UDC: 656.13
https://doi.org/10.25198/2077-7175-2026-2-90


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GRAPH-ANALYTICAL METHOD FOR CALCULATING THE REQUIRED NUMBER OF ROLLING STOCK FOR OPERATION ON URBAN PASSENGER TRANSPORT ROUTES

A. A. Tsarikov 1, D. G. Nevolin 2
Ural State University of Railway Transport, Yekaterinburg, Russia
1 e-mail: zarikof@mail.ru
2 e-mail: innotrans@mail.ru

Abstract. At the current stage of development of Russian cities, the level of motorization of the population has reached such values when the street and road network has practically exhausted its capacity. To solve this problem, it is necessary to develop urban passenger transport, including improving the quality of service. At the same time, along with priority access, urban passenger transport should be comfortable and require minimal operating costs. Given the above, a more detailed selection of rolling stock used on the route is required, as well as new methods for calculating its quantity.

At the same time, modern regulatory requirements impose significant restrictions on the working and rest schedules of drivers. This complicates the process of scheduling the operation of rolling stock on the line.

The purpose of this study is to develop a modern methodology for selecting rolling stock and calculating its required quantity at different times of the day.

The approaches used. When developing the necessary method, a review of domestic literature was conducted in terms of the formulas and materials used for selecting rolling stock on the route and calculating its quantity. These were analyzed in terms of their shortcomings, which are critical for modern passenger transportation conditions.

Results. A graph-analytical method has been developed for calculating the required number of rolling stock, which allows for the use of buses of several classes of capacity in the calculations. This method takes into account the restrictions imposed by regulatory documents on the work and rest schedules of drivers, as well as the intra-hour and hourly unevenness of passenger traffic.

Further research is expected to be conducted in the direction of developing recommendations for the use of rolling stock of various classes, depending on the values of maximum passenger flows on the route, as well as its hourly unevenness.

Key words: urban passenger transport, passenger flow, rolling stock structure, coefficient of unevenness by hours of the day.

Cite as: Tsarikov, A. A., Nevolin, D. G. (2026) [Graph-analytical method for calculating the required number of rolling stock for operation on urban passenger transport routes]. Intellekt. Innovacii. Investicii [Intellect. Innovations. Investments]. Vol. 2, pp. 90–105. – https://doi.org/10.25198/2077-7175-2026-2-90.


References

  1. Azemsha, S. A., Kravchenya, I. N. (2021) [Evaluation of the effectiveness of optimizing the schedule of urban passenger transport on duplicate routes]. Vestnik Sibirskogo gosudarstvennogo avtomobil’no-dorozhnogo universiteta. [Bulletin of the Siberian State Automobile and Road University]. Vol. 1, pp. 72–85. – http://doi.org/10.26518/2071-7296-2021-18-1-72-85. (In Russ.).
  2. Azemsha, S. A., Starovojtov, A. N., Skirkovskij, S. V (2013) [Optimization of vehicle traffic intervals during urban passenger transportation in regular services]. Vestnik Belorusskogo gosudarstvennogo universiteta transporta: Nauka i transport. [Bulletin of the Belarusian State University of Transport: Science and Transport]. Vol. 2, pp. 52–57. (In Russ.).
  3. Bannov, G. G. (2024) [Optimization of the rolling stock structure of urban passenger ground transport]. Fundamental’nye i prikladnye issledovaniya molodyh uchyonyh : Sbornik materialov VIII Mezhdunarodnoj nauchno-prakticheskoj konferencii studentov, aspirantov i molodyh uchyonyh, priurochennoj k prazdnovaniyu 300-letiya Rossijskoj akademii nauk, Omsk, 25–26 aprelya 2024 goda [Fundamental and Applied Research by Young Scientists: Collection of Materials of the VIII International Scientific and Practical Conference of Students, Postgraduates, and Young Scientists Dedicated to the 300th Anniversary of the Russian Academy of Sciences, Omsk, April 25–26, 2024. – Omsk: Siberian State Automobile and Road University (SibADI)], pp. 185–193. (In Russ.).
  4. Volodkin, P. P., Dyachkova, O. M., Ryzhova, A. S. (2015) [Determining the required number of buses on routes based on the travel interval, using the example of Khabarovsk]. Transport: nauka, tekhnika, upravlenie. Nauchnyj informacionnyj sbornik. [Transport: Science, Technology, Management. Scientific Information Collection]. Vol. 3, pp. 28–32. (In Russ.).
  5. Dryuchin, D. A. (2025) [Methods for optimizing the structural parameters of urban passenger transport]. Mir transporta i tekhnologicheskih mashin. [The world of transport and technological machines]. Vol. 1–3, pp. 52–61. – http://doi.org/10.33979/2073-7432-2025-1-3(88)-52-61. (In Russ.).
  6. Kotenkova, I. N., Lebedev, E. A., Rassoha, V. I. (2025) [On the issue of passenger transport priority in cities]. Progressivnye tekhnologii v transportnyh sistemah : Materialy XIX Vserossijskoj nauchno-prakticheskoj konferencii s mezhdunarodnym uchastiem, Orenburg, 20–22 noyabrya 2024 goda. – Orenburg: Orenburgskij gosudarstvennyj universitet [Progressive Technologies in Transport Systems: Proceedings of the 19th All-Russian Scientific and Practical Conference with International Participation, Orenburg, November 20–22, 2024. Orenburg: Orenburg State University], pp. 239–248. (In Russ.).
  7. Lavrentev, A. A. (2025) [Analysis of trends in the development of the urban passenger transport bus fleet structure]. Upravlenie kachestvom v transportnoj i social’noj sferah : sbornik materialov XLVII Vserossijskoj studencheskoj nauchnoj konferencii, Orenburg, 01–08 aprelya 2025 goda. – Orenburg: Orenburgskij gosudarstvennyj universitet [Quality Management in the Transport and Social Spheres: Collection of Materials from the XLVII All-Russian Student Scientific Conference, Orenburg, April 01–08, 2025. Orenburg: Orenburg State University]. pp. 50–54. (In Russ.).
  8. Konovalova, T. V., et al. (2024) [Methodology for ensuring priority conditions for urban passenger transport]. Mir transporta. [The world of transport]. Vol. 2, pp. 70–80. – http://doi.org/10.30932/1992-3252-2024-22-2-7. (In Russ.).
  9. Orlov, A. L. (2009) [Automobility throughout the country: pros and cons]. Rossijskoe predprinimatel’stvo [Russian entrepreneurship]. Vol. 9–1, pp. 98–102. (In Russ.).
  10. Parshakova, K. A., Yakunin, N. N., Yakunina, N. V. (2024) [The impact of passenger flow characteristics on the efficiency of daily traffic intervals]. Transport Rossijskoj Federacii. Zhurnal o nauke, praktike, ekonomike [Transport of the Russian Federation. Journal on Science, Practice, and Economics]. Vol. 4, pp. 43–46. (In Russ.).
  11. Ryabov, I. M., Kashmanov, R. Ya. (2019) [Improving the organization of passenger service on the route by using buses of different capacities]. Vestnik Sibirskogo gosudarstvennogo avtomobil’no-dorozhnogo universiteta. [Bulletin of the Siberian State Automobile and Road University]. Vol. 3, pp. 264–275. (In Russ.).
  12. Fadeev, A. I., Fomin, E. V. (2018) [Methodology for solving the problem of determining the optimal structure of the fleet of public passenger transport vehicles] Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta. [Bulletin of Irkutsk State Technical University.] Vol. 1, pp. 218–227. – http://doi.org/10.21285/1814-3520-2018-1-218-227. (In Russ.).
  13. Carikov, A. A. (2021) [Problems with servicing urban passenger transport routes during peak hours]. Dal’nij Vostok : problemy razvitiya arhitekturno-stroitel’nogo kompleksa. [The Far East: Problems of Architectural and Construction Complex Development]. Vol. 1, pp. 205–209. (In Russ.).
  14. Yakunina, N. V. (2011) [Improving the methodology for determining the structure of urban passenger motor transport rolling stock]. Vestnik Orenburgskogo gosudarstvennogo universiteta [Bulletin of Orenburg State University]. Vol. 10, pp. 13–19. (In Russ.).
  15. Yakunina, N. V., Yakunin, N. N. (2011) [Methodology for determining the structure of urban passenger motor transport rolling stock based on aggregated indicators of transport mobility]. Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta. [Bulletin of Irkutsk State Technical University]. Vol. 4, pp. 96–99. (In Russ.).
  16. Yacenko, S. A. (2016) [Analysis of methods for calculating the need for buses on urban routes]. Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta [Bulletin of Irkutsk State Technical University]. Vol. 5, pp. 193–202. – http://doi.org/10.21285/1814-3520-2016-5-193-202. (In Russ.).
  17. Cao, Zh., Ceder, A., Zhang, S. (2019) Real-time schedule adjustments for autonomous public transport vehicles. Transportation Research Part C: Emerging Technologies. Vol. 109, pp. 60–78. – http://doi.org10.1016/j.trc.2019.10.004. (In Eng.).
  18. Lopez-Ramos, F. (2014) Integrating network design and frequency setting in public transportation networks: a survey. SORT. Vol. 38. No. 2, pp. 181–214. (In Eng.).
  19. Lui, T., Ceder, A. (2018) Integrated public transport timetable synchronization and vehicle scheduling with demand assignment: A bi-objective bi-level model using deficit function approach. Transportation Research Part B: Methodological. Vol. 117, pp. 935–955. – http://doi.org/10.1016/j.trb.2017.08.024. (In Eng.).
  20. May, A. D. (2013) Urban Transport and Sustainability: The Key Challenges. International Journal of Sustainable Transportation. Vol. 7. No. 3, pp.170–185. – http://doi.org/10.1080/15568318.2013.710136. (In Eng.).
  21. Van, Nes R., Hamerslag, R., Immers, B. H. (1988) Design of public transport networks. Transportation Research Record, pp. 74–83. (In Eng.).

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