Evidence of long range dependence and self-similarity in urban traffic systems

Transportation simulation technologies should accurately model traffic demand, distribution, and assignment parameters for urban environment simulation. These three parameters significantly impact transportation engineering benchmark process, are also critical in realizing realistic traffic modeling situations. In this paper, we model and characterize traffic density distribution of thousands of locations, intersection, and roadways around the world. The traffic densities are generated from millions of images collected over several years and processed using computer vision techniques. The resulting traffic density distribution time series are then analyzed. It is found using the goodness-of-fit test that the traffic density distributions follow heavy-tail models such as Weibull in over 90% of analyzed locations. Moreover, a heavy-tail gives rise to long-range dependence and self-similarity, which we studied by estimating the Hurst exponent (H). Our analysis based on seven different Hurst estimators strongly indicates that the traffic distribution patterns are stochastically self-similar (0.5 ≤ H ≤ 1.0). We believe this is an important finding that will influence the design and development of the next generation traffic simulation techniques and also aid in accurately modeling traffic engineering of urban systems. In addition, it shall provide a much-needed input for the development of smart cities.