One million electric vehicles in Poland – insights from an agent-based model

In agent-based modeling (ABM), a (usually) complex system is modeled as a collection of autonomous entities called agents. Agents interact with each other and their environment, asses their situation and make decisions based on some given set of rules. Those decisions may then trigger different actions of the entities.

In the last decades, ABM has become an important modeling approach, successfully applied in many branches of science. A distinct feature of ABM is the ability to explore the dynamics of a modeled system by analyzing local interactions between agents – something that is often out of reach for pure mathematical methods. Even the simplest agent-based models can exhibit complex behavior patterns and give some insight into the dynamics of the real-world systems that they emulate. That is actually the reason why ABM is getting more and more on popularity – it allows a modeler to bridge the gap between microscopic interactions between the agents and the emergent behavior of the system as a whole.

Patrycja Kowalek, a student of Applied Mathematics at the Wrocław University of Science and Technology (WUST) decided to use ABM to investigate the market penetration of electric vehicles in Poland. She conducted her research for the master thesis under the supervision of Janusz Szwabiński, an associate professor in the Faculty of Pure and Applied Mathematics at WUST. Her work was inspired by the Electromobility Development Plan of the Polish government that assumes one million electric cars in year 2025 (i.e. 4% of the market share). She developed a model of the Polish car market with car owners being agents. Financial, social and ecological aspects were taken into account by the agents to decide on buying a car. As for the social part for instance, the agents were put on a Watts-Strogatz network with rewiring probability in the small world regime (i.e. high clustering coefficient and short average path length), and the social influence was implemented via the well-known q-voter model with independence.

The model was initialized with the data from Polish Central Statistical office and simulated on a computer with help of Monte Carlo methods. Different scenarios (e.g varying electricity and petrol prices, mass media campaigns, government’s subventions) have been taken into account. In most of the scenarios the Polish government’s target for 2025 has not been met. However, significant subventions or petrol prices higher than 5.5PLN/liter may fuel the diffusion of electric cars in the Polish market. In the figure below for instance, the impact of the petrol price on the adoption of the cars is shown.


Agent-based modeling has been already recognized at WUST as an important modeling tool , that often complements a more traditional approach based on mathematical equations. Since October 2016 courses related to ABM are offered for students of Applied Mathematics within the specialty “Computational Mathematics” and enjoy a lot of interest from them.

By Patrycja Kowalek, student, and Janusz Szwabiński, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology

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