Andy getting into the detail might get us somewhere. 

There a few Space Syntax papers that deal with the network geometry, incidence angle between global line/local line/line length/line density of the network and dealing in particular with this question of how the Space Syntax network representation implicitly and probably quite elegantly capture the road hierarchy you mentioned "local road -> local distributor -> trunk road -> local distributor -> local road" without the need of a separate algorithm doing the job. There is as well some untested causation model, at some stage to do so we will have to move into structural equation modelling. Alan is that not the plan anyway?

If you are interested we could forward these papers to you.

When you look at a processed axial map the resolution of this question seems relatively clear so it seems then that a kind of cost function mechanism is already there too - have you ever seen a supergrid axial map or choice map of London quite compelling about the relationship between global and local distributor.
How come, probably simply because this is the way that the network is designed - breaking the line relation to the global distributor, making more turn, relative large block, is the way for example residential area networks are designed (lot of exception there, but then lot of social problems and/or costs too) and if you have a regular grid, the grid is usually more interrupted than usual. In reverse the global direct fast link usually are more or less strait and longer than others, so more connectivity (unless an orbital, still it picks all the radials which are more or less strait and made of longer segments). 

All this become quite obvious when you start to overlay a land use map with an axial map and look at residential area, where are the odd corners shops, activity area are different again etc. What is the morphology of the network, according to land uses, the high street network and so on. Perhaps what has been lacking in the Space Syntax literature is combined representation of land use and axial map beyond the confine of main centrality - it would probably be more convincing. It goes quite well hand in hand with researches by others about block sizes and centralities. In reverse transport modelling because they do model only a skeleton network cannot quite see all of that, do they? 

I must say I have difficulty to imagine two routes one having the fewest change of direction and taking two hours and one having more change taking 30 min - I would go with 30 min versus 35-40 min but 2 hours sounds far fetched - we can imagine it, it may exist but I ask myself how many more change and how come it would make such a difference. It may exists but it is probably very rare so I would not make too much of it, still like to see one. We are dealing with probabilistic phenomena. I would not make a big deal of few one off, would that be the exceptions that confirm the rule. And I like to see the social consequences - the everyday life of it - it might look like a Jacques Tati's movie. In a certain way if it was generalised and normal, a kind of flip over spatial culture, I don't think it would make a big problem to the Space Syntax modelling. 

On public transport network there are French studies on six different cities regarding the relationship between modal change and public transport share. Last year, during in a meeting with you I mentioned the results of that study. It shows that 0, 1 and 2 modal changes represent almost constantly about 86% public transport users on every city. 
The split is the following, pretty stable in all cities: 40% for no change, 30% for 1 change and 16% for 2 changes. 
The interesting part of the study was that the six cities, for work destination, have very different public transport shares, varying from 30% to above 90% - some sort of constant at work despite very variable situations. I spotted that constant because it correspond to the local 2 changes of direction space syntax measure that is used for pedestrian movement analysis - time /distance cost - spatial / cognitive? I doubt that the former would deal very well with the cities morphology differentials but until shown lets withhold conclusion.  

I am aware that work destination does represent less and less and about 40% of all trips

The author conclusions were that it is probably down to the relationship between the public transport network morphology and the overall city network morphology. At least in France one of the biggest stated challenges in transportation studies is to understand that morphological relationship. They are relatively clear that distance time and cost is not the answer. But as you said it does not inform policy and action yet - well what tool would they use? And you know this is all in French so who care! Another French cultural exception.

Public transport modal change beyond two is the exception - we can think of alternative modelling techniques lets leave aside monetary costs; 
- a cost function that track distance, time, modal change with exponential cost as they accumulate, or with a reverse decay function - probably complex and a lot of calculation anyway
- the alternative is just to count change of direction from everywhere to everywhere and decide how many change of direction you want to limit the calculation to go to, pretty blunt but would do the job well. Because you can chose which level of change of direction you can go to you can adjust in case you find a network from a particular spatial culture where the most complicated one are the fast one :)

Sorry, if I made generalisation about transportation modeller, it was not meant to be all-inclusive. Over the past few years my transactions with that world made me understand that conventional approach is more the rule than the exception with the niceties of over complication when you go to conferences seminar and symposium - it was just an inductive inference.
_______________________________
 
Alain Chiaradia
_______________________________