Classical and fractal analysis of vehicle demand on the ferry-boat system

Abstract

Transportation problems are important complex systems because of the increased number of vehicles in cities. In this paper, we study time series of vehicle demand by using the ferry-boat system between Salvador city and Itaparica island, in Bahia, Brazil. We compare the traditional demand analysis (ARIMA method) with the self-affine ones (the scaling exponent α and the density of crossing points ρ). In addition, taking into account the inherent self-affine behavior we study the stationary states of this dynamic process by using a nonlinear Fokker–Planck equation. The present findings indicate that the scaling exponent α describes some properties of flux of vehicles using the ferry-boat system. The behavior of α gives an alternative explanation about demand analysis, and the nonlinear Fokker–Planck equation presents a solution close to the stationary behavior of this complex dynamical analysis.