In the following reference,

Todosiev, E.P., 1963. The action point model of the driver-vehicle system (Doctoral dissertation, The Ohio State University).

on page 16, an idealized relative acceleration-relative speed diagram is shown (figure 1 attached below). On this figure, the vertical axis is:

relative acceleration = acceleration of lead vehicle - acceleration of following vehicle.

And the horizontal axis is:

relative speed = speed of lead vehicle - speed of following vehicle

The assumption is that the lead vehicle is moving at uniform speed, therefore the change in the relative acceleration is brought about only by the acceleration of following vehicle. Following is the definition of action point in the above reference:

"The action point is defined as the point where the acceleration changes sign".

In the figure 1, the sign of acceleration at point A changes only because the following vehicle decelerates. So, the action point is A. It is easily identifiable on figure 1 using da-dv diagram.

But in the observed vehicle trajectories, the lead vehicle does not move at a uniform speed. Consider figure 2 which is a smoothed version of an observed vehicle trajectory. The axes are same as figure 1, except the units.

What should be considered an action point now? 

1) Is it the point where relative acceleration changes sign?

2) Is it the point where the relative acceleration changes magnitude (regardless of sign)?

3) Or do we have to look at the acceleration of following vehicle only to see when it changes sign (and figure 2 is of no use)?