In order to match the energy demand of electric vehicles to the capacity of the power grid, it is fundamental to understand the occupancy of charging stations and react accordingly. A Markov model of a fast charging station for Lithium-ion batteries, the most prevalent type today, is proposed. Li-Ion batteries present a two-step charging profile, which makes energy management particularly challenging. A wide range of situations is covered by considering three types of scenarios with and without waiting lines. The analytical results obtained from the steady state solution of the Markov model reveal the behavior of multiple variables of interest: availability of the charging station to accept new customers (in terms of space and energy), number of customers, energy consumption, and power utilization. From the results, indicators for assessing the quality of service (QoS) of the charging station are derived. Based on these indicators, customers may decide to wait or head toward another station. The owners of stations, in turn, can predict the impact of investments in space and energy provisioning, when devising capacity planning strategies.