Tra ﬃ c Volumes as a Modal Split Parameter

: Tra ﬃ c volume depends on several indicators. The most important are the degree of motorization, mobility, and especially the travel time and travel cost factor. The article presents an analysis of the possibility of using mobility surveys and tra ﬃ c counts to achieve a balance between supply and demand. The frequency of congested tra ﬃ c and over-capacity volumes are determined. By analyzing the trip information captured in the mobility surveys, we detected the strata causing the highest demand—economically active people with “job” as the purpose of their trip. The study area includes the Kysuce region and the city of Žilina in Slovakia. Three scenarios are processed in the article. Scenario 0 deﬁnes the current state, scenario 1 deﬁnes the situation with free-of-charge public transport, and scenario 2 represents a targeted modal split where saturation is not exceeded. The aim is to shift passengers to public transport and increase the share of public transport in the modal split. Scenario 2 is also presented in terms of saved emissions as an additional factor of relocating passengers from private to public transport. In terms of fare, we found a small change in the modal split with free-of-charge public third graph (2-1) complements the between speed The of the The last graph presents the interrelation of tra ﬃ c volumes, steps, on roads


Introduction
Traffic problems are undoubtedly a reflection of several variables, such as the quality of the infrastructure, the demand for transport, and the strong transport habits of the population. Increased urbanization has led to the continuous expansion of some large cities and an increase in the number of people and vehicles in these cities. This has led to problems such as increasing travel distance and travel costs within the city and an increase in urban congestion and environmental degradation. Therefore, priority should be given to the development of public transportation and the improvement of public transportation services for the sustainable development of transportation services [1]. Promoting and developing public transport and land use should be coordinated at the urban level [2,3]. Mutual support and comprehensive utilization of resources can achieve a reasonable distribution of vehicles on roads, improve travel efficiency, and reduce urban pollution and noise [4][5][6][7][8]. Urbanization leads to high-density development of land in urban areas for the increasing population and causes high-intensity traffic demand [9]. The population density will also generate a demand for travel by public transport. The value and location of land around the public lines affect the population density and choice of transport mode of residents [10,11]. The preference for public transport is conditioned by local traffic habits. The choice of transport mode for any trip depends on the subjective perception of its benefits. Any change in the regular rhythm of mobility will be reflected in various indicators, such as traffic volumes, travel time, and, finally, environmental impact.
Automobile congestion reduction policies, particularly travel demand management strategies, have had lower than expected effects for a variety of reasons. The public transport (PuT) concept could be one explanation for this; if people positively value travel, they may be less sensitive to behavior have shown that public transportation development and land use should be coordinated at the urban level [2,3] through mutual support and comprehensive utilization of resources between the two [5][6][7] to achieve a reasonable distribution of vehicles on roads, improve travel efficiency, and reduce urban pollution and noise [8].
This article will analyze in more detail the mobility relations between regions and the modal split for the most common purpose of travel-the trip to work. Rapid population growth can greatly increase traffic loads on arteries in metropolitan areas, regardless of their regional location. According to statistical data from the Slovak suburban area, the number of households with cars is growing faster than in cities. The population's dependence on cars is growing intensively as a result of daily population movements to central cities for work, schools, and services. This is a consequence of the massive suburbanization around large cities [24]. This trend is noticeable when comparing the development of the gross domestic product (GDP) and the motorization rate in the Žilina City region (ZSK). The data are shown in Figure 1.
Sustainability 2020, 12, x FOR PEER REVIEW 3 of 20 shown that public transportation development and land use should be coordinated at the urban level [2,3] through mutual support and comprehensive utilization of resources between the two [5][6][7] to achieve a reasonable distribution of vehicles on roads, improve travel efficiency, and reduce urban pollution and noise [8]. This article will analyze in more detail the mobility relations between regions and the modal split for the most common purpose of travel-the trip to work. Rapid population growth can greatly increase traffic loads on arteries in metropolitan areas, regardless of their regional location. According to statistical data from the Slovak suburban area, the number of households with cars is growing faster than in cities. The population's dependence on cars is growing intensively as a result of daily population movements to central cities for work, schools, and services. This is a consequence of the massive suburbanization around large cities [24]. This trend is noticeable when comparing the development of the gross domestic product (GDP) and the motorization rate in the Žilina City region (ZSK). The data are shown in Figure 1. Considering the capacity of the transport system, we focused on maintaining an acceptable ratio between the volumes and capacity of the transport system. Here, we concentrated on road profiles with regularly exceeded saturation. These profiles are usually unsatisfactory in terms of measuring surface evenness or excessive emission load [25,26]. Saturation flow is a very important road traffic performance measure of the maximum rate of flow of traffic. The term "saturation" is most often associated with the evaluation of intersections. Saturation flow rate is defined as the equivalent hourly rate at which previously queued vehicles can traverse intersections under prevailing conditions, assuming that a green signal is available at all times and no lost times are experienced [20].
Several factors should be considered when evaluating public transit benefits and costs. The main indicators of these are [27] accessibility, [28] journey time, [29] departure frequency, [30] cost, and [31] safety. Value of travel time (VOT) is one of the key inputs to travel demand models and is important for management and appraisal of transport investment decisions. The value of travel time can be defined as the price people are willing to pay to acquire an additional unit of time. The value of travel time has most often been determined by estimating mode choice models and evaluating the marginal rate of substitution between the cost and travel time of the alternative modes [32]. According to the results of the modeled current travel time and the measured speed, we used a travel cost as the base factor of the modal split change. The evaluation of statistical indicators proved that the values of travel time and travel price are statistically significant. The travel time will change with the increase in travel speed. The mode choice can be set by the mathematical model according to the measured data (mobility survey). The article deals with the idea of re-evaluating the transport mode in favor of public transport for trips to work between two regions during the early peak period. The data from mobility surveys and traffic volume surveys were used in the analysis.  Considering the capacity of the transport system, we focused on maintaining an acceptable ratio between the volumes and capacity of the transport system. Here, we concentrated on road profiles with regularly exceeded saturation. These profiles are usually unsatisfactory in terms of measuring surface evenness or excessive emission load [25,26]. Saturation flow is a very important road traffic performance measure of the maximum rate of flow of traffic. The term "saturation" is most often associated with the evaluation of intersections. Saturation flow rate is defined as the equivalent hourly rate at which previously queued vehicles can traverse intersections under prevailing conditions, assuming that a green signal is available at all times and no lost times are experienced [20].
Several factors should be considered when evaluating public transit benefits and costs. The main indicators of these are [27] accessibility, [28] journey time, [29] departure frequency, [30] cost, and [31] safety. Value of travel time (VOT) is one of the key inputs to travel demand models and is important for management and appraisal of transport investment decisions. The value of travel time can be defined as the price people are willing to pay to acquire an additional unit of time. The value of travel time has most often been determined by estimating mode choice models and evaluating the marginal rate of substitution between the cost and travel time of the alternative modes [32]. According to the results of the modeled current travel time and the measured speed, we used a travel cost as the base factor of the modal split change. The evaluation of statistical indicators proved that the values of travel time and travel price are statistically significant. The travel time will change with the increase in travel speed. The mode choice can be set by the mathematical model according to the measured data (mobility survey). The article deals with the idea of re-evaluating the transport mode in favor of public Sustainability 2020, 12, 10252 4 of 21 transport for trips to work between two regions during the early peak period. The data from mobility surveys and traffic volume surveys were used in the analysis.
The article covers a description of the study area, the methodology of research, results, and discussion. The main goal of the article is to describe the strength of traffic habits for regular trips to work from the perspective of the modal split. We used the traffic flow theory and the modal split theory to achieve a combination of two independent measurements of traffic characteristics. The final discussion was based on a comparison of data from the three proposed scenarios. Scenario 0 defines the current state. Scenario 1 defines the situation with free-of-charge public transport. Scenario 2 represents a targeted situation where saturation is not exceeded. The aim is to shift passengers to public transport and increase the share of public transport in the modal split. Scenario 2 is also presented in terms of saved emissions owing to relocation of passengers from private transport. In terms of fare, we found a small change in a modal split depending on the free-of-charge public transport. We consider the issue of emissions to be an important mirror of the results of a targeted change in the division of transport work.

Study Area
Žilina is a center of northwest Slovakia and one of the largest towns of the Slovak Republic. It is a seat of administration of the Žilina Region (158,096 inhabitants), one of the eight regions of the Slovak Republic. The Žilina self-governing region with an area of 6801 km 2 lies [33] in the north-western and northern part of Slovakia, bordering Poland and the Czech Republic.
The Kysuce region, as a part of the Žilina region, covers the north-western part of the Slovak Republic with an area of 934 km 2 . The territory has two administrative units, namely the district ofČadca (90,068 inhabitants) and Kysucké Nové Mesto (32,868 inhabitants). The region covers 1.9% of the area of the Slovak Republic. It is also unique for its location at the border of three countries-Slovakia, the Czech Republic, and Poland-making it a strong transit region for cross-border traffic [19]. Almost 27,000 cars pass through the region every day, including approximately 5000 trucks. Although a railway line with strong regional support runs parallel to the road I/11, only about 3500 people are transported daily between the two largest settlements-Čadca and Žilina, of which almost 2200 are travelling during the morning rush hour. Almost 4000 inhabitants are transported by buses and 1200 inhabitants travel daily from the districts ofČadca and Kysucké Nové Mesto to Žilina [1]. The traffic accident rate of the section is high, including fatal accidents.
As a result of the above situation, a transport "funnel" was created at the mouth of the Kysuce region to the regional city of Žilina with regular congestion. The delay reaches up to several hours. The transit traffic is often lead through a diversion through the Czech Republic despite the extension of the trips by 170 km [33]. The location of the Kysuce region and the city of Žilina is shown in Figure 2. The economy of the region is concentrated mainly in the cities and their surroundings along the line of development axes. In terms of the number of enterprises per thousand inhabitants, the Kysuce region does not reach the average of the Žilina region. In the Kysuce region, there is only one employer with more than 1000 employees (INA Kysuce, a.s.) who can be considered a key employer in the region. The main engine of growth in industrial production in the Slovak Republic and the Žilina Region in the observed decade was mainly the automotive industry and related industries. The automotive industry added value at a rate of 4.4% in the Slovak Republic, which is approximately three times higher than the EU-27 average, and continues to grow. Slovakia is the world's biggest car producer per capita, as well as the seventh biggest car producer in the EU. The automobile manufacturer Kia Motors is located near the city of Žilina, 9 km from the city center [24].
leave the use of PUT transport is the poor environment of bus stations and stops and the arrivals a them, for example, the absence of P&R and B&R systems, and insufficient equipment for handling and providing information to passengers. ŽSK noted that the number of regional buses transported passengers decreased from almost 50 million in 2005 to 25 million trips in 2018.

Materials and Methods
The analysis of the traffic situation in the region was part of the SUMP (Sustainable Urban Mobility Plan) of the Žilina Region [24], which is coordinated by the authors' department. The SUMP included surveys and analyses as well as a multimodal transport model. The mobility surveys were processed as a part of the input data for SUMP. The Žilina region mobility survey was implemented in the period between 2016 and 2017. To cover at least all 11 districts, 6231 households were surveyed in the net sample, which represents 18,300 persons. The sample includes full households in order to analyze the household context of mobility. All persons in the sample reported their mobility on one ordinary working day (Tuesday, Wednesday, Thursday). The method of directly contacting households was used for the survey. Each area (transport zone) had a set sample according to individual population groups. The current data from the Slovak Statistical Office was used for specifying the credible sample. Next, the survey was performed in every village where the minimum requirement of 10 households was met. Every interviewee was assigned to a predetermined population group. The database contained 33,688 trip descriptions. Almost 50% of them contained the activity "job" (attraction or production). Economically active people represented almost 67% o the total inhabitants. The transport mode "car driver" was selected for 42% of work trips.
Data from the mobility survey were mainly used to set up a demand model. The results are matrices of transport relations. These matrices show the number of trips between two zones for a selected time interval. Theoretically, such data are calculated for the given time intervals to describe all the characteristics of the passenger load. However, in practice it depends on the existing traffic models [35].
For the subsequent analysis, we used the transport model of the Žilina self-governing region (approximately 650,000 inhabitants). The mentioned tour-based model used 16 person groups in the region, 14 person groups in the surrounding area, 11 structural properties and activities, and 22 activity pairs. The described study presents one specific demand stratum: employed populationtrips to work. Employees make up 40% of the total population. Travel for work makes up nearly 56% of the study area (based on mobility survey). [36] Figure 3 presents a graphical view of the There is a strong development (urbanism, demography, economy, social area, transport infrastructure) corridor in Bratislava-Žilina-Košice in the territory of ŽSK. The mutual availability of FUA (functional urban area) centers located in the corridor line has already reached relatively high-quality parameters, which are partially degraded by insufficient capacity in critical sections of the road network and the unfinished modernization of the main railway line. In the important connecting lines of the settlement/transport corridor in the Váh valley, there is the Kysuce region, which has a significant settlement and transport corridor along the Kysuca river. The status of existing transport infrastructure corridors does not reach the desired quality and capacity level (in the case of Kysúce, the highest level of the European core TEN-T). The reason for this is the insufficient supply of public transport and its low competitiveness (speed, convenience) [22]. The main reason why passengers leave the use of PUT transport is the poor environment of bus stations and stops and the arrivals at them, for example, the absence of P&R and B&R systems, and insufficient equipment for handling and providing information to passengers. ŽSK noted that the number of regional buses transported passengers decreased from almost 50 million in 2005 to 25 million trips in 2018.

Materials and Methods
The analysis of the traffic situation in the region was part of the SUMP (Sustainable Urban Mobility Plan) of the Žilina Region [24], which is coordinated by the authors' department. The SUMP included surveys and analyses as well as a multimodal transport model. The mobility surveys were processed as a part of the input data for SUMP. The Žilina region mobility survey was implemented in the period between 2016 and 2017. To cover at least all 11 districts, 6231 households were surveyed in the net sample, which represents 18,300 persons. The sample includes full households in order to analyze the household context of mobility. All persons in the sample reported their mobility on one ordinary working day (Tuesday, Wednesday, Thursday). The method of directly contacting households was used for the survey. Each area (transport zone) had a set sample according to individual population groups. The current data from the Slovak Statistical Office was used for specifying the credible sample. Next, the survey was performed in every village where the minimum requirement of 10 households was met. Every interviewee was assigned to a predetermined population group. The database contained 33,688 trip descriptions. Almost 50% of them contained the activity "job" (attraction or production). Economically active people represented almost 67% of the total inhabitants. The transport mode "car driver" was selected for 42% of work trips. Data from the mobility survey were mainly used to set up a demand model. The results are matrices of transport relations. These matrices show the number of trips between two zones for a selected time interval. Theoretically, such data are calculated for the given time intervals to describe all the characteristics of the passenger load. However, in practice it depends on the existing traffic models [35].
For the subsequent analysis, we used the transport model of the Žilina self-governing region (approximately 650,000 inhabitants). The mentioned tour-based model used 16 person groups in the region, 14 person groups in the surrounding area, 11 structural properties and activities, and 22 activity pairs. The described study presents one specific demand stratum: employed population-trips to work. Employees make up 40% of the total population. Travel for work makes up nearly 56% of the study area (based on mobility survey). [36] Figure 3  Žilina is the natural center of the region, especially for work-related travel. A more detailed analysis of data from the Kysuce region and the city of Žilina confirmed this link. Work-related travel to Žilina accounts for approximately 60% of the traffic for the Čadca district and 75% for the Kysucké Nové Mesto district [24]. The relative rate of the work-related travel destinations for the Kysuce districts is shown in Figure 4.  Žilina is the natural center of the region, especially for work-related travel. A more detailed analysis of data from the Kysuce region and the city of Žilina confirmed this link. Work-related travel to Žilina accounts for approximately 60% of the traffic for theČadca district and 75% for the Kysucké Nové Mesto district [24]. The relative rate of the work-related travel destinations for the Kysuce districts is shown in Figure 4.
Žilina is the natural center of the region, especially for work-related travel. A more detailed analysis of data from the Kysuce region and the city of Žilina confirmed this link. Work-related travel to Žilina accounts for approximately 60% of the traffic for the Čadca district and 75% for the Kysucké Nové Mesto district [24]. The relative rate of the work-related travel destinations for the Kysuce districts is shown in Figure 4. For a detailed analysis, the profile on the road I/11 (E 75) was selected. It is located between two regions-Žilina and Kysuce districts. The European route E 75 is part of the international E-road network, a series of main roads in Europe. The E 75 starts at the town of Vardø in Norway by the Barents Sea, and it runs south through Finland, Poland, the Czech Republic, Slovakia, Hungary, Serbia, North Macedonia, and Greece [37]. It is part of a multimodal Baltic-Adriatic Corridor [38] ( Figure 5).
The city of Žilina is the regional capital and offers many job opportunities. The cross-section was also selected due to the high traffic load. The measurement took place in the autumn of 2018 and the spring in 2019. Both measurements lasted 14 days. Long-term measurement was important to capture  For a detailed analysis, the profile on the road I/11 (E 75) was selected. It is located between two regions-Žilina and Kysuce districts. The European route E 75 is part of the international E-road network, a series of main roads in Europe. The E 75 starts at the town of Vardø in Norway by the Barents Sea, and it runs south through Finland, Poland, the Czech Republic, Slovakia, Hungary, Serbia, North Macedonia, and Greece [37]. It is part of a multimodal Baltic-Adriatic Corridor [38] (Figure 5).  We analyzed the theoretical changes in the modal split. The analysis mainly included data from the profile traffic count, mobility survey, and environmental statistics. Through the density of the traffic flow, we determined the real capacity of the road. Then we determined the share of drives that needed to be converted to another mode of transport in the morning rush hour by comparing the hourly peak volumes with the capacity. The software BIOGEME was used to calculate the efficiency of commuting by multiple means of transport. The attractiveness of the public transport in the modal split was recalculated by changing the travel cost, which is one of the most significant variables in mode choice [32].

Traffic Flow Characteristics
Traffic flow varies in time and space. When considering the flow of traffic along a highway, three The city of Žilina is the regional capital and offers many job opportunities. The cross-section was also selected due to the high traffic load. The measurement took place in the autumn of 2018 and the spring in 2019. Both measurements lasted 14 days. Long-term measurement was important to capture several variations of traffic. Analysis of volumes showed the recurrence of congestions. Data from the entire survey were used as a part of the calibration data for the transport model. A detailed analysis of traffic flow characteristics was prepared for the present study of over-capacity volumes. We analyzed the theoretical changes in the modal split. The analysis mainly included data from the profile traffic count, mobility survey, and environmental statistics. Through the density of the traffic flow, we determined the real capacity of the road. Then we determined the share of drives that needed to be converted to another mode of transport in the morning rush hour by comparing the hourly peak volumes with the capacity. The software BIOGEME was used to calculate the efficiency of commuting by multiple means of transport. The attractiveness of the public transport in the modal split was recalculated by changing the travel cost, which is one of the most significant variables in mode choice [32].

Traffic Flow Characteristics
Traffic flow varies in time and space. When considering the flow of traffic along a highway, three descriptors are of considerable significance: the speed and the density or concentration, which describe the quality of service experienced by the stream; and the flow or volume, which measures the quantity of the stream and the demand on the highway facility. The speed is the space mean speed, the density or concentration is the number of vehicles per unit length of the highway, and the flow is the number of vehicles (N) passing a given point on the highway per time unit (T). The relationship between these parameters of the flow may be derived as follows. Consider a short section of the highway of length L in which q vehicles pass a point in the section during a time interval T, with all the vehicles traveling in the same direction [39].
The volume flowing [39] is The density is k = average no. o f vehicles travelling over L L The average number of vehicles traveling over L is given by where t is the time of travel of the ith vehicle over the length L; then The volume (or flow rate), length of vehicles, and speeds are the only direct measurements at a point. Density is the number of vehicles occupying a given length of a lane or roadway at a particular instant [40]. Density can be calculated from point measurements when speed is available, but one would have to question the meaning of the calculation, as it would be density at a point [41].
The measurement of the real density over extended lengths comes at a cost. First, it requires detectors on both ends of the segment. If it is ultimately found that a single value of density per lane can be used to infer capacity drop at a variety of bottleneck types, then detector placement might become more worthy of consideration [22]. The fundamental diagram is a graphical illustration of the equation of the state of traffic, i.e., the functional relationship between the parameters of traffic volume q, traffic density k, and the mean momentary, i.e., section-related speed v, and represents a curve in three-dimensional space. The orthogonal projections of the curve onto the planes, each spanned by two parameters, result in the familiar fundamental diagram shown in Figure 6. The resulting three diagrams enable a variety of information about the characteristics of traffic flow over a cross-section to be depicted and are referred to as the q-v diagram, the q-k diagram, and the k-v diagram [42]. curve in three-dimensional space. The orthogonal projections of the curve onto the planes, each spanned by two parameters, result in the familiar fundamental diagram shown in Figure 6. The resulting three diagrams enable a variety of information about the characteristics of traffic flow over a cross-section to be depicted and are referred to as the q-v diagram, the q-k diagram, and the k-v diagram [42]. The fundamental diagram demonstrates that, for the same traffic volume ql, two different qualities of traffic flow can occur. The threshold qmax separates for qi < qmax the range of high speeds at low traffic densities, i.e., the free and stable flow of traffic, from the range with relatively low speeds and high traffic densities, i.e., the range of unstable and interrupted traffic flow. Empirical studies reveal that the transition between a stable and unstable traffic state does not run continuously, as shown in Figure 1 in an idealized form. Rather, in case of high traffic load triggered by disturbances, a transition from the stable to the unstable range takes place [42]. This transition is associated with a significant drop in traffic volume. In light of these considerations, May and Keller [43] characterized three forms of traffic that occur: • Free traffic at high speeds and low traffic volumes and densities.

•
Partially constricted traffic, up to the range of maximum traffic volumes, optimal speed, and traffic density.

•
Constricted traffic with high traffic densities, low traffic volumes, and speeds. The fundamental diagram demonstrates that, for the same traffic volume q l , two different qualities of traffic flow can occur. The threshold q max separates for q i < q max the range of high speeds at low traffic densities, i.e., the free and stable flow of traffic, from the range with relatively low speeds and high traffic densities, i.e., the range of unstable and interrupted traffic flow. Empirical studies reveal that the transition between a stable and unstable traffic state does not run continuously, as shown in Figure 1 in an idealized form. Rather, in case of high traffic load triggered by disturbances, a transition from the stable to the unstable range takes place [42]. This transition is associated with a significant drop in traffic volume. In light of these considerations, May and Keller [43] characterized three forms of traffic that occur: • Free traffic at high speeds and low traffic volumes and densities.

•
Partially constricted traffic, up to the range of maximum traffic volumes, optimal speed, and traffic density.

•
Constricted traffic with high traffic densities, low traffic volumes, and speeds.
The efficiency of the traffic system depends on the capacity of the traffic infrastructure. This capacity is defined as the "largest volume of traffic that traffic flow can reach at a given distance and traffic conditions at the cross-section determined for this flow" [44]. It is determined by the density of the platoon of vehicles and the speed with which the platoon passes through the cross-section [11].
In this study, the traffic load and the maximum volume, which we determined from the relationship between the volume and density of the traffic flow, were further analyzed.

Modal Split
Mode choice models determined the traveler's mode selection, e.g., car or public transport. The input variables indicate all possible available modes of transport and proportions of travelers who would use each mode of transport. For example, consider a binary logit model of whether a person takes a given action, such as buying a new product. The behavioral model is specified as follows. The person would obtain some net benefit, or utility, from taking the action. This utility, which can be either positive or negative, consists of a part that is observed by the researcher, βx, where x is a vector of variables and β is a vector of parameters and a part that is not observed, ε: U = βx+ ε. The person takes the action only if the utility is positive, that is, only if doing so provides a net benefit. The probability that the person takes the action, given what the researcher can observe, is therefore P = I[β x + ε > 0] f (ε)dε, where f is the density of ε. Assume that ε is distributed logistically, such that its density is f (ε) = e −ε /(1 + e −ε ) 2 2 with the cumulative distribution F(ε) = 1/(1 + e −ε ). Then the probability of the person taking the action is [45][46][47] (5) For any x, the probability can be calculated exactly as P = exp(β x)/(1 + exp(β x)). Other models also have closed-form expressions for the probabilities. Multinomial logit, nested logit, and ordered logit are prominent examples [48].
The Multinomial Logit Model (MNL) is widely used for analyzing travel-related choice problems, such as travel mode choice, route choice, etc. MNL assigns a utility to each alternative i for decisionmaker n, noted as Uni, and the utility function is composed of two parts, namely the deterministic part (travel time, waiting time, car ownership) and the random part (ε) [49]. The Formula (5) may also be written in terms of the probabilities of the multinomial logit model, P. The choice between J (greater than 2) categories, with dependent variables y n = 1, 2, 3, . . . , J and explanatory variables x n is defined as a conditional MNL model (6) [45,46].
The utility functions are defined for each demand stratum (strata). The demand stratum constitutes the basic demand object for calculating trip generation, trip distribution, and mode choice. It links an activity chain with one-or several-person groups (in the trip-based model with the exactly one-person group) [50]. The utility function refers to the complete utility; x n is a vector of the values of each factor and αn is a vector of the utility weights of each factor. As can be seen, mathematically utility is the scalar product of the factors and their weights. It is practical if the sum of the utility weights is 1 [41]. The factors can also be defined as continuous variables or as a group of discrete variables. The stated preference method can also be used to test alternative hypotheses [17]. The utility function also contains a variable, ASC_"mode". ASC_"mode" refers to the alternative specific constants (ASC) of the first three alternatives. The alternative-specific constants indicated the commuters' inherent preferences among four labeled alternatives [40].
The factor (B) was calculated using the software Biogeme. The software was developed by Michel Bierlaire, Ecole Polytechnique Fédérale de Lausanne, Switzerland [50,51]. It is an open-source freeware designed for the maximum likelihood estimation of parametric models in general, with a special emphasis on discrete choice models [49].

Emission View
One of the additional aims of this study was to determine the amount of protection of the environment caused by a targeted change of the modal split. The methodology for calculating the greenhouse gas production of CO 2 or a CO 2 equivalent was taken from the US EPA methodology.
All numerical values given are in accordance with this methodology. The intention was primarily to quantify the possible savings in CO 2 production for the chosen scenario.
Greenhouse gases are gases in the atmosphere such as water vapor, carbon dioxide, methane, and nitrous oxide that can absorb infrared radiation, trapping heat in the atmosphere. In 2017, the ratio of carbon dioxide emissions to total greenhouse gas emissions (including carbon dioxide, methane, and nitrous oxide, all expressed as carbon dioxide equivalents) for passenger vehicles was 0.989. The amount of carbon dioxide emitted per liter of motor gasoline burned is 2.35 × 10 −3 metric tons, as calculated in "liters of gasoline consumed" [52]. Passenger vehicles are defined as two-axle four-tire vehicles, including passenger cars, vans, pickup trucks, and sport/utility vehicles. In 2017, the weighted average of the combined fuel economy of cars and light trucks was 9.48 km per liter. The average vehicle kilometers traveled (VKT) in 2017 was 18,489 km per year [53].
To determine annual greenhouse gas emissions per passenger vehicle, the following methodology was used: VKT (average vehicle kilometers traveled per year) was divided by average gas mileage to determine liters of gasoline consumed per vehicle per year. Liters of gasoline consumed was multiplied by carbon dioxide per liter of gasoline to determine carbon dioxide emitted per vehicle per year. Carbon dioxide emissions were then divided by the ratio of carbon dioxide emissions to total vehicle greenhouse gas emissions to account for vehicle methane and nitrous oxide emissions [53].
Due to rounding, performing the calculations given in the equations below (7) where VKT is average vehicle kilometers travelled per year [54].

Analysis of Traffic Count
The database was based on measurements in the Žilina self-governing region. The traffic counts were carried out in September and October of 2018. The survey included roads with various functions and categories. We analyzed 52 cross-sections. Data were recorded for seven consecutive days from 00:00 to 23:59. The following variables were recorded by radar Sierszega 04: direction, speed, and vehicle distances. The database was aggregated into 15-min intervals and then into hourly intervals. Subsequently, the data were analyzed in the Matlab program. An example of the evaluated parameters of the over-capacity assignment of traffic flow for road I/11 is shown in Figure 7.  The first graph (1-1) presents the relationship between speed and traffic volumes. The second (1-2) demonstrates the relationship between traffic density and traffic volumes. These two data sets were used for evaluation of the real capacity. The maximum value of the traffic volumes per hour was nearly 1800 veh/h. The third graph (2-1) complements the ratio between speed and density. The value of density increases as the speed decreases. The last graph presents the interrelation of traffic volumes, speed, and density. In the following steps, we focused on roads that regularly exceeded capacity.
We specifically focused on the travel direction from Kysuce to Žilina. The selected direction The first graph (1-1) presents the relationship between speed and traffic volumes. The second (1-2) demonstrates the relationship between traffic density and traffic volumes. These two data sets were used for evaluation of the real capacity. The maximum value of the traffic volumes per hour was nearly 1800 veh/h. The third graph (2-1) complements the ratio between speed and density. The value of density increases as the speed decreases. The last graph presents the interrelation of traffic volumes, speed, and density. In the following steps, we focused on roads that regularly exceeded capacity.
We specifically focused on the travel direction from Kysuce to Žilina. The selected direction includes a significant proportion of morning trips to work. The necessary change in the modal split will subsequently be shown in the afternoon. We assume that the workers use the same transport mode for the trip from work as for the trip to work.
The total histogram of the traffic load in individual hourly intervals during the measurement is presented in Figure 8. It presents hourly traffic volumes as the sum of the four 15-min intervals. The maximum hourly volumes are balanced during the main working hours (05:00-17:00). This indicates a constant state of road congestion. The maximum hourly volumes were between 1800 and 1900 veh/h. Hourly traffic volumes under 1000 veh/h were measured during the weekend.
The first graph (1-1) presents the relationship between speed and traffic volumes. The second (1)(2) demonstrates the relationship between traffic density and traffic volumes. These two data sets were used for evaluation of the real capacity. The maximum value of the traffic volumes per hour was nearly 1800 veh/h. The third graph (2-1) complements the ratio between speed and density. The value of density increases as the speed decreases. The last graph presents the interrelation of traffic volumes, speed, and density. In the following steps, we focused on roads that regularly exceeded capacity.
We specifically focused on the travel direction from Kysuce to Žilina. The selected direction includes a significant proportion of morning trips to work. The necessary change in the modal split will subsequently be shown in the afternoon. We assume that the workers use the same transport mode for the trip from work as for the trip to work.
The total histogram of the traffic load in individual hourly intervals during the measurement is presented in Figure 8. It presents hourly traffic volumes as the sum of the four 15-min intervals. The maximum hourly volumes are balanced during the main working hours (05:00-17:00). This indicates a constant state of road congestion. The maximum hourly volumes were between 1800 and 1900 veh/h. Hourly traffic volumes under 1000 veh/h were measured during the weekend.  The graph ( Figure 5) shows the ratios between traffic flow and traffic density k, or space mean speed v m . The measured vehicle flow started decreasing after capacity. Using a MatLab script, we calculated the capacity for a traffic flow of 1550 veh/h. The theoretical capacity (HCM 2015) was 1800 veh/h) [20].
The next step covered the comparison of hourly volumes with the determined real capacity. Figure 9 shows the average hourly numbers and the number of vehicles above capacity. The graph on the right shows the ratio between space mean speed and traffic volumes (the speed-flow relationship). The graph presents the speed-flow of similar data dependence. In the analysis, we used maxima from the ratio of density and traffic volumes (graph on the left) because of the smaller maximum of the function. The LOS (Level of Service) was also evaluated by traffic density [21,55]. In total, we detected 288 states exceeding the hourly capacity. We analyzed exceedances on each measurement day. Furthermore, we considered the average capacity exceedances in the calculation. For illustration, the values of the maximum over-capacity volumes are shown in Figure 10. The maximum value of the exceeding volumes was 350 veh/h from all measured days. The average maximum of exceedance was 202 veh/h. exceeding the hourly capacity. We analyzed exceedances on each measurement day. Furthermore, we considered the average capacity exceedances in the calculation. For illustration, the values of the maximum over-capacity volumes are shown in Figure 10. The maximum value of the exceeding volumes was 350 veh/h from all measured days. The average maximum of exceedance was 202 veh/h.   9 shows the average hourly numbers and the number of vehicles above capacity. The graph on the right shows the ratio between space mean speed and traffic volumes (the speed-flow relationship). The graph presents the speed-flow of similar data dependence. In the analysis, we used maxima from the ratio of density and traffic volumes (graph on the left) because of the smaller maximum of the function. The LOS (Level of Service) was also evaluated by traffic density [21,55]. In total, we detected 288 states exceeding the hourly capacity. We analyzed exceedances on each measurement day. Furthermore, we considered the average capacity exceedances in the calculation. For illustration, the values of the maximum over-capacity volumes are shown in Figure 10. The maximum value of the exceeding volumes was 350 veh/h from all measured days. The average maximum of exceedance was 202 veh/h.   The obtained data of the over-capacity volumes could be presented on several levels including as a saturation ratio and as an opportunity to motivate inhabitants to change travel behavior. The analyzed count point on the road I/11 was purposefully selected for the possibility of using a parallel railway.
In the next section, we classified all over-capacity volumes as a regular trip to work. This scenario describes the consequences of the transfer of selected parts of car trips to public transport. The changes in the modal split were analyzed by the conversion of the over-capacity volumes to trips to work. The differences between car trips and public transport trips were also presented from an environmental point of view.

Utility of Work-Related Travel
As mentioned above, we aimed to express the value of over-capacity volumes from several perspectives. One of them was the mathematical mode choice model (modal split) based on the utility theory.
The results below are derived from the mobility survey data. All data filters were used only at the demand strata definition (person group, trip purpose). Trips shorter than 2 km were considered for the evaluation of the utility function set data. These trips did not affect traffic on road I/11. The utility functions for the modal split of the employed persons contained observed values: Accessibility (Dos).
The modal split was set for these seven transport modes (V1-V7): Car passenger (OAs), • Bus (City BUS), • Regional Bus, • Train (Vlak). Figure 11 shows the definition of the utility function in the modal split model for the selected sample.

railway.
In the next section, we classified all over-capacity volumes as a regular trip to work. This scenario describes the consequences of the transfer of selected parts of car trips to public transport. The changes in the modal split were analyzed by the conversion of the over-capacity volumes to trips to work. The differences between car trips and public transport trips were also presented from an environmental point of view.

Utility of Work-Related Travel
As mentioned above, we aimed to express the value of over-capacity volumes from several perspectives. One of them was the mathematical mode choice model (modal split) based on the utility theory.
The results below are derived from the mobility survey data. All data filters were used only at the demand strata definition (person group, trip purpose). Trips shorter than 2 km were considered for the evaluation of the utility function set data. These trips did not affect traffic on road I/11. The utility functions for the modal split of the employed persons contained observed values: Accessibility (Dos).
The modal split was set for these seven transport modes (V1-V7): Car passenger (OAs), • Bus (City BUS), • Regional Bus, • Train (Vlak). Figure 11 shows the definition of the utility function in the modal split model for the selected sample. Figure 11. The definition of the Utility function in BIOGEME.
The sample for the database trips file was extracted from the mobility survey of the Žilina selfgoverning region. The parameters of the utility function and model characteristics are presented in Table 1. The sample for the database trips file was extracted from the mobility survey of the Žilina self-governing region. The parameters of the utility function and model characteristics are presented in Table 1.

Mode Choice Scenarios
Travel time and travel costs are the most significant variable in all the models. The negative coefficient for travel time and travel cost indicated the decreased utility. The utility values were associated with increased travel time and travel cost. The determination of mode choice probability was performed for three scenarios: Scenario 0 covered the real state during the morning peak. The figure below shows the differences between mobility data and the modeled data of the mode choice (Scenario 0). The largest portion of data (56%) was the transport mode "car driver". Figure 11 shows the comparison of observed and modeled modal split. The total differences were lower than 1%. We used Scenario 0 as a basic file.
Scenarios that were characterized by a change in the utility of trips by car and public transport were evaluated. The difference (in percentage expression of the modal split) compared to Scenario 0 is shown in Figure 12.

.3. Mode Choice Scenarios
Travel time and travel costs are the most significant variable in all the models. The negativ efficient for travel time and travel cost indicated the decreased utility. The utility values wer sociated with increased travel time and travel cost. The determination of mode choice probability wa erformed for three scenarios: Scenario 0 covered the real state during the morning peak. The figure below shows th ifferences between mobility data and the modeled data of the mode choice (Scenario 0). The larges ortion of data (56%) was the transport mode "car driver". Figure 11 shows the comparison o bserved and modeled modal split. The total differences were lower than 1%. We used Scenario 0 a basic file.
Scenarios that were characterized by a change in the utility of trips by car and public transpor ere evaluated. The difference (in percentage expression of the modal split) compared to Scenario shown in Figure 12. In Scenario 1, the region transport study evaluated the sufficient capacity for public transpor or this reason, we changed the travel costs with a focus on public transport. The utility parameter ere set as zero fares for the public transport mode (train and bus). However, such an interventio id not have the desired effect. The traffic caused by car drivers decreased by 3%. In Scenario 1, the region transport study evaluated the sufficient capacity for public transport. For this reason, we changed the travel costs with a focus on public transport. The utility parameters were set as zero fares for the public transport mode (train and bus). However, such an intervention did not have the desired effect. The traffic caused by car drivers decreased by 3%.
Scenario 2 covered a focused scenario that presented the power of the modal split changes in favor of non-collapsing road transport when the saturation of traffic flow was under 1.0. Zero cost of public transport did not change the utility for trips to work by car (car driver) significantly. We increased the value of the car cost from 0.15 to 0.35 €/km. As a result, we reached the goal of reducing the number of trips to work by car by almost 10% (Figure 13). The aim of the research was also to prove that there is a positive impact of reducing emissions for target scenario 2. We can assume a greenhouse gas Scenario 2 covered a focused scenario that presented the power of the modal split changes in vor of non-collapsing road transport when the saturation of traffic flow was under 1.0. Zero cost o ublic transport did not change the utility for trips to work by car (car driver) significantly. W creased the value of the car cost from 0.15 to 0.35 €/km. As a result, we reached the goal of reducing e number of trips to work by car by almost 10% (Figure 13). The aim of the research was also to rove that there is a positive impact of reducing emissions for target scenario 2. We can assume eenhouse gas CO2 savings of 935 t/year in the case of a reduction in vehicle volumes by 202 veh/h The Equivalent to CO2 emissions are presented in Table 2 [18]. From an environmental point o iew, the amount of 935 t CO2 saved per year represents approximate savings of EUR 23,375 at EUR /t CO2.

Discussion
In general, traffic analyses and traffic models are based on several surveys and databases nding their interconnection increases the credibility of the final results. The presented issu mbines traffic-sociological data with the traffic load of the infrastructure. The desired result is pacity-balanced state with the possible use of public transport capacities.
The study of the drivers' behavior in the transport process is the aim of several studies [56][57][58][59] is indicated that the basic characteristics (for example, speed or acceleration) vary depending on The Equivalent to CO 2 emissions are presented in Table 2 [18]. From an environmental point of view, the amount of 935 t CO 2 saved per year represents approximate savings of EUR 23,375 at EUR 25/t CO 2 .

Discussion
In general, traffic analyses and traffic models are based on several surveys and databases. Finding their interconnection increases the credibility of the final results. The presented issue combines traffic-sociological data with the traffic load of the infrastructure. The desired result is a capacitybalanced state with the possible use of public transport capacities.
The study of the drivers' behavior in the transport process is the aim of several studies [56][57][58][59]. It is indicated that the basic characteristics (for example, speed or acceleration) vary depending on the location (city, village, suburban, etc.). The presented research analyzed the critical situation on one of the main routes of TEN-T corridors in Slovakia. The enormous increase in regional traffic and the high ratio of the transit traffic, resulting from the region's location at the three-state border, is the cause of regular traffic congestion. One way to improve this is to change the traffic mode and move users to public transport (PuT). The possibilities of the change have been defined based on mobility data and monitoring of traffic volumes, especially during the morning peak hours. The reduction of congestion, significantly reducing the negative effects on the environment, was analyzed using definitions of modeled Scenario 1.
The travel time and travel cost mainly affect the choice of destination, route decision, and the choice of transport mode. In this study, we searched for possibilities for equilibrium between supply and demand for transport systems. The purpose of the presented analysis was only analysis of regular trips. The most numerous trips are work-related travel during morning peak hours. The real route capacity was determined by density and speed of the traffic flow. Data were gathered over four weeks at the regularly-congested location. Capacity and other traffic analyses typically focus on the peak-hour traffic volume, because it represents the most critical period for operations and has the highest capacity requirements. The peak-hour volume is not a constant value from day to day or from season to season [33]. We take into account that the change of real capacity limits will change the value of the over-capacity volume. Here, we considered the average values.
We evaluated the volumes, which exceeded the saturation state during the measurement. The average maximum of exceedance was 202 veh/h. The maximum value of exceedance during all measured days was 350 veh/h. From the results of the mobility survey, we identified the ratio of routes with the purpose "job". Our task was to model the state where a theoretically smooth traffic flow is achieved. The equilibrium state was determined by the change of modal split of regular trips to work. The aim was to determine the impact of the price, as it is easily identifiable on regular trips. The utility theory was used to determine the changes in travel costs to achieve a capacity equilibrium. We analyzed Scenario 1 with 100% subsidized public transport. The results of the modal split for Scenario 1 did not ensure the targeted equilibrium state. Scenario 2 was taken from Scenario 1 with an increase in the cost of a trip by car. The car cost increased from 0.15 €/km to 0.35 €/km. The total increase in public transport was 10%. The mathematical model shows the power of transport habits. In addition to the impact on the risk of congestion, the transfer of users to PuT also resulted in a significant reduction in the environmental impact.
Road transport accounts for 72% of total greenhouse gas emissions of the transport sector (EEA, 2018). Ongoing energy efficiency improvements in road transport have played a key role in limiting the increase of road transport emissions. Such improvements were brought about in part by increasingly stringent technical standards, including the fleet average CO 2 emission requirements for new passenger cars and vans. The analyzed Scenario 2 could save 935 t CO 2 (EUR 23,375 at EUR 25/t CO 2 ). This value is equivalent to 202 passenger vehicles driven for one year or the energy consumption of approximately 108 households for one year [52]. A modal shift away from road transport is a key element of the EU's decarbonization ambitions. The White Paper explicitly states the ambition to shift 30% of road transport for distances over 300 km to rail and waterborne transport by 2030 and more than 50% by 2050.
Research suggests that drivers who have the opportunity to travel for free on public transport for a long time are likely to change their traffic habits [60]. The main goal of the presented study was to connect the road and public transport capacities from the point of view of mutual balance. Specifically, 10% of regular journeys by car could be transferred to public transport. The results also point to a strong link between residents and their cars. The model showed a willingness to travel in a passenger car to work more expensive by a maximum of 0.2 €/km (scenario 2). This value reflects the potentials of public transport as such. These are mainly the availability, transfer time, and quality of travel. This knowledge can support the results of a traffic survey in the town of Frýdek Místek (60 km away from Žilina in the Czech Republic), where there is free public transport not only in the town, but also in light villages. The respondents sorted characteristics (travel-time, frequency, safety, comfort on the board, feasibility, accessibility, and price) according to the most important to the least important by grading them on a scale from 1 to 7. The price represents a strong element in respondents' attitudes, but due to the fare-free bus pass, it is not taken into a consideration. What turned out to be crucial for the respondents was safety, travel-time (speed), and frequency. The order of the pyramid demonstrates the quality of the public transport service [61].
On the other hand, free public transport has an impact mainly on leisure activities [61]. These are usually regular trips in a relatively short time. However, this finding is at odds with our marginal condition for regular trips to work. In the next part of the research, we would like to focus on a detailed assessment of the benefits of the trip and include other factors such as emissions, conforming to the modal split analysis. As is indicated in [62], the emission was found to be positively related to the car and motorcycle mode, but was negatively linked with the proportion of bicycle, walk, and public transport mode. As a result, changing mode from motorized to non-motorized modes and the shift from private transport to public transport could bring great benefit for sustainable urban growth. For job trips, the change of about 15% of a modal split from car to NMVS (Non-Motorized Vehicles) or bus will lead to the reduction in emission per trip by half. The same effect has a 4.3% shift from motorcycle to NMVS or the bus.
The long-term development of the analyzed rural areas by investments in the traffic sector needs to be implemented. The investments have to reflect the pressing needs of the local population in terms of mobility to lay the groundwork for development. At the same time, these investments would effectively stimulate economic and social development, as well as territorial cohesion. The availability of public transportation, the increase of service quality for passengers, better management of routes, and the establishment of integrated traffic systems in public transportation would contribute to changing emigration trends of the rural areas, thus improving the quality of life in the analyzed region.
The added value of the analysis is the possibility of data using for transport modelling process and, finally for traffic prognosis, modal split included. According to [63], the SUMP will build the business as usual (BAU) scenario and at least two alternative low carbon scenarios with their defined actions to be taken in the short-and the long-term. In practice, however, there are many factors by which we can achieve the desired results. On the one hand, unpopular strict scenarios can be proposed, on the other hand, the changes can be gradually introduced, thus achieving the gradual effect in the perception of the benefits of individual means of transport. The results of our study point to the possibilities of the interconnection of transport systems.
In the future, we would like to continue the complex analysis of the impact of modal split with consideration of changing climatic conditions, pavement maintenance, and serviceability factors [64,65]. The presented research activities will be extended by analyses of other significant effects of the modal split in favor of PuT.
Author Contributions: The authors contributed equally to this research work and they were all involved in an integrated way in the various stages of this research including conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing-original draft preparation, writing-review and editing, visualization, supervision, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript. shift from motorcycle to NMVS or the bus.
The long-term development of the analyzed rural areas by investments in the traffic sector needs to be implemented. The investments have to reflect the pressing needs of the local population in terms of mobility to lay the groundwork for development. At the same time, these investments would effectively stimulate economic and social development, as well as territorial cohesion. The availability of public transportation, the increase of service quality for passengers, better management of routes, and the establishment of integrated traffic systems in public transportation would contribute to changing emigration trends of the rural areas, thus improving the quality of life in the analyzed region.
The added value of the analysis is the possibility of data using for transport modelling process and, finally for traffic prognosis, modal split included. According to [63], the SUMP will build the business as usual (BAU) scenario and at least two alternative low carbon scenarios with their defined actions to be taken in the short-and the long-term. In practice, however, there are many factors by which we can achieve the desired results. On the one hand, unpopular strict scenarios can be proposed, on the other hand, the changes can be gradually introduced, thus achieving the gradual effect in the perception of the benefits of individual means of transport. The results of our study point to the possibilities of the interconnection of transport systems.
In the future, we would like to continue the complex analysis of the impact of modal split with consideration of changing climatic conditions, pavement maintenance, and serviceability factors [64,65]. The presented research activities will be extended by analyses of other significant effects of the modal split in favor of PuT.
Author Contributions: The authors contributed equally to this research work and they were all involved in an integrated way in the various stages of this research including conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing-original draft preparation, writing-review and editing, visualization, supervision, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.