Docker supports (supported?) what LXC supported, which was relative CPU shares. I am not sure it would help if it supported something else (like quota minimum/maximum). When the IO subsystem is hit with a memory intensive workload that thrashes swap, all your guarantees go out the window. From my perspective (staring at top while an interactive terminal is not responding), it's the kernel that owns the CPU shares being used, and the IO volume, and it looks like the container is "almost idle" because most of the CPU time is being spent by the kernel.

I don't know if it's that something Docker can fix. It might be something kernel devs can fix, though.