Many people use ISP-provided router that choked when there are a lot of open connections. A torrent client will usually try to open as many connections as possible, pushing the router to the limit. Under that condition, if another user join the network and tried to browse the internet, he'll encounter a lot of connection timeout error. The only way to avoid this issue is to configure the torrent client to play nice (limit the number of connections) or tweak the router QoS settings to lower priority for torrents traffic (not sure if it's possible with encrypted torrents).

source: my apartment shares a single dsl router to all its tenants