Estimation of Transport Potential in Regional Rail Passenger Transport by Using the Innovative Mathematical-Statistical Gravity Approach
- passenger flow between i-th and j-th places;
- gravity constant;
- source/origin potential of i-th place;
- destination potential of j-th place;
- deterrence function.
2. Materials and Methods
- Determination of actual transport needs.
- Determination of current travel motives.
- Classification of the transport service type.
- Definition of factors affecting transport services.
- Determination of transport potential.
- Determination of the range of railway infrastructure.
- Proposal for final timetable standards.
- Final timetable construction.
3.1. Transport Potential Based Formula
- Number of inhabitants belonging to the track line section under review.
- Momentum of the population.
- Transport distance.
- Availability of the railway station and stop.
- Overlapping with road.
- Continuity of the assessed section to other railway lines.
- The monitored area’s attractiveness.
3.2. Assignment of the Resulting Value of the Range of Transport Services
- The scale will be determined based on the calculation of the resulting value of Kp on the selected 30 transport sessions. Subsequently, assigning the resulting values to the different ranges of traffic, which will be marked with Roman numerals (I–X), including determining the optimum number of trains and the optimal number of seats;
- The sample of 30 transport sessions contains all transport sessions (track sections between individual centers) on Slovak railway networks in the Zilina and Trencin regions (with the exception of the Trencianska Tepla–Trencianske Teplice railway line). In the next step railway lines in western part of Slovakia (Bratislava–Trnava, Bratislava–Galanta, Bratislava–Kvetoslavov, Kuty–Skalica, Zohor–Zahorska Ves, Zohor–Plavecky Mikulas, Jablonica–Brezova pod Bradlom and Zbehy–Radosina), in central Slovakia (Breznicka–Katarinska Huta) and in eastern Slovakia (Plesivec–Slavosovce, Kosice–Kechnec, and Banovce nad Ondavou–Velke Kapusany) were analyzed. This selection covers transport sessions with different ranges of traffic: extremely high, extremely low and medium high transport potential are expected to make the subsequent data as relevant as possible;
- The following scale shall be based on the resulting Kp values on the analyzed transport lines, and the standard deviation shall be calculated from each of the resulting Kp values as a standard deviation:The number of monitored transport sessions is N for each session potential xi and the average value of Kp is .
- After the calculation, the individual ranges of the traffic services are determined by deducting the standard deviation (or its half value) from the average until the zero value is reached and then adding the same number of particular values, which can be express by:
- In the research 10 ranges of traffic service with 10 equally wide intervals were established, so it is preferable to consider half of the standard deviation, using this formula:
- However, after this step, it may be necessary to modify the said interval width, as it is very important to adjust the scale in such a way that it actually corresponds to the individual values that can be achieved on each transport route;
- Calculations of the transport potential Kp are given in Table 1, in which the main characteristics of the transport session (line type, number of line tracks, line lengths, as well as subsequent calculations of arithmetic mean and standard deviation) are expressed. The sessions are listed from the highest value to the lowest value of Kp potential.
- Following the width determination of the resulting Kp intervals for each range of service, the recommended daily number of pairs of all links, the recommended daily capacity, and the total number of all seats in all vehicles on session links shall be assigned to these ranges. The recommended capacity interval for individual ranges of transportation services is relatively wide, since it is necessary to consider individual extreme values of capacity of individual links. In fact, it is possible that one regional link can have a capacity of 50 seats (appropriate for motor unit) and another regional link can have a capacity of 480 seats (appropriate for a train set of wagons);
- For segments of regional and suburban transport services, recommended regional values are introduced in the Table 4; it is expressed in specified optimal number of train pairs as well optimal number of seats on all vehicles operated on the transportation session.
- Whether the region is attractive for tourism and whether there are tourist attractions (recreational, spa, sports, cultural, commercial, social, or other) close to the railway line;
- Whether most jobs, schools, universities, offices, etc. are concentrated in the region (from these centers it is necessary to ensure optimal transportation service);
- Whether the railway line is in direct parallel with the road;
- Whether the transport route is part of a railway line which is of important transit significance or only of local significance and the railway line is terminated at the head station;
- What is the general transport momentum trend in the region under review (but this data is rarely available).
4. Discussion and Conclusions
Conflicts of Interest
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|Transport Session||Railway Line Type||Tracks Number of Line||Railway Line Length (km)||Transport Potential Coefficient Kp||Range of Transportation Services|
|Trencianska Tepla–Horne Srnie||Regional||1||8||1821.07||VII|
|Kuty–Skalica na Slovensku||Regional||1||26||1056.32||III|
|Jablonica–Brezova pod Bradlom||Regional||1||12||912.26||II|
|Banovce n/O–Velke Kapusany||Regional||1||26||729.84||II|
|Nove Mesto n/V–Myjava||Regional||1||36||705.34||II|
|Average value Kp||1226.78|
|Standard deviation from individual values δ||583.482|
|Half of the standard deviation δ/2||291.741|
|Range of Transportation Service||Interval Width|
|X||2685.49 and more|
|Range of Transportation Service||Interval Width|
|X||3001 and more|
|Range of Transportation Service||Transport Potential Range Kp||Optimal Number of Train Pairs in Both Directions||Optimal Number of Seats for all Lines in Both Directions|
|I||0–700||4||up to 500 seats|
|X||3001 and more||50 and more||2500 and more|
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Gasparik, J.; Dedik, M.; Cechovic, L.; Blaho, P. Estimation of Transport Potential in Regional Rail Passenger Transport by Using the Innovative Mathematical-Statistical Gravity Approach. Sustainability 2020, 12, 3821. https://doi.org/10.3390/su12093821
Gasparik J, Dedik M, Cechovic L, Blaho P. Estimation of Transport Potential in Regional Rail Passenger Transport by Using the Innovative Mathematical-Statistical Gravity Approach. Sustainability. 2020; 12(9):3821. https://doi.org/10.3390/su12093821Chicago/Turabian Style
Gasparik, Jozef, Milan Dedik, Lukas Cechovic, and Peter Blaho. 2020. "Estimation of Transport Potential in Regional Rail Passenger Transport by Using the Innovative Mathematical-Statistical Gravity Approach" Sustainability 12, no. 9: 3821. https://doi.org/10.3390/su12093821