On the calibration of the combined distribution-assignment model

We consider a model which combines gravity model trip distribution and equilibrium assignment. This model contains a free parameter which must be fixed using supplementary information, that is, the model must be calibrated. It is natural to ask which supplementary information is sufficient to determine the free parameter. We show here that under very weak hypotheses each of the quantities, the entropy H or the total assignment cost F, is alone sufficient to determine the free parameter. In contrast, it is shown by means of a counterexample that even under very strong hypotheses, the total cost C is not sufficient.