Editing Route assignment (section)

==Integrating travel demand with route assignment==
It has long been recognized that travel demand is influenced by network supply. The example of a new [[bridge]] opening where none was before inducing additional traffic has been noted for centuries. Much research has gone into developing methods for allowing the forecasting system to directly account for this phenomenon. Evans (1974) published a [[Thesis|doctoral dissertation]] on a mathematically rigorous combination of the gravity distribution model with the equilibrium assignment model. The earliest citation of this integration is the work of Irwin and Von Cube, as related by Florian et al. (1975), who comment on the work of Evans:

"The work of Evans resembles somewhat the algorithms developed by Irwin and Von Cube ['Capacity Restraint in Multi-Travel Mode Assignment Programs' H.R.B. Bulletin 347 (1962)] for a transportation study of [[Toronto]]. Their work allows for feedback between congested assignment and trip distribution, although they apply sequential procedures. Starting from an initial solution of the distribution problem, the interzonal trips are assigned to the initial shortest routes. For successive iterations, new shortest routes are computed, and their lengths are used as access times for input the distribution model. The new interzonal flows are then assigned in some proportion to the routes already found. The procedure is stopped when the interzonal times for successive iteration are quasi-equal."

Florian et al. proposed a somewhat different method for solving the combined distribution assignment, applying directly the Frank-Wolfe algorithm.   Boyce et al. (1988) summarize the research on Network Equilibrium Problems, including the assignment with elastic demand.