The quantum internet will allow for communication via qubits, enabling for improved clock synchronization, blind quantum computing and quantum key distribution. Key components of such a quantum network are quantum repeaters, which help to overcome the exponential loss of photons in optical fibers. In this thesis we focus on one type of quantum repeater based on atomic ensembles. In particular, we build a versatile and elaborate simulation model based on a discrete event simulator for quantum networks, capable of simulating quantum repeater chains of arbitrary length with a vast range of tunable simulation parameters. We validate this model by comparing it to an analytical one and investigate the effects of additional sources of noise that cannot be taken into account in the analytical model. Furthermore, we give a detailed theoretical overview and performance comparison of two types of quantum memories based on atomic ensembles: atomic frequency comb and electromagnetically induced transparency. Finally, we present two integer linear programming formulations for determining the optimal positioning of quantum repeaters in two spatial dimensions and demonstrate their use on a European-scale network.