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Nowadays, electric vehicles (EVs) significantly affect transportation as they provide a more environmentally friendly alternative to traditional fossil-fueled automobiles. Electric vehicles, which depend on energy stored in batteries, significantly contribute to environmental preservation and comply with worldwide efforts to tackle climate change. However, the growing demand for electric vehicles causes traditional power grids under pressure emphasizing the necessity of establishing a suitable infrastructure for charging electric vehicles. Charging stations are becoming increasingly critical since they allow for the recharging of electric vehicles and play a significant role in stabilizing the power system. In order to optimize charging station infrastructure with multiple servers, the current research incorporates a Markovian queueing modeling approach. The primary objective of the study is to address queue management concerns and boost overall productivity. Considering the real-world challenges, a queue-based stochastic model for multi-server EV systems and individual feedback strategies is developed. Subsequently, a transition state diagram is provided by balancing the input-output rates between the adjacent states. Next, the system of Chapman-Kolmogorov differential-difference equations is formulated to help understand mathematical modeling better. The matrix method is employed to demonstrate the state probability distribution in equilibrium. The infographics are utilized and incorporated for better visualization of the research findings. For a better understanding from an individual's point of view, numerous managerial insights are provided. Lastly, several concluding remarks and future perspectives are provided that can help decision-makers and practitioners to construct and analyze economic strategies based on EV management systems.