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The modeling of electric car charging stations is essential for determining the required number of chargers in order to ensure the required service quality. In this paper we propose a new estimation method for the stochastic modeling of electric car charging stations, based on Markov arrival process (MAP). The input of the proposed model is empirical data for the arrival and service process of electric cars, given as histograms: the number of arriving cars during a fixed time slot (5 minutes in our case) and the histogram of service times (in 5 minutes granularity). The fact that observations on the continuous time process of car charging are available in discrete time steps poses a modeling challenge, which was not considered before. We propose a procedure to fit the observed data with a continuous time MAP of order 2 such that three moments and a correlation parameter of the discrete time observations are matched with three moments and the correlation parameter of the continuous time MAP for the given time interval. We implemented the fitting procedure in MATLAB and verified the obtained model of car charging station against simulation. As the MAP model of the arrival processes is reasonably close to the observations, the obtained MAP/G/c queue allows a more accurate dimensioning of car charging station than the previously applied ones.

Capacity Planning of Electric Car Charging Station Based on Discrete Time Observations and MAP(2)/G/c Queue