Should axis label change depending on time on line graphs?

I have a line graph showing number of items in queue from right now and 24 hours back in time.

I have a range of different options to chose from.

First, there are two different ways of showing the data; per hour or per minute, i.e. show it like "8:00AM" or "8:28AM". The :00-way looks cleaner, but the problem is that if it is 08:54AM it will show the time of 08:00AM since it can not go forward in time (to 09:00AM although it would be more accurate).

1)

This is the :00-way, looks kind of clean, very detailed, i.e. you can easily see the number on the curve at one specific time.

This is what it would look like six hours later, all numbers will change:

2)

This is the :54-way. Looks a little cluttered, but serves it purpose of showing the exact time. This option will also create another question, should the numbers in the axis change each minute? Will the user think it looks weird when all numbers change even though he didn't do any action to make it change? If the numbers should not change each minute: Will the user be confused when the time is not corrent anymore?

This is what it would look like six hours later:

3)

This is a different way of showing the time. This is only showing the time right now and a "-24h" to symbolize that the graph shows the queue from now and 24 hours back in time.

The downside of this is that the user might find it hard to know what time it is in the middle of the graph.

This is what it would look like six hours later, pretty much the same except 1 (sometimes 2) numbers:

4)

The fourth option is kind of like the third option, but instead of the :00-way, it is with the :54-way.

What way would be the best practice? A good thong to know is that I will have four line graphs next to each other, which might make it very cluttered if there are too many numbers. Or does any of you have another opinion?

I hope I was able to make myself clear, otherwise I will answer any doubts :)