Multimodal assignment to congested networks: fixed-point models and algorithms

This paper presents an elastic demand multimodal assignment model with transit costs depending on car flows in the case of non-exclusive bus lanes (shared lanes). This assumption implies 'non-separable' cost functions and therefore it is not generally possible to demonstrate the uniqueness of the equilibrium solution and the convergence of solution algorithms, only with the conditions proposed in literature. This model is a multimodal model because the mode choice depends on congested costs for both modes. In this paper a condition on demand models for uniqueness of equilibrium solutions is stated; that condition implies some hypotheses on transit cost functions. At this time, it is not yet proved that Logit models adopted in the proposed multimodal formulation satisfy this condition except for some test networks, as reported in the paper. However, tests on a real network showed the convergence of algorithms and uniqueness of the solution. Moreover a comparison among performances of solution algorithms is reported. Research perspectives will be addressed to prove in general way the applicability of the proposed condition for the transit-congested multimodal assignment model.