Editing Route assignment (section)

==Integrating travel choices==
The urban transportation planning model evolved as a set of steps to be followed, and models evolved for use in each step.  Sometimes there were steps within steps, as was the case for the first statement of the [[Lowry model]].  In some cases, it has been noted that steps can be integrated.  More generally, the steps abstract from decisions that may be made simultaneously, and it would be desirable to better replicate that in the analysis.

Disaggregate demand models were first developed to treat the mode choice problem.  That problem assumes that one has decided to take a trip, where that trip will go, and at what time the trip will be made.  They have been used to treat the implied broader context.  Typically, a nested model will be developed, say, starting with the [[probability]] of a trip being made, then examining the choice among places, and then mode choice.  The time of travel is a bit harder to treat.

Wilson's doubly constrained entropy model has been the point of departure for efforts at the aggregate level.  That model contains the constraint

<math>t_{ij}c_{ij}=C</math>

where the <math>c_{ij}</math> are the link travel costs, <math>t_{ij}</math> refers to traffic on a link, and C is a resource constraint to be sized when fitting the model with data.  Instead of using that form of the constraint, the monotonically increasing resistance function used in traffic assignment can be used.  The result determines zone-to-zone movements and assigns traffic to networks, and that makes much sense from the way one would imagine the system works – zone-to-zone traffic depends on the resistance occasioned by congestion.

Alternatively, the link resistance function may be included in the objective function (and the total cost function eliminated from the constraints).

A generalized disaggregate choice approach has evolved as has a generalized aggregate approach.  The large question is that of the relations between them.  When we use a macro model, we would like to know the disaggregate behavior it represents.  If we are doing a micro analysis, we would like to know the aggregate implications of the analysis.

Wilson derives a [[Gravity model|gravity-like model]] with weighted parameters that say something about the attractiveness of origins and destinations.  Without too much math we can write probability of choice statements based on attractiveness, and these take a form similar to some varieties of disaggregate demand models.