what does it mean for a to BJT operating at the edge between the active and saturation modes?
Once a junction gets saturated, it takes awhile for it to react and come out of saturation. I believe this is where the "Charge Control" model, or Gummel-Poon model, comes into play.

The time delay for a saturated junction to react is modelled by waiting for a capacitor to discharge. From Wikipedia, the basic model is:



Courtney of Berkely, you can look through associated math here.