When built, quantum repeaters will allow the distribution of entangled quantum states across large distances, playing a vital part in many proposed quantum technologies. Enabling multiple users to connect through the same network will be key to their real-world deployment. Previous work on repeater technologies has focussed only on simple entanglment production, without considering the issues of resource scarcity and competition that necessarily arise in a network setting. In this paper we simulated a thirteen-node network with up to five flows sharing different parts of the network, measuring the total throughput and fairness for each case. Our results suggest that the Internet-like approach of statistical multiplexing use of a congested link gives the highest aggregate throughput. Time division multiplexing and buffer space multiplexing were slightly less effective, but all three schemes allow the sum of multiple flows to substantially exceed that of any one flow, improving over circuit switching by taking advantage of resources that are forced to remain idle in circuit switching. All three schemes proved to have excellent fairness. The high performance, fairness and simplicity of implementation support a recommendation of statistical multiplexing for shared quantum repeater networks.