Research on the non-linear characteristics of traffic flow system under different scalings

The fact that the traffic flow system is a complex and non-linear system is extensively accepted by academe. The quantitative depiction research on complexity and non-linearity of traffic flow system is now in the ascendant. This paper focuses on the problem of how system scaling affects the complexity degree of a system. Firstly, Lyapunov index, relevancy dimension and the Lempel-Ziv algorithm are introduced for scientific depiction of the non-linear characteristics of traffic flow system. Based on measurements, three actual time headway sequences and three 20s-period traffic flow sequences are gained. By the simulation of the traffic flow system, five traffic flow sequences are obtained whose periods are 1 min, 2 min, 3 min, 4 min and 5 min, respectively. By calculating the Lyapunov index, relevancy dimension and Lempel-Ziv complexity degree of above traffic flow sequences, it was found that chaos, fractal and high complexity degree existed in the time headway sequences, but the complexity degree was gradually reduced with the gradually increasing scaling. So four conclusions and two hypotheses are obtained: 1 the complexity degrees of the same system are different under different scaling 2 negative correlation exists between the complexity degree and the depicting scaling of a system to a certain extent.