You can use Promise.race to wait for the first resolved promise.

Abusing notation a bit,

var a = new Queue();

var b = new Queue();

a.read(() => some callback);

b.read(() => some callback);

And code continues here without blocking.

To be honest, I think you could do the same in any (slightly) modern language.

Is the read() call running a task in the background? In that case, that's equivalent to launching two threads. For n queues, you'd need n tasks, and they'd hang in the background in case they never get a result and take up memory.