Methods of the theory of transport macrosystems for mass service dynamics and auto insurance

Introduction. The article presents methods of the theory of transport macrosystems for increasing the level of technical readiness of motor transport after an accident. The problems leading to a decrease in the efficiency of transport systems during repairs at the expense of insurance companies have been identified. A mathematical model is given to describe a transport system consisting of elements vehicles and their numerous states at the service station. The properties of the elements under the study have been described.

Methods and materials. The theory of transport macrosystems has been used, which is based on the theory of macrosystems, a well-known scientific theory. Among its tasks there are statements about the distribution of elements into subsets of states and problems of the equilibrium of the entire system. In macroscopic systems, by definition, the stochastic behavior of a large number of elements is transformed into the deterministic behavior of the system. A macrosystem is a dynamic converter of the chaotic behavior of elements into a set of behavior parameters (phase variables) forming a small-dimensional space. Therefore, within the framework of the theory of macrosystems, the basic concepts of maximizing entropy at equilibrium states of the system are used. In this case, the macrostate distribution function is selected depending on the method of filling elements of some states from the corresponding subsets; the necessary values of a priori probabilities and evidence of parametric properties of models of macrosystems with various statistics (Fermi, Einstein and Boltzmann distributions). The description of the research object is given, which is a transport system consisting of vehicles that require repair based on the fulfillment of obligations by insurance companies.

Results. The paper presents the results of calculations which have demonstrated the nature of the dependencies between the capacities of multiple states, a priori probabilities and the number of cars under repair at the service station within the framework of the theory of transport macrosystems. The distributions of vehicles corresponding to the equilibrium states with the selected initial data are established.

Discussion and conclusion. Within the framework of this investigation, the following tasks have been solved: the possibility of research based on the methods of the transport macrosystems theory to solve the problems of finding equilibrium in road transport systems after an accident has been proved; some problems have been identified in interaction between the service station and the Insurer in approving the cost of repair for damaged vehicles. Some approaches to provide interaction between the service station and the Insurer in the field of repair of damaged ve­hicles for auto insurance based on the possibilities of mathematical modeling in substantiating the methods have been proposed.

1. Tetin I.A. Modeling the strategy of an insurance company in the context of the insurance activity cycle] Bulletin of Tomsk State University. Economics. 2017; No. 38. (In Russ.).

2. Dammer D.D. Mathematical model of an insurance company in the form of a mass service system with an unlimited number of devices taking into account one-time insurance payments. Information technology and mathematical modeling (ITMM-2016). 2016; (In Russ.).

3. Nikolaycheva A.M. Trends in digitalization and automation of service station processes. Management accounting. 2021; 7 (2) (In Russ.).

4. Mamedov E.N. Game-theoretic optimization of insurance methods in the field of motor transport] SCIENCE AND WORLD. 2013. (In Russ.).

5. Nesterenko I.S. Design of a customer zone that allows increasing demand for the services of car service stations. International Research Journal. 2022; 1 (115). (In Russ.). DOI: 10.23670/IRJ.2022.115.1.112

6. Nesterenko G.A., Nesterenko I.S., Zaloznov I.P. Using BIM technologies to improve the efficiency of development and operation of enterprises for car maintenance and sales. International Research Journal. 2023; 11 (137). (In Russ.). DOI: 10.23670/IRJ.2023.137.14

7. Zakharov N.S., Kozin E.S. Technological design of vehicle service stations using genetic algorithms. International Journal of Advanced Studies : Transport and Information Technologies.2024; 14 (2). (In Russ.). DOI: 10.12731/2227-930X-2024-14-2-296

8. Phi-Hung Nguyen. Automotive Service Quality Investigation Using a Grey-DEMATEL Model. Computers, Materials & Continua. 2022; 73 (3). DOI: 10.32604/cmc.2022.030745

9. Revina I.V. Trifonova E.N. Car Service Optimization Based on Simulation. Journal of Physics: Conference Series. 1791 (2021) 012084. DOI: 10.1088/1742-6596/1791/1/012084

10. Bugrimov V., Sarbaev V. Optimization of the system of management of stores of the car service with the help of imitation simulation. MATEC Web of Conferences. 334, 01022. 2021; (In Russ.). DOI: 10.1051/matecconf/202133401022

11. Krynke M., Mazur M. Innovative Work Order Planning with Process Optimization Using Computer Simulation in the Automotive Industry, in the Case of Repair Workshops. Periodica Polytechnica Transportation Engineering. 2024. DOI: 10.3311/pptr.23546

12. Budnikova I.K., Mardanova A.M. Modeling of financial activities of an insurance company. Information technologies in construction, social and economic systems. 2020. No. 1. (In Russ.).

13. Popkov Yu.S. The concept of entropy in systems analysis. Collection of works of the V-th International scientific and practical conference-biennale. Under the general editorship of G.B. Kleiner, S.E. Shchepetova. M.: Publisher: Limited Liability Company “Prometheus Publishing House”. 2018. (In Russ.). DOI: 10.33278/SAE-2018.rus.027-028

14. Agureev I.E., Akhromeshin A.V. Mathematical model of transport behavior based on the theory of transport macrosystems. World of Transport. 2021. 19. No. 6 (97). DOI 10.30932/1992-3252-2021-19-6-2. (In Russ.)

15. Hosein P.A Data-Driven Pricing Strategy for Automobile Insurance Policies. 2022 5th Asia Conference on Machine Learning and Computing (ACMLC). DOI: 10.1109/ACMLC58173.2022.00009

16. Xie Sh. Analyzing the Influence of Telematics-Based Pricing Strategies on Traditional Rating Factors in Auto Insurance Rate Regulation. Mathematics. 10.3390/math12193150, 12, 19, (3150). 2024. DOI: 10.3390/math12193150

17. Henckaerts R., Antonio K. The added value of dynamically updating motor insurance prices with telematics collected driving behavior data. Insurance: Mathematics and Economics, 10.1016/j.insmatheco.2022.03.011, 105, (79-95). 2022. DOI:10.1016/j.insmatheco.2022.03.011

18. Masello L., Sheehan B., Castignani G., Guillen M., Murphy F. Predictive Modeling for Driver Insurance Premium Calculation Using Advanced Driver Assistance Systems and Contextual Information. IEEE Transactions on Intelligent Transportation Systems. 10.1109/TITS.2024.3518572, 26, 2, (2202-2211). 2025; DOI: 10.1109/TITS.2024.3518572

19. Kushelev I.Yu. Implementation of innovative information technologies in the insurance market in Russia: telematics in car insurance] Entrepreneur’s Guide. 2023;16 (2). (In Russ.). https://doi.org/10.24182/2073-9885-2023-16-2-110-119

20. Lang F., Riegel L. Acceptance of online customer channels for damage claims in Germany. Information Technology and Management. 10.1007/ s10799-023-00404-z26:1(101-116) Online publication date: 1-Mar-2025. DOI:10.1007/s10799-023-00404-z

21. McDonnell K., Murphy F., Sheehan B., Masello L., Castignani G. Deep learning in insurance. Expert Systems with Applications: An International Journal. DOI: 10.1016/j.eswa.2023.119543217: C. Online publication date: 1-May-2023. DOI: 10.1016/j.eswa.2023.119543

22. Li H., Luo X., Zhang Z., Jiang W., Huang S. Driving risk prevention in usage-based insurance services based on interpretable machine learning and telematics data. Decision Support Systems. 10.1016/j. dss.2023.113985172:C. Online publication date: 1-Sep-2023. DOI: 10.1016/j.dss.2023.113985

23. Brühwiler L., Fu Ch., Huang H., Longhi L., Weibel R. Predicting individuals’ car accident risk by trajectory, driving events, and geographical context. Computers, Environment and Urban Systems. 2022; Volume 93. DOI: 10.1016/j.compenvurbsys.2022.101760

24. Cunha L., Bravo J. M. Automobile Usage-Based-Insurance: Improving Risk Management using Telematics Data. 2022 17th Iberian Conference on Information Systems and Technologies (CISTI), 10.23919/CISTI54924.2022.9820146. 2022; (1-6), DOI: 10.23919/CISTI54924.2022.9820146

25. Ortega M., Quintanilla J., Ong E.R., Ramos M.R., Trinidad C.J. Asfalis: A Web-based System for Customer Retention Strategies Optimization of a Car Insurance Company Using Cohort and Churn Analysis. 2023 International Conference on Inventive Computation Technologies (ICICT). DOI: 10.1109/ICICT57646.2023.10134149

26. Manko B.A. Erie Insurance: Monitoring technology in the car insurance market and the issue of data privacy. Journal of Information Technology Teaching Cases. 2022; 10.1177/20438869221117571, 13 (2): 193-198. DOI:10.1177/20438869221117571