Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

Abstract

In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.

Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

“…Neither the exact equations and their numerical solution nor the fitted models can capture such behaviour, leading to substantial differences in the predicted traffic jam time for apparently similar initial conditions. This sensitivity explains a phenomenon experienced by any driver on the road-the apparent spurious formation of traffic jams following smooth conditions in what seemed to be dense but fluid traffic [48][49][50]. It also suggests that traffic jam alleviation measures should focus on reducing the number of incoming vehicles on the road (namely, f ) and accelerating relaxation times.…”

Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

“…Neither the exact equations and their numerical solution nor the fitted models can capture such behaviour, leading to substantial differences in the predicted traffic jam time for apparently similar initial conditions. This sensitivity explains a phenomenon experienced by any driver on the road-the apparent spurious formation of traffic jams following smooth conditions in what seemed to be dense but fluid traffic [48][49][50]. It also suggests that traffic jam alleviation measures should focus on reducing the number of incoming vehicles on the road (namely, f ) and accelerating relaxation times.…”

Analysis of Principles and Applications of Chaos Theory

“…In the book 'The Fractal Geometry of Nature' by Mandelbrot, a hypothesis states that self-affinity is displayed financial time series. Self-affinity encompasses the same idea of self-similarity but allows more flexibility in degrees of similarity across scales [28]. Self-similarity is a key to the state of present financial marketthe process of self-replication is chaotic.…”

Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review

“…The study also reveals some critical issues raised while applying the chaos concept in hydrology. Similarly, a review of the application of chaos theory in traffic flow patterns was reported in [24]. In both works, some of the reviewed methods reported for the short-term forecasting are correlation dimension, Lyapunov exponent, Kolmogorov entropy, SVM, ANN, nonlinear prediction, and dynamic neural network.…”

Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

“…Neither the exact equations and their numerical solution nor the fitted models can capture such behaviour, leading to substantial differences in the predicted traffic jam time for apparently similar initial conditions. This sensitivity explains a phenomenon experienced by any driver on the road-the apparent spurious formation of traffic jams following smooth conditions in what seemed to be dense but fluid traffic [48][49][50]. It also suggests that traffic jam alleviation measures should focus on reducing the number of incoming vehicles on the road (namely, f ) and accelerating relaxation times.…”

Analysis of Principles and Applications of Chaos Theory

“…In the book 'The Fractal Geometry of Nature' by Mandelbrot, a hypothesis states that self-affinity is displayed financial time series. Self-affinity encompasses the same idea of self-similarity but allows more flexibility in degrees of similarity across scales [28]. Self-similarity is a key to the state of present financial marketthe process of self-replication is chaotic.…”

Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review

“…The study also reveals some critical issues raised while applying the chaos concept in hydrology. Similarly, a review of the application of chaos theory in traffic flow patterns was reported in [24]. In both works, some of the reviewed methods reported for the short-term forecasting are correlation dimension, Lyapunov exponent, Kolmogorov entropy, SVM, ANN, nonlinear prediction, and dynamic neural network.…”

Understanding Complex Traffic Dynamics with the Nondimensionalisation Technique

“…Neither the exact equations and their numerical solution nor the fitted models can capture such behaviour, leading to substantial differences in the predicted traffic jam time for apparently similar initial conditions. This sensitivity explains a phenomenon experienced by any driver on the road-the apparent spurious formation of traffic jams following smooth conditions in what seemed to be dense but fluid traffic [48][49][50]. It also suggests that traffic jam alleviation measures should focus on reducing the number of incoming vehicles on the road (namely, f ) and accelerating relaxation times.…”

Analysis of Principles and Applications of Chaos Theory

“…In the book 'The Fractal Geometry of Nature' by Mandelbrot, a hypothesis states that self-affinity is displayed financial time series. Self-affinity encompasses the same idea of self-similarity but allows more flexibility in degrees of similarity across scales [28]. Self-similarity is a key to the state of present financial marketthe process of self-replication is chaotic.…”

Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review

“…The study also reveals some critical issues raised while applying the chaos concept in hydrology. Similarly, a review of the application of chaos theory in traffic flow patterns was reported in [24]. In both works, some of the reviewed methods reported for the short-term forecasting are correlation dimension, Lyapunov exponent, Kolmogorov entropy, SVM, ANN, nonlinear prediction, and dynamic neural network.…”