(Revised) For converging certain large demand models with "feedback" toward equilibrium between demand and congested travel times, the author has already found by trial-and-error that much runtime can be saved by allowing assignments in the early iterations of the demand model to stop at larger relative gaps than in the later iterations, without seeming to impede overall model convergence. This study seeks a basis beyond trial-and-error to decide how much convergence is enough for assignments only used for feedback, and to know where runtime can be saved without impairing the model's overall progress toward equilibrium.

(The well-cited paper of similar title by Boyce, Ralevic-Dekic and Bar-Gera, on the other hand, relates gaps to link-flow stability of the final assignments of given travel demands.)

Skim-error experiments begin with skims following a well-converged assignment. Those trips are then reassigned at various relative-gap stopping levels. Skims from the less-converged assignments are compared to those from the best-converged, in terms of the average and root-mean-square difference, and maximum deviation. Separate experiments with different periods of the day, congestion levels, modeled locations, congestion-delay functions, software and assignment algorithms each yield a set of data points for relative skim error (compared to well-converged) versus relative gap of the assignment.

Relative average skim errors (compared to those from their respective well-converged assignments), from the variety of models tested, are found to cluster around a fairly consistent general relationship with relative gap.

Additional comparisons were made upon different versions of a model differing only be the choice of a constant relative gap criterion in all assignments, to compare the rates and limits of convergence. The present tests find that the relative gap chosen does not affect the rate of convergence, until measures of successive-iteration skim changes drop to the magnitude of the skim errors indicated by the above tests. Whenever this occurs, the skims may continue indefinitely to fluctuate, with skim successive-differences comparable to those skim errors.

These findings give more direction to the scheduling of relative gaps in a model's feedback iterations, and also identify situations where a model's successive skim changes may understate skim errors due to the assignment convergence level.