Transport system modelling based on analogies between road networks and electrical circuits

Alexander V. Tolmachev, Evgeny V. Sinitsyn, Dmitrii A. Brusyanin


This article describes a probabilistic mathematical model which can be used to analyse traffic flows in a road network. This model allows us to calculate the probability of distribution of vehicles in a regional road network or an urban street network. In the model, the movement of cars is treated as a Markov process. This makes it possible to formulate an equation determining the probability of finding cars at key points of the road network such as street intersections, parking lots or other places where cars concentrate. For a regional road network, we can use cities as such key points.
This model enables us, for instance, to use the analogues of Kirchhoff First Law (Ohm's Law) for calculation of traffic flows. This calculation is based on the similarity of a real road network and resistance in an electrical circuit. The traffic flow is an analogue of the electric current, the resistance of the section between the control points is the time required to move from one key point to another, and the voltage is the difference in the number of cars at these points. In this case, well-known methods for calculating complex electrical circuits can be used to calculate traffic flows in a real road network. The proposed model was used to calculate the critical load for a road network and compare road networks in various regions of the Ural Federal District.


probabilistic mathematical model, traffic flows, Ohm’s Law, Kirchhoff’s First Law, regional road network, traffic management

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Antoniadi, G. D., & Tsоuprikov, A. A. (2015). Analysis of the problem areas in the Krasnodar transport network and activities to discharge them. Polythematic Online Scientific Journal of Kuban State Agrarian University, 8(112), 1–10.

Chowdhury, D., Santen, L., & Schadschneider, A. (2000). Statistical physics of vehicular traffic and some related systems. Physics Reports, 329(4-6), 199–329.

Volkov, D. O., Garichev, S. N., Gorbachev, R. A., & Moroz, N. N. (2015, November). Mathematical simulation of transport network load with a view to assessing viability of building new types of network systems. In: 2015 International Conference on Engineering and Telecommunication (EnT) (pp. 20–23). IEEE. (In Russ.)

Yakimov, M. R. (2013). Transport planning: creation of transport models of cities. Moscow: Logos. (In Russ.)

Crisostomi, E., Kirkland, S., & Shorten, R. (2011). A Google-like model of road network dynamics and its application to regulation and control. International Journal of Control, 84(3), 633–651.

Melnikov, V. R., Krzhizhanovskaya, V. V., Boukhanovsky, A. V., & Sloot, P. M. (2015). Data-driven modeling of transportation systems and traffic data analysis during a major power outage in the Netherlands. Procedia Computer Science, 66, 336–345. (In Russ.)

Bessonov, L. A. (1996). Theoretical Foundations of Electrical Engineering. Electrical circuits. Moscow: Higher School. (In Russ.)

Landau, L. D., & Lifshits, E. M. (2005). Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media. 4th ed. Moscow: Fizmatlit. (In Russ.)

Astratova, G., Sinicin, E., Toporkova, E., Frishberg, L., & Karabanova, I. (2017, June). Mechanism of information model development for company brand assessment within marketing strategy. In: International Conference on Trends of Technologies and Innovations in Economic and Social Studies 2017 (pp. 20–25). Atlantis Press. (In Russ.)

Amosova, N. N., Kuklin, B. A., & Makarova, S. B. (2001) Probabilistic sections of mathematics. St. Petersburg. (In Russ.)

Leskovec, J., Rajaraman, A., & Ullman, J. D. (2014). Mining of massive datasets. Cambridge University Press.

Chartrand, G., & Zhang, P. (2013). A first course in graph theory. New York: Courier Corporation.

Guze, S. (2014). Graph Theory Approach to Transportation Systems Design and Optimization. TransNav: International Journal on Marine Navigation and Safety of Sea Transportation, 8, 571–578.

Kumar Bisen, S. (2017). Application of Graph Theory in Transportation Networks. International Journal of Scientific research and Management, 5(7), 6197–6201. DOI: 10.18535/ijsrm/v5i7.48

Likaj, R., Shala, A., Mehmetaj, M., Hyseni, P., & Bajrami, X. (2013). Application of graph theory to find optimal paths for the transportation problem. IFAC Proceedings Volumes, 46(8), 235–240.

Géron, A. (2017). Hands-on machine learning with Scikit-Learn and TensorFlow: concepts, tools, and techniques to build intelligent systems. O’Reilly Media, Inc. 17. Mukhanov, V. V., & Babenko A. G. (2009). Calculation of Complex Circuits. Yekaterinburg: GOU VPO USTU – UPI. (In Russ.)


Copyright (c) 2019 Alexander V. Tolmachev, Evgeny V. Sinitsyn, Dmitrii A. Brusyanin

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