Route assignment
We first want to know the present pattern of traffic delay and then what would happen if the addition were made.
Ratios of travel time were used, tempered by considerations of costs, comfort, and level of service.
The Chicago Area Transportation Study (CATS) researchers developed diversion curves for freeways versus local streets.
The issue the diversion approach did not handle was the feedback from the quantity of traffic on links and routes.
It goes this way: The planning study is to support investments so that a good level of service is available on all links.
Using the travel times associated with the planned level of service, calculations indicate how traffic will flow once improvements are in place.
Knowing the quantities of traffic on links, the capacity to be supplied to meet the desired level of service can be calculated.
Dafermos (1968) applied the Frank-Wolfe algorithm (1956, Florian 1976), which can be used to deal with the traffic equilibrium problem.
To assign traffic to paths and links we have to have rules, and there are the well-known Wardrop equilibrium conditions.
The user optimum equilibrium can be found by solving the following nonlinear programming problem
An example from Eash, Janson, and Boyce (1979) will illustrate the solution to the nonlinear program problem.
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.
Wilson's doubly constrained entropy model has been the point of departure for efforts at the aggregate level.
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.
Wilson derives a 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.
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.
Their work allows for feedback between congested assignment and trip distribution, although they apply sequential procedures.
For successive iterations, new shortest routes are computed, and their lengths are used as access times for input the distribution model.
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.
Eash et al., for instance, studied the road net on DuPage County where there were about 30,000 one-way links and 9,500 nodes.
Start with an all or nothing assignment, and then follow the rule developed by Frank-Wolfe to iterate toward the minimum value of the objective function.
It uses an efficient search procedure to move the calculation rapidly toward the optimal solution.)
We would not want to draw any general conclusion from the slow application observation, mainly because we can find counter examples about the pace and pattern of technique development.
The problem statement and algorithm have general applications across civil engineering -– hydraulics, structures, and construction.
Cyclists have been found to prefer designated bike lanes and avoid steep hills.
