In this paper, a general deterministic process model for traffic assignment is described, such that the equilibrium pattern is a fixed-point state. A simple but effective approach, based on exponential smoothing, is followed to model both user cost and choice updating processes. Then, conditions assuring the stability of a fixed-point state, which means that it is an attractor, are analysed with respect to main parameters, such as demand, behaviour dispersion, derivatives of link cost functions, etc. as well as habit and yesterday experience weight. As reported in previous papers, results obtained from numerical simulations pictorially confirm theoretical expectations. In this paper a formal stability analysis was carried out, concerning firstly attractor definition, when different from fixed-points, through Poincare characteristic Multipliers and secondly a-periodic attractor identification, through fractality measures. Then a bifurcation analysis was carried out for fixed-point attractors, to investigate equilibrium pattern stability. Obtained results, confirming numerical results, show that when a fixed-point attractor loses its stability, several types of attractors may occur, such as k-periodic, quasi-periodic, a-periodic, depending on conditions on dynamic process parameters. The effect on the length of transients before convergence to an attractor as well as the role of the starting state are also discussed. The results in this paper indicate that the equilibrium approach, which does not allow for an explicit stability analysis, may fail to effectively describe the state of the system relevant to analysis and design. For the covering abstract see ITRD E126595.
Abstract