I don't know if this applies to your question, but I know about a theoretical model that was developed to predict where a pilot will look (and I think it could be generalized to driving). It is the SEEV (Salience, Effort, Expectancy, Value) model.
According to the SEEV model (Wickens, Helleberg, Goh, Xu, Horrey, 2001), four main factors could influence visual attention allocation: Salience (salient objects are likely to capture visual attention), Effort (people tend to minimize both eye and head movements), Expectancy (monitoring sources of high task-relevant event rate), and Value (monitoring sources of high task-relevant importance).
Here's the reference:
Wickens, C.D., Helleberg, J., Goh, J., Xu, X., Horrey, W.J. (2001). Pilot task management: Testing an attentional expected value model of visual scanning. Technical Report ARL-01-14/NASA-01-7.
Rob Alexander, at University of York, is working on a related task for autonomous vehicles. His concern is not so much the complexity at any given time, but how to measure whether you have tested the vehicle in a sufficiently wide range of circumstances.
To answer your question more directly, you've got a chicken-and-egg evaluation problem when the question is phrased as you have phrased it. No matter what measure of complexity you come up with, how do check whether it is valid?
Let's say you find that "more complex" situations make no difference on driver performance. What would you have actually worked out? Probably just that your measure of "more complex" isn't very useful.
Let's say you find out that "more complex" situations make drivers perform worse. Cue a total lack of surprise in everyone who reads the results. What you'll have actually done is indirectly validate the complexity measure rather than learned something about drivers. I say indirectly, because a correlation between a multi-element measure and a dependent variable doesn't tell you which elements are causing the variation, unless you designed the experiment that way in the first place.
Arguably, the complexity of a road situation should be measured by measuring its impact on drivers. A complex situation is one where drivers perform consistently worse on the driving task, with non-situation variables controlled. That then allows you to validly determine what increases or decreases the complexity.
In that case it isn't a theoretical model at all. It's an empirical model in search of an explanatory theory.
I could have misunderstood your question though. Are you looking for a measure of complexity which is already shown to validly relate to driver behaviour, that you can take away to use for another purpose?
Thanks you Andrew for your comment, indeed your thoughts are not far from the challenges I have now in my researcher.
I agree completely with your thoughts about how the complexity of a road situation should be measured by measuring its impact on drivers. Indeed, the difficulty of any task (i.e. driving) is function of the number of responses required and the time allocated for given task. Hence two variables are involved, time span, and amount of information that must be assimilated prior task execution. A shorter time and higher amount of information increase the difficulty (or complexity) of the tasks. So in a road system, given one scenario, how to measure that information required for executing the driving task without disruptions?
In the driving task, under non-distracted conditions, the vehicle and environment are the main sources of information, to the extent that any of these provide a greater amount of information we will have a more complex driving task. How a change in the “car complexity” interacts with an increase in the “environmental complexity” having driving performance as the main outcome? Does this have any safety implications and to what degree?
The reason for this is the same that Rob Alexander, consider and control a wide range of circumstances for empirical studies (In my case is explicitly simulator based studies) and have a framework for classifying different scenarios in terms of the “complexity” they add to the driving task.
This is just one question in which I have been working on recently. It is fascinating how there are many studies analyzing driver behaviors with increments of complexity in the vehicles, but not many references to the importance of controlling the environmental complexity.