How do you plot overlapping durations?
Since you want to show so much data, I think that your best choice is going interactive. Check out this demo, it is close to what you want but not quite. 

It is very difficult to show a lot of data in a single diagram, together with the finest details and the bird-eyes view. But you can let the user interact and look for the details. To show counts, one option is to use color-coding. Take a look at this image (code here): .

Here rgb channels have been used to encode (the logarithm of) the number of active events (red), events starting (green) and events ending (blue) for windows of different size. The X axis is time, and the Y axis represents window size, that is, duration. Thus, a point with coordinates (10, 4) represents the interval of time that goes from 10 to 14. 

To make a lot of data more detailed, it could be a good idea to make the diagram zoomable (like in the demo before), and to give the user the possibility of visualizing just one channel/magnitude.