An Iterative Process

Try Again

If at first you don't succeed (first you don't succeed),

Dust yourself off, and try again

You can dust it off and try again, try again

'Cause if at first you don't succeed (first you don't succeed),

You can dust it off, and try again

Dust yourself off and try again, try again

In mathematics, trying again is called iterating.

The User Equilibrium assignment in Travel Demand Models is an iterative process.  Those iterations  are of the Frank-Wolfe algorithm in order to compute an equilibrium volume.  Between iterations, the IMPEDANCE is updated.  NO other attributes,  especially capacity, should be changed until the equilibrium process is completed.  Changing the formula for impedance, or any link attributes, except the volume, during this process violates the assumptions of the Frank-Wolfe algorithm that is being used.

This does not mean that the initial link capacities are absolutely correct.  Capacities on links are most often based on characteristics of the design for that link, e.g. lane width.  However there are circumstances where the capacity depends  not only on the design characteristics of the link, but on the volumes on this or other links. 

·    For example, the capacity of a link approaching a signalized intersection is a function of the green to Cycle Length, g/C, of that signal.  An initial assumption has to be made for the g/C ratio before the volumes are known, but technically the g/C ratio is a function of the approach volume on that link divided by the approach volumes of all links approaching that intstection.  Those volumes are precisely what is being computed in the assignment iterations.

·   Similarly, the capacity of truck climbing lanes depends on the truck percentage on that link as well as truck percentages of adjacent links.  These percentages will not be known until after the assignment iterations are complete.

This issue is not unique to assignment. It can occur whenever an iterative process is used.  Assumptions may be made in order to solve the process, but these assumptions may be inconsistent with the solution.  In fact the Travel Demand Modeling process often already has such a feedback loop .  In order to distribute and find the mode choice in creating a trip table, it is necessary to know the impedances, e.g. skim times, between zones for each mode, which are not really known until after that trip table is assigned.  A feedback loop uses the impedances based on the initial assignment to update the inputs to trip distribution and mode choice.

A similar process is proposed for assignment.  Assumptions are made for network link capacities in order to solve for volumes on that network.  After the assignment ( NOT DURING THE ASSIGNMENT), the capacities can be recomputed based on the volumes which were assigned.  If these capacities are significantly different than the capacities that were assumed before the assignment began, then the link capacities should be updated and a new assignment should begin. This process should continue until the capacities that were assumed as the input to the assignment are sufficiently consistent with the capacities computed from the volumes that are output from the assignment.