Multi-vehicle assignment with elastic vehicle choice behaviour: Fixed-point, deterministic process and stochastic process models

New types of vehicles, such as electricity-powered and/or autonomous cars or buses, are under rapid development, but the time needed to turn the existing stock of traditional vehicles, such as privately-owned human-driven fossil fuelled passenger cars, will likely last several years during which mixed traffic is expected. Moreover, the likely effects of the introduction of such vehicles may not be necessarily positive. Thus, a careful analysis of their various impacts through well designed tools is needed. Main tools for transportation systems analysis are based on methods for travel demand assignment to a transportation network, commonly used to support transportation project assessment and evaluation. The original contribution of this paper is twofold. First, a modelling approach to multi vehicle type assignment is proposed, in this approach the user choice proportions among vehicle types available to users are the results of an explicit choice behaviour model instead of input data as in all existing papers on multi-vehicle assignment. This approach is applied for analysing assignment to transportation networks including Fixed-Point models for equilibrium assignment and Deterministic and Stochastic Process models for day-to-to dynamic assignment. Second, statistical methods are introduced to study the bifurcation of SP models, in order to account for the stochasticity of such models. In particular, the Hartigan's Dip statistic, which measure the degree of unimodality of a distribution, showed to be the most effective one in identifying bifurcation in SP models. Fixed-point stability and bifurcation analysis are carried out too, and some simple numerical examples are also discussed. Reported results show that innovative vehicles with less impact on congestion than traditional ones may not have a positive effect on equilibrium stability since negative effect of reducing route choice dispersion may be compensate the positive effects on congestion.