region, which includes the proposal of regional lines in the area under consideration, the proposal of the timetable, and the determination of transfer points in the area under consideration. The second step is the determination of the optimal transport service for the addressed line based on a multicriteria analysis. It is important to define the criteria for individual variants and determine the weights of the criteria and subcriteria. Subsequently, the utility of the selected variants is calculated, and the optimal transport service variant is selected. Figure 5 shows the transport service structure of the area under consideration. This structure is valid within the selected territory (region of Prešov), due to the individual links affecting the establishment of the transport service system of a specific region.

Among the methods for multicriteria evaluation, the most effective analytical multilevel method in this case is the AHP method [54]. The AHP method is based on a pairwise comparison of the degree of significance of individual criteria and the degree to which the evaluated variants satisfy these criteria. The relative weights of the criteria (determined by pairwise comparisons) differ naturally under different conditions and circumstances. The evaluation is in both cases (comparison of the significance of the criteria and the degree of fulfilment of the criteria) based on the so-called expert estimation, in which experts in each field compare two criteria or how two variants fulfil a given criterion, evaluating how one element (criterion or variant) is more significant or better than the other. Specifically, they evaluate it by the number of points on the selected scale (see

Table 1. Descriptors according to the AHP method [53].

Score	Descriptor
1	Element A is as important/good as element B
3	Element A is more significant/better than element B
5	Element A is much more significant/better than element B
7	Element A is many times more significant/better than element B
9	Element A is more significant/better than element B

).

Therefore, the methodology works with the relative determination of the degree of fulfilment of a specific criterion, namely, one specific variant (A) versus another specific variant (B), while only determining the extent to which variant A fulfils the given criterion in comparison to variant B. It is not possible to compare more than two variants at the same time. In the case of the occurrence of more than two variants of the traffic service system, it is necessary to compare all possible pairs of variants (A versus B) in this way, and only based on the results will the overall order of all variants be determined.

For the assessment of significance or suitability, it is recommended to use a point scale equipped with the so-called descriptors (see Table 1). To more finely distinguish the elements within the compared pairs, it is also possible to use the values 2, 4, 6, and 8 in the “Number of points” column.

Owing to the technical specifics of the AHP method (and the practical use of the proposed multicriteria analysis system), it is necessary to define the selection criteria of the service system on the line such that they can be divided into several common groups (two to four general criteria), which may subsequently include two to four logically related subcriteria. The proposed breakdown of the proposed criteria is presented in

Table 2. General criteria and subcriteria for choosing a transport system on the line (authors).

General Criteria	Subcriteria
Availability of transport	Availability of boarding and alighting points
	Status of boarding, alighting, and transfer points
	Regularity and even daily coverage
	Integration potential
Quality of transport from the perspective of a passenger on board	Passenger safety
	Speed
	Travel comfort
	Operational reliability
Public sector costs	Demand for subsidies
	Infrastructure investment
Impact of transport on the external environment	Impact on the environment
	Socioeconomic development of the area
	Transport problems caused

.

The criteria do not include the fare amount (or the costs to users of the transport system), as they are assumed to be the same for all service variants.

Multicriteria Analysis Methods

Multicriteria evaluation is a comprehensive evaluation method that minimises the degree of subjectivity when choosing a suitable alternative (e.g., routing or modal characteristics of a public passenger transport line). For example, in [55], a multicriteria evaluation of the potential of introducing high-speed railway routes in Turkey was presented. In the case of multicriteria evaluation, it is important to consider the aspects of different evaluation criteria and assign weights to individual criteria. This method has also been used in previous research [56]. Using a multicriteria evaluation tool, the authors developed a solution for optimising public transport performance.

The task of multicriteria evaluation is to describe objective reality when selecting a variant using standard procedures and thus formalise the given decision-making problem (convert it to a mathematical model of a multicriteria decision-making situation). If the proposal allows for several variants of line management in a certain area, it will not make sense to assess transport service systems using individual lines. It is also necessary to separate a segment from the network—a complete set of transport routes—which is affected by the variant line solution; however, it is valid that this variability in the line solution does not affect the routing of the lines in the rest of the network. In this case, each permissible transport service system (as a variant within the multicriteria analysis) must be defined for the segment and not for individual lines.

Multicriteria analysis consists of two basic steps, which are the determination of criteria weights and the evaluation of the overall usefulness of individual variants. Several methods are available to determine the weights of the criteria and the optimal variant. Although the AHP method is one of the most objective and accurate methods of multicriteria decision making, it has several shortcomings. One of the most serious problems is the burden of some steps of its application with a certain degree of subjectivity. It is therefore necessary to create a tree structure as accurately as possible to minimise the subjective influences of the evaluation subject. Despite the disadvantages of the AHP method, this method is used in our research. One of the possible solutions, which partially removes the subjective problem and which we used in our research, is to carry out an evaluation with the participation of a group evaluation subject, i.e., several experts in the given field. The method of determining the weights of the criteria and evaluating the overall usefulness of individual variants can fully consider the specifics of different regions and locations, as well as different conventional or nonconventional transport service systems applicable to the service of any line or a complete set of traffic routes. An important advantage of the AHP method is that it includes the entire process of multicriteria evaluation, i.e., weighing the criteria and determining the overall utility of the variants. Therefore, it is possible to program a comprehensive and internally coherent process of multicriteria analysis for transport service systems. A pairwise comparison of the significance of the criteria to determine their relative weights considers the current traffic, socioeconomic, and natural specifics of the territory served by the proposed line, as well as its potential. An example of the division of the variant design of the routing and the functional layers of the lines in terms of the node hierarchy into segments is shown in Figure 6. For variant A, the black line (or line) represents the main railway line. For variant B, the blue line is the main bus line. Within each variant, thin coloured lines (red, green, and purple) are associated with railway, bus, or city lines, which for each variant form a complete set of transport routes, i.e., one segment.

5. Results

The proposal for the routing of the layers of the public passenger transport lines respects the natural gradient of the settlements in the lower categories to those in the higher categories. It is also observed that a maximum of one transfer is required from any settlement to the relevant district city. Figure 7 shows 93 residential units in the area under consideration which do not have the character of a district city. According to this proposal, most of these settlements have a direct connection with the relevant district city. For the purposes of smoothly connecting these settlements with the respective district city, the proposal envisages synchronised transfer connections at the junctions of Raslavice (railway station), Hanušovce nad Topľou mesto (railway stop), and Giraltovce (bus station).

A fundamental benefit of the proposed line network (Figure 7) is the systematic introduction of an express layer for regional public passenger transport. This primarily serves to expand the radius of daily commuting by public passenger transport to Prešov, which, in addition to increasing the attractiveness of public passenger transport, also brings about an increase in the labour force mobility in the region and, therefore, a positive impact on the economic development of the region.

In this case, the express layer of regional public passenger transport has only zone service characteristics. In total, the proposal defines four main zonal lines (

Table 3. Proposal of four main zonal lines (authors).

Line	Stop Service (Section)	Express Service (Section)
Prešov–Vranov nad Topľou–Humenné	Vranov nad Topľou–Humenné	Prešov–Vranov nad Topľou
Prešov–Kobyly–Bardejov	Kobyly–Bardejov	Prešov–Kobyly
Prešov–Giraltovce–Svidník	Giraltovce–Svidník	Prešov–Giraltovce
Prešov–Giraltovce–Stropkov	Giraltovce–Stropkov	Prešov–Giraltovce

).

Perhaps the most significant difference from the current situation is the expansion of the radius of an attractive daily commute via public transport to Prešov (according to the methodology, a maximum of 45–50 min from boarding the first to exiting the last means of public passenger transport) to include the cities of Bardejov and Vranov nad Topľou (having a total of 54,980 inhabitants), which are located at a practically identical distance from Prešov (approximately 45 km). Currently, the travel time by public transport between these cities and Prešov is approximately 60 min, which has led to the predominant use of individual automobile transport (travel time of approximately 40 min).

The specific line is the Prešov–Bardejov railway connection. In terms of the proposal, this has the characteristics of a stop, but given the primary importance of this line, which is the connection of the district of Bardejov to the long-distance rail transport system, this line is included among the main lines, of which there are five. Figure 8 shows the boundaries of the circuits of the attractive daily commute to Prešov. The limit indicates a time of approximately 45 min from boarding the first vehicle to exiting the last vehicle on the way to the centre of Prešov. Settlements located between the marked border and the destination of the visit (Prešov city) are considered part of the circle of attractive visits to Prešov.

In Figure 8, the border of attractive commuting with individual automobile transport is indicated using blue dots (by attractive commuting, we mean a small number of short lines with a relatively high frequency and short transfer-waiting times). The red dots indicate the border of attractive commuting when using public passenger transport in the current state, and the green dots indicate the boundary of an attractive commute to Prešov within the framework of public passenger transport when applying the transport service system proposal. This would expand the current circle of attractive commuting in the framework of public passenger transport to 16 additional cities and villages (Bardejov, Vranov nad Topľou, Klušov, Osikov, Tročany, Abrahámovce, Lopúchov, Kalnište, Lužany pri Topli, Marhaň, Lascov, Brezov, Železník, Babie, Vlača, and Ďurďoš).

One of the most fundamental features of the proposed public passenger transport system in the area under consideration is the network-wide timetable (30 min, 60 min, and 120 min connection intervals), which includes a system of time-synchronised transfer links in the relevant transfer nodes and transport directions.

Transfer nodes with harmonised transfer links in the relevant directions are Hanušovce nad Topľou mesto (railway stop), Raslavice (railway station), Giraltovce (bus stop Giraltovce cultural house (bus stop), Kuková, Rázcestie (bus stop), Podlipníky (bus stop), Lipníky (bus stop), Lada (bus stop), Janovce (bus stop), Hertník (bus stop), Kľušovská Zábava (bus and railway stop), Kurima (bus stop), and Stuľany (bus stop).

5.1. Proposal of Regional Lines

This section describes the individual public passenger transport lines in terms of routes, times, connections, and other relevant parameters. Main lines (train and zone buses) are indicated by the letter A, and other lines (bus stops) by the letter B. The construction of individual lines and the overall network takes into consideration the effects of public passenger transport on the external environment, based on the socioeconomic, transport, and natural–urbanisation characteristics of the affected area.

Table 4. Proposal of regional lines in the region of Prešov (authors).

Line	Direction of the Line	Line	Direction of the Line
A1	Hanušovce nad Topľou–Vranov nad Topľou–Strážske–Humenné	B8	Prešov–Hanušovce nad Topľou–Vranov nad Topľou
A2	Prešov–Raslavice–Bardejov	B9	Giraltovce–Železník–Kuková–Stuľany
A3	Prešov–Kobyly–Bardejov	B10	Prešov–Lipníky–Železník–Giraltovce
A4	Prešov–Giraltovce–Svidník	B11	Prešov–Raslavice–Janovce–Hertník
A5	Prešov–Giraltovce–Stropkov	B12	Bardejov–Brezovka–Kurima–Kožany
B1	Raslavice–Koprivnica–Marhaň–Giraltovce	B13	Bardejov–Janovce–Tročany
B2	Bardejov–Kurima–Marhaň–Giraltovce	B14	Bardejov–Lukavica–Rešov
B3	Raslavice–Stuľany–Kochanovce	B15	Bardejov–Hervartov–Kružlovská Huta–Kríže
B4	Bardejov–Kochanovce–Hankovce–Marhaň	B16	Giraltovce–Kalnište
B5	Bardejov–Šiba–Hertník–Raslavice	B17	Prešov–Kapušany–Čelovce
B6	Hanušovce nad Topľou mesto–Babie–Giraltovce	B18	Prešov–Lada–Okružná
B7	Hanušovce nad Topľou mesto–Radvanovce–Pavlovce	B19	Šarišská Poruba–Lada–Zimná Studňa
		B20	Bardejov–Hažlín–Lipová–Kurima

shows an overview of the proposed regional lines in the region of Prešov.

The system travel times were estimated based on the currently valid travel schedules. The time positions of the lines depend on the current time positions of the express trains on the Košice–Žilina–Bratislava line at Kysak station (according to timetable 2023/2024), as well as the proposed time positions for connecting passenger trains on the Košice–Prešov–Lipany line at Prešov station.

Table 5. Fragment of the proposed timetable of the railway line Košice–Prešov–Lipany (authors).

Departure						Railway Station		Arrival
4.03	5.03	6.03	7.03	8.03		Lipany		5.56	6.56	7.56	8.56	9.56
4.06	5.06	6.06	7.06	8.06		Rožkovany		5.53	6.53	7.53	8.53	9.53
4.09	5.09	6.09	7.09	8.09		Červenica		5.50	6.50	7.50	8.50	9.50
4.12	5.12	6.12	7.12	8.12		Pečovská Nová Ves		5.47	6.47	7.47	8.47	9.47
4.16/17	5.16/17	6.16/17	7.16/17	8.16/17		Sabinov		5.42/43	6.42/43	7.42/43	8.42/43	9.42/43
4.21	5.21	6.21	7.21	8.21		Orkucany		5.39	6.39	7.39	8.39	9.39
4.25	5.25	6.25	7.25	8.25		Šarišské Michaľany		5.35	6.35	7.35	8.35	9.35
4.30	5.30	6.30	7.30	8.30		Veľký Šariš		5.30	6.30	7.30	8.30	9.30
4.36/37	5.36/37	6.36/37	7.36/37	8.36/37		Prešov mesto		5.21/23	6.21/23	7.21/23	8.21/23	9.21/23
4.40/45	5.40/45	6.40/45	7.40/45	8.40/45		Prešov		5.13/19	6.13/19	7.13/19	8.13/19	9.13/19
4.52	5.52	6.52	7.52	8.52		Kendice		5.07	6.07	7.07	8.07	9.07
4.56	5.56	6.56	7.56	8.56		Drienovská Nová Ves obec		5.04	6.04	7.04	8.04	9.04
5.00	6.00	7.00	8.00	9.00		Ličartovce		5.00	6.00	7.00	8.00	9.00
5.03	6.03	7.03	8.03	9.03		Obišovce		4.56	5.56	6.56	7.56	8.56
5.06/07	6.06/07	7.06/07	8.06/07	9.06/07		Kysak		4.52/53	5.52/53	6.52/53	7.52/53	8.52/53
5.19	6.19	7.19	8.19	9.19		Košice		4.40	5.40	6.40	7.40	8.40
Arrival								Departure

shows a several-hour fragment of the proposed timetable on the line Košice–Prešov–Lipany.

The proposed timetable respected the current infrastructure parameters, the current time positions of the express trains of the line Košice–Žilina–Bratislava, as well as the needs of the local frequency of passengers. The proposal envisages an all-day 60 min interval of trains without supplementation with non-system trains. A total of three trainsets are required to meet this timetable. In the case of the deployment of modern low-floor regional sets (e.g., 671 by the operator Železničná spoločnosť Slovensko series, in short ZSSK), additional time savings can be expected owing to the better dynamic characteristics of the vehicles or the faster exchange of passengers at stops.

5.2. Determination of the Optimal Transport Service for a Specific Line

In the model of the multicriteria evaluation of variants of the transport service on a specific line of public passenger transport, the zone line Prešov–Hanušovce nad Topľou–Vranov nad Topľou–Strážske–Humenné is proposed, with accelerated travel in the Prešov–Vranov nad Topľou section owing to its usability for daily commutes from Vranov nad Topľou to Prešov. This is a model-based evaluation of the two variants. The multicriteria evaluation of service systems is performed on segments of the transport network while taking into consideration the impact of public passenger transport on the external environment (based on socioeconomic, transport, and natural–urbanisation characteristics of the affected environment). The variants considered were as follows:

• Zone service by rail transport at 60 min intervals of connections all day throughout the week, using four pieces of light low-floor motor units with a seating capacity of approximately 170;
• Zone service comprises a bus service at intervals of 60 min in the peak season and on weekends and 30 min in the peak season, using eight units of standard large buses with approximately 55 seats.

The biggest difference concerns the service of Strážske, where the route of the railway line deviates significantly from the road and bypasses the city itself. While the bus station is in the centre of the city, the railway station is located on its outskirts, outside the attractive walking distance from the city centre or important residential areas. Strážske railway station is an alternative to the Strážske bus stop, which is a railway crossing. This is a location that is relatively close to the Chemko Strážske industrial complex. Certain differences in favour of the bus service also concern the stops Šarišské Lúky (railway station vs. bus stop), Vranovské Dlhé (railway vs. bus stop), and Hanušovce nad Topľou mesto (trains vs. Hanušovce nad Topľou, square (buses)).

The total regular travel time on the line in any direction is approximately 75 min for the rail service option. The total regular travel time on the line in any direction with the option of a bus service is approximately 90 min or 50 min for the accelerated Prešov–Vranov nad Topľou section plus 40 min on the stop section Vranov nad Topľou–Humenné.

The service of the line in the period from approximately 4.00 a.m. to 0.00 requires an offer of 20 pairs of connections per day at a 60 min interval. In the case of congestion during the peak periods (5.00 a.m.–9.00 a.m. and 2.00 p.m.–6.00 p.m.), for a 30 min interval, there are 28 pairs of connections during the working day (i.e., the bus service option). The total length of the line is 70 km with the option of service by rail transport and 74 km with the option of service by bus transport.

The rail service variant, i.e., 20 pairs of connections per day during the entire week, thus provides a total transport performance during a standard week (five working days plus weekends) at the level of 19,600 train kilometres per week.

The bus service variant, i.e., 20 pairs of connections per day on weekends and 28 pairs of connections per day on weekdays, in turn provides a total transport performance during a standard week at the level of 26,640 bus kilometres per week.

5.3. Determination of the Weights of Criteria and Subcriteria

The setting of the weights of the general criteria is shown in Figure 9, and the setting of the weights of the subcriteria according to the individual general criteria is shown in Figure 10. The pairwise comparison of the importance of the criteria for determining their relative weights respects both the current transport, socioeconomic, and natural specifics of the territory served by the proposed line as well as its potential, especially from the perspective of workforce mobility, time losses, and health risks to residents resulting from unproductive and stressful time spent in transport or from the perspective of tourism development. The numbers on the scales represent the individual descriptors. Individual descriptors are given by the position of the sliding button on the scale visible in Figure 9 and Figure 10.

Table 6. Weight of individual criteria (authors).

Criterion	Weight (%)
1. Availability of transport	36.36
2. Quality of transport from the perspective of a passenger on board	36.36
3. Public sector costs	9.09
4. Impact of transport on the external environment	18.18

shows the weighting of individual criteria.

Table 7. Matrix of criteria for calculating the consistency index (authors).

Consistency Index						0.00%
	Crit 1	Crit 2	Crit 3	Crit 4	Weight (%)	Normalised Weight (%)
Crit 1	1	1	4	2	1.68	0.36
Crit 2	1	1	4	2	1.36	0.36
Crit 3	1/4	1/4	1	1/2	0.42	0.09
Crit 4	1/2	1/2	2	1	0.84	0.18

shows the calculation of normalised weights according to the matrix of criteria, based on which we obtain the consistency index.

The methodology for determining the weights of the given set of criteria, as well as a detailed explanation of individual subcriteria, is described in the Methodology section. Also, in the Methodology section, the method of the multicriteria evaluation of different service variants and the criteria for choosing the optimal service variant on the network segment are described. The setting of the weights for the general criteria is shown in Figure 9.

The pairwise comparison of the importance of the criteria in order to determine their relative weights respects the current traffic, socioeconomic, and natural specifics of the territory served by the proposed line, as well as its potential, especially from the point of view of labour force mobility, time losses, and the health risks of residents arising from unproductive and stressful time spent in transport or from the point of view of the development of tourism.

The numbers on the scales represent individual descriptors, as explained in the Methodology section. In all cases, the consistency index has a value below 5%, which means that all statements (expressed by descriptors 1–9) are consistent; that is, there are no contradictions. The setting of the weights of the subcriteria according to the individual general criteria is shown in Figure 10.

Descriptors are always shown in mirror order on the scale because they take both positive and negative values for each pairwise comparison. A positive descriptor value always refers to the element to which it is closest. The descriptors 1, 3, 5, 7, and 9 represent “good”, “better”, “much better”, “times better”, and “absolutely better”, respectively. All criteria are evaluated similarly to what is shown in Figure 10. Based on the calculations according to Table 6 and Table 7, the consistency index is 1.81%.

In Figure 10, we can also see that descriptor 5 in the first comparison says that the availability of boarding and alighting points is a much more important subcriterion than the status of boarding, alighting, and transfer points, or on the contrary, the status of boarding, alighting, and transfer points is a much less important subcriterion than the availability of boarding and alighting points. Multicriteria analysis was used to calculate the utility variants for each general criterion. Based on the results of the multicriteria analysis, the optimal variant of the transport service on the examined line was determined.

Table 8. The resulting multicriteria evaluation of variants on the examined line (authors).

General Criteria	General Criteria Weight	Subcriteria	Subcriteria Weight
			Relative	Absolute
Availability of transport	36.36%	Availability of boarding and alighting points	33.95%	12.35%
		Status of boarding, alighting, and transfer points	7.72%	2.81%
		Regularity and even daily coverage	50.26%	18.27%
		Integration potential	8.08%	2.94%
Quality of transport from the perspective of a passenger on board	36.36%	Passenger safety	33.16%	12.06%
		Speed	41.69%	15.16%
		Travel comfort	16.10%	5.85%
		Operational reliability	9.05%	3.29%
Public sector costs	9.09%	Demand for subsidies	83.33%	7.58%
		Infrastructure investment	16.67%	1.52%
Impact of transport on the external environment	18.18%	Impact on the environment	7.76%	1.36%
		Socioeconomic development of the area	66.80%	12.15%
		Transport problems caused	25.74%	4.68%

and

Table 9. Resulting multicriteria evaluation of variants A and B (authors).

General Criteria	Degree of Fulfilment of the Subcriteria		Evaluation According to General Criteria		Evaluation by Subcriteria
	Variant A	Variant B	Variant A	Variant B	Variant A	Variant B
Availability of transport	33.33%	66.67%	35.91%	64.09%	4.12%	8.23%
	66.67%	33.33%			1.87%	0.94%
	33.33%	66.67%			6.09%	12.18%
	33.33%	66.67%			0.98%	1.96%
Quality of transport from the perspective of a passenger on board	87.50%	12.50%	77.79%	22.21%	10.55%	1.51%
	75.00%	25.00%			11.37%	3.79%
	90.00%	10.00%			5.27%	0.59%
	33.33%	66.67%			1.10%	2.19%
Public sector costs	10.00%	90.00%	16.67%	83.33%	0.76%	6.82%
	50.00%	50.00%			0.76%	0.76%
Impact of transport on the external environment	25.00%	75.00%	71.27%	28.73%	0.34%	1.02%
	75.00%	25.00%			9.11%	3.04%
	75.00%	25.00%			3.51%	1.17%
Resulting evaluation of the overall usefulness of the variants					55.82%	44.18%

summarise the entire process of determining the relative weights of the general criteria and their subcriteria in percentage terms, as well as the assessment of the extent to which individual variants (A and B) meet this set of criteria, also in relative percentage terms (A vs. B), where the sum of the resulting values of both variants gives 100%. It is necessary to consider the fact that the weights of individual criteria depend on the specific circumstances of a specific location in a specific region. These circumstances are variable in nature and vary significantly in space. In practice, this means that the weights of the criteria cannot be fixed. The weight of individual criteria changes in space, even if the object of transport is a population with very similar social and economic characteristics or transport needs. Any fixed weights would therefore make it impossible to use a multicriteria evaluation of transport service systems in practice; they would not allow reflecting the specific needs and characteristics of a specific region or location.

The final assessment of the overall usefulness of variants A and B must reach 100%, while the mutual ratio of the fulfilment of the set of criteria and subcriteria (defined by proportional weights) is in favour of variant A (55.82%) against variant B (44.18%).

6. Discussion

At the national and regional levels, strategic development materials and legislative rules are currently being designed to facilitate the systematic development of public transport. The ideal initial state for the effective use of procedures is a complex transport model that describes all the relevant transport and transportation characteristics of the functional region. In the case of the evaluation of the overall usefulness of individual variants, when evaluating complex systems such as the transport service systems of regional public passenger transport lines (or complete sets of transport routes), it would be extremely difficult in practice to assess the variants individually (absolutely) (if not impossible) to objectively assess the degree of fulfilment of a specific criterion by a specific variant. Therefore, the methodology works with the relative determination of the degree of fulfilment of a specific criterion, namely, one specific variant (A) against another specific variant (B), while determining only how much more or less variant A meets the given criterion compared to variant B. With such a procedure, it is impossible to compare more than two variants simultaneously. In the event of the occurrence of more than two variants of the transport service system, it is necessary to compare all possible pairs of variants in this manner (A versus B), and the overall order of all variants is determined based only on the results of the comparison of individual pairs of variants.

The multicriteria analysis consists of two basic steps: the determination of criteria weights and the evaluation of the overall usefulness of individual variants. There are several methods available for determining the weights of the criteria and for determining the optimal variant. Although the AHP method is one of the most objective and exact methods of multi-criteria decision-making, it has several shortcomings. One of the most serious issues is the burden of some steps of its application having a certain degree of subjectivity. It is therefore necessary to create a tree structure as precisely as possible to minimise the subjective effects of the evaluation subject. Despite its disadvantages, we decided to use this method in our research. One possible solution that partially eliminates the subjective problem and which we used in our research is to carry out an evaluation with the participation of a group evaluation entity, i.e., several experts in the given field. The method of determining the weights of the criteria and evaluating the overall usefulness of individual variants can fully take into consideration the specifics of various regions and locations as well as various conventional or nonconventional transport service systems applicable to the service of any line or a complete set of transport routes. An important advantage of the AHP method is that it includes the entire process of multicriteria evaluation, i.e., both the weighting of the criteria and the determination of the overall usefulness of the variants. By means of the consistency index, the system can alert the user to contradictions (including the intensity of their severity) in the process of the relative evaluation of criteria weights. Therefore, it is possible to program an integral and internally coherent process of multicriteria analysis for transport service systems. The paired comparison of the significance of the criteria to determine their relative weights takes into consideration the current transport, socioeconomic, and natural specifics of the territory served by the proposed line, as well as its potential.

Regional public passenger transport lines were designed in terms of routes, times, connections, and other relevant parameters. The main lines are train and bus lines (indicated as A), and the other lines are bus stops (indicated as B). A timetable on the Košice–Prešov–Lipany line was also proposed, while considering the current parameters of the infrastructure, the current time positions of the express trains on the Košice–Žilina–Bratislava line in Kysak, and the needs of the local frequency of passengers. In terms of the availability of entry and exit points and the integration potential, variant B is slightly superior owing to the more convenient location of the bus stop compared to the railway station in Hanušovcie and Topľou and the more convenient location of the bus station compared to the railway station in Strážske. In the case of option B, these points are both more accessible to the residents of the given cities, but they also enable an easier spatial connection with the connecting lines of public passenger transport, as well as with bicycle transport and individual automobile transport, i.e., easier integration of transport. Passenger safety, speed, and travel comfort are essential benefits of the rail transport variant for the line under consideration. In terms of the conditions of boarding, exiting, and transfer points, variant A is slightly superior owing to the relatively modern Prešov railway station (allowing, for example, barrier-free access of immobile passengers to vehicles) as well as the relatively higher culture of the environment compared to other railway stations and bus stations. From the perspective of regularity and uniform coverage of the day, variant B has a slight advantage, owing to the 30 min interval of connections at peak periods (compared to the all-day 60 min interval for variant A). From the viewpoint of operational reliability, variant B is slightly superior because of the practically negligible failure rate of the vehicles in operation, which, based on the common experience of passengers in railway transport, certainly cannot be claimed for variant A. The demand for the number of subsidies needed to cover the loss from services in the public interest is approximately eight times higher with variant A than with variant B. The individual variants do not require any investment in transport infrastructure (transport route plus boarding, exit, and transfer points and related facilities) for their implementation. Therefore, their comparison is inconclusive from this perspective.

Regional bus transport in Slovakia is characterised by a lower average production of pollutants and noise per passenger kilometre compared to regional rail transport using diesel traction [57]. The relative assessment of environmental impacts is in favour of option B. For the socioeconomic development of the territory, a fundamental requirement is a system travel time between the cities of Prešov and Vranov nad Topľou that does not exceed the limit of an attractive daily commute (45 min), which can only be achieved by rail transport. Therefore, the assessment from the perspective of the socioeconomic development of the territory is based on the benefits of option A. The final evaluation of the overall usefulness of variants A and B indicates the mutual ratio of fulfilment of the set of criteria and subcriteria and is in favour of variant A, which reached 55.82% in the evaluation. Variant B reached 44.18% in the overall evaluation.

The optimal service option for the zone line Prešov–Hanušovce nad Topľou–Vranov nad Topľou–Strážske–Humenné is, therefore, in terms of the procedure described above, variant A: zone service by rail transport with a 60 min interval of connections throughout the day (during the whole week), a defined constellation of stops, and the use of four pieces of light low-floor engine units with a seating capacity of approximately 170. The proposal consists of systematic repairs based on the original state of traffic service. The proposal for the management of public passenger transport lines in the assessed region is focused on approaches orientated towards all parties involved. The paper provides a quick and quantified assessment of line service within a complex territory, where, within the framework of the AHP evaluation method, we focus on four main criteria, which are the accessibility of transport, the quality of transport from the passenger’s point of view, the costs of the public sector, and the impact of transport on the external environment, which covers environmental factors. Compared to the studies examined in the literature review, this research was mostly focused on the proposal of public passenger transport lines in the form of linear programming; some were focused only on the customer (passenger), others were focused only on the operator, or on a part of a certain territory. These investigations did not consider the wide spectrum of this problem. Compared to these studies, our research is orientated towards a complex area in which complex changes are addressed and are ready to be included in an integrated transport system. This research includes the requirements of all parties involved (operators, passengers, and contractors of transport services in the region).

Public transportation must meet many requirements and passenger expectations in terms of directness, frequency, availability, reliability, low cost, speed, punctuality, regularity, accurate information, comfort, vehicle crowding, cleanliness, connections, environment, courtesy, staff, safety, and security. The main goal of this proposal was to fulfil all the above requirements. The results of this research prove that a functional transport system in a region that meets all the above requirements can be developed and can be used within an integrated transport system.

7. Conclusions

The economic development of Slovakia and the associated increase in the degree of automobilization are resulting in an increasingly intense pressure on road networks, primarily in regional cities and their metropolitan areas. Owing to this long-term trend, after decades of general disinterest, the subject of competitive public passenger transport based on an integrated transport system has gradually become the focus of the attention of various clients of public passenger transport services.

Customer acceptance of a public transport system is highly dependent on the quality of the service provided, especially compared to alternatives such as individual transport. If only weak connections are offered for an origin–destination pair, passengers may choose to use an alternative mode of transport or stay at home. Therefore, the quality of a public transport system, from the perspective of passengers, is a key objective in the design of public transport systems, in addition to infrastructural constraints, operational constraints, and budgetary considerations.

The proposal of structured regional lines of public passenger transport can be applicable for an integrated transport system and is briefly and simply applied within the selected compact territory of a network transport nature (the region bounded by the cities of Prešov, Bardejov, Giraltovce, and Hanušovce nad Topľou, including important extraterritorial overlaps) too. The reason for using this proposal is also the fact that it can be directly used for the newly created integrated transport system in eastern Slovakia.

The resulting proposal meets the requirements of a network-wide time schedule, attractive connectivity at transfer nodes in all directions, significance from the viewpoint of daily commuting, significant expansion of the radius of attractive commuting by public transport to the economic centre of the region, and highly efficient use of means of transport and human labour.

The limitations of our research result from the usual habits of the travelling public, since when creating or optimising transport services in a region that is to be part of an integrated transport system, it is necessary to start from the original traffic services, knowledge of the area being addressed, and the usual habits of the travelling public, adapting the proposal to the requirements of interested parties (operators, contractors of public passenger services, and passengers) and the needs of the travelling public. Another limitation of our research is that it is not possible to create such a model on the basis of simulation or the creation of an algorithm within the framework of the construction of the proposal for transport services in the region of Prešov, as this process includes a large number of requests from interested parties that complicate the effective creation of a transport model, and in this case, none of the stakeholders are satisfied with the result. Therefore, it was necessary to create this model based on our own experience and knowledge of the addressed area, our knowledge of the habits of the travelling public in the given area, and the logical and gradual incorporation of the individual requirements of interested parties so that the resulting model is effective, economically advantageous, and motivating for travellers as well. However, we remain of the opinion that every model of transport service must change over time and adapt to current conditions.

Possible proposals for further research can be the creation of simulations that will consider all the specifics that this research considers and transform them into a simulation environment, thus eventually identifying other gaps in the field of traffic service design. Another proposal for the improvement of future research can be the analysis and monitoring of the established proposal directly in practice and the search for other innovative solutions for the efficiency and functionality of an integrated transport system. Furthermore, the potential of using micromobility to connect to the railway as a carrier line in an integrated passenger transport system can be explored. The expansion of future research may also concern the design of transport services for regions in Slovakia that are not yet part of an integrated transport system. Since each self-governing region in Slovakia is specific and sensitive to its traffic service, it would be a good solution to also focus on other self-governing regions and find errors that prevent the introduction of an integrated transport system in these regions.