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In order to increase the penetration of electric vehicles, a network of fast charging stations that can provide drivers with a certain level of quality of service (QoS) is needed. However, given the strain that such a network can exert on the power grid, and the mobility of loads represented by electric vehicles, operating it efficiently is a challenging and complex problem. In this paper, we examine a network of charging stations equipped with an energy storage device and propose a scheme that allocates power to them from the grid, as well as routes customers. We examine three scenarios, gradually increasing their complexity. In the first one, all stations have identical charging capabilities and energy storage devices, draw constant power from the grid and no routing decisions of customers are considered. It represents the current state of affairs and serves as a baseline for evaluating the performance of the proposed scheme. In the second scenario, power to the stations is allocated in an optimal manner from the grid and in addition a certain percentage of customers can be routed to nearby stations. In the final scenario, optimal allocation of both power from the grid and customers to stations is considered. The three scenarios are evaluated using real traffic traces corresponding to weekday rush hour from a large metropolitan area in the US. The results indicate that the proposed scheme offers substantial improvements of performance compared to the current mode of operation; namely, more customers can be served with the same amount of power, thus enabling the station operators to increase their profitability. Further, the scheme provides guarantees to customers in terms of the probability of being blocked (and hence not served) by the closest charging station to their location. Overall, the paper addresses key issues related to the efficient operation, both from the perspective of the power grid and the drivers satisfaction, of a network of charging stations.