Contrived hypothetical: It's tuesday evening, and I'm updating my to-do's before tomorrow. I have 3 hours after work, and 3 tasks:

1) A meeting (Important Urgent) 1 or 2 hours

2) Buy a gift for someone's birthday (Important - can be done any time but must be done) 1 hour

3) Check the marketplace for a limited sale (Urgent - much better if done immediately, but doesn't matter so much if not done) 1 hour

If task 1 takes only one hour, I do 3 then 2. If it takes two hours, I do 2.

There's two contexts above. Obviously as you pointed out, once you actually get to doing a task, there's only one context. But the point is that when adding a task to your to-do list you don't yet necessarily know what that future context will be.

Your choices here are to either make a priority queue for every possible future context (reasonable for this simple case, but doesn't scale to a more complex one), or mark tasks with the relevant information that will let you easily assemble the appropriate priority queue on the fly, once the context becomes clear.

And what happens if your time-estimates are wrong; or unbounded?

You have two tasks (one Urgent, one Important) and 10 days at your disposal.

If each task takes at least 4 days, which one do you do first?

> But the point is that when adding a task to your to-do list you don't yet necessarily know what that future context will be.

I am not talking about pushing tasks on the queue. I am taking about popping them off the queue.

If you don't know how long a particular task takes how do you decide whether to pop a task off your Urgent or Important queue?

Just-in-Time prioritisation under uncertainty is hard.