A study on the stability of the probit-based multi-modal transport assignment model

In this study, the properties on perturbation stability of stochastic dynamic processes are provided. The probit based multi-modal transport assignment model considered in this paper can have multiple equilibria because of the asymmetric link disutility functions. An examination on the uniqueness and stability of the multi-modal transport assignment model is carried out by using a simple example. The demand on a single OD pair is assumed to choose between bus and auto depending on their disutility functions. The examination is carried out by assuming the interaction effect of the road congestion caused by autos and buses. As the results, the following three findings are obtained: (i) if the condition on the uniqueness of solution is violated, in general, there are three solutions; (ii) one of three solutions is stable in terms of perturbation stability; and (iii) the trajectory of dynamic system is determined by the domains where each equilibrium dominates.