DEVELOPMENT OF A METHOD FOR DELIMITING THE WAGON FLEET IN THE THEORY OF A LINEAR CITY BASED ON THE PRINCIPLES OF CLASSIFIERS

Danish Scientific Journal No102, 2025 103 DEVELOPMENT OF A METHOD FOR DELIMITING THE WAGON FLEET IN THE THEORY OF A LINEAR CITY BASED ON THE PRINCIPLES OF CLASSIFIERS Zadorozhniy V. Candidate of technical sciences, associate professor, associate professor Chair «Stations and cargo work», Rostov State Transport University (RSTU), Rostov-on-Don Bakalov M. Candidate of technical sciences, associate professor, associate professor Chair «Management of Maintenance Works», Rostov State Transport University (RSTU), Rostov-on-Don https://doi.org/10.5281/zenodo.17741006 Abstract This paper develops an economic-geographical approach to the territorial distribution of rolling stock based on the principles of cluster analysis. The synthesis of k-means algorithms and the center-of-gravity method allows us to identify the optimal location of key transport infrastructure elements. Implementation of this methodology is aimed at reducing the operational load on infrastructure facilities and improving the efficiency of transportation operations. Keywords: railway transport; wagon fleet; clustering; economic-geographical method, k-means method. A significant structural challenge has recently emerged within the Russian railway network concerning the pronounced heterogeneity of its freight wagon fleet by type of rolling stock. This imbalance is a direct consequence of the sector's transition from a centralized fleet management system to a model of decentralized ownership and operational control. This shift has inadvertently led to a sharp increase in the operational load on the railway infrastructure. The scale of the issue is underscored by the continuous growth of the total freight wagon fleet, which reached 1,381.9 thousand units as of December 2024 with a working fleet (active fleet) of 1,202.7 thousand units (Fig. 1). A critical manifestation of this problem is the surplus of empty wagons within the working fleet. These idle wagons occupy the tracks of freight and marshalling yards for extended periods, which significantly reduces their processing and sorting capacity. While lowactivity stations could, in theory, serve as holding areas for these empty wagons with minimal transport losses, their track capacity is insufficient for this purpose. Consequently, there is a pressing need for the development of advanced methods for managing wagon flows. The objective is to establish a rational framework for the temporary storage (idling) and strategic positioning of empty rolling stock across the network, thereby alleviating congestion and optimizing overall system efficiency. Fig. 1 – Dynamics of the common and working parks (all types of rolling stock) in 2021-2024, thousand units Finding the optimal location for a station for empty wagons can be compared to the transportation problem of finding the optimal location for a logistics distribution terminal. A logistics distribution centers (LDC) is defined as a rail transport hub where the dispatch of empty wagons, their downtime, and subsequent redirection to other stations are optimal [1, 2]. The theoretical foundations for locating facilities include several key factors and models that help optimize their placement. Well-known methods include the trial point method [3], the Reilly-Converse method [4], the center of gravity method, and other methods, including clustering methods and, in particular, the k-means method [5]. Let us consider the numerical implementation of the method development. The road region includes stations of the required type of work. 104 Danish Scientific Journal No102, 2025 − "M" region: "R", "P", "I", "ST", "NV", "A", "SV", "B", "SK", "G", "NL", "K", "V"; We'll cluster the stations using the k-means method to divide them into clusters within the road region. We'll run 10 iterations for region "M." Using the "elbow" method, we determined that 5 clusters are optimal for this region. Below, we'll list just a few of the iterations used in further calculations (Fig. 2, 3). Fig. 2 – 1st iteration of the "M" region Fig. 3 – 4th iteration of the "M" region Danish Scientific Journal No102, 2025 105 We will empirically identify roads for region "M" using three iterations of the k-means cluster analysis. We will then find a potential LDC location for each cluster in the iteration. So, for the "M" region we select the 1st and 4th iterations (Fig. 2, 3) and obtain, below we present the results of rational placement of LDC for several clusters (Fig. 4, 5): For the 1st iteration, regions are divided into clusters: 1) "R", "P", "I" Fig. 4 – LDC for the 1st cluster of the 1st iteration using the center of gravity method 2) "ST", "NV", "A", "SV" Fig. 5 – LDC for the 2nd cluster of the 1st iteration using the center of gravity method Conclusion The presented simulations enable the determination of optimal locations for transport infrastructure facilities through a combined methodological approach. This framework serves both as an advancement of the economic-geographic method and a basis for preliminary planning. Furthermore, the model allows for the adjustment of proposed LDC sites to align with realworld constraints, ensuring their integration with existing infrastructure. 106 Danish Scientific Journal No102, 2025 Acknowledgements The research was supported by the Russian Science Foundation grant No. 24-29-00869, https://rscf.ru/project/24-29-00869/ References: 9. Chislov O. N., Zadorozhniy V. M., Bogachev V. A., Kravets A. S., Bogachev T. V., Bakalov M. V. Mathematical modeling of cargo flow distribution in a regional multimodal transportation system // Transport Problems. 2021. Т. 16. № 2. С. 153–165. 10. Thai, V. V. & Grewal, D. (2005). Selecting the location of distribution centre in logistics operations: a conceptual framework and case study. Asia Pacific Journal of Marketing and Logistics, 17(3), 3‑24. 11. Lukinsky V.S. Logistics and Supply Chain Management: Textbook and Workshop for the Academic Bachelor's Degree / V.S. Lukinsky, V.V. Lukinsky, N.G. 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