Synthesis of the advance in and application of fractal characteristics of traffic flow.
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Synthesis of the advance in and application of fractal characteristics of traffic flow.

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      Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields of science. This project provides a synthesis of existing applications of fractal theory in various fields, as well as its potential applications in traffic management. The specific information gathered and summarized in this report includes: (1) a synthesis of fractal applications in fields that share similarities with transportation networks, such as electrical networks, and in fields outside of transportation; (2) a synthesis of fractal applications that have been proven effective in traffic flow; (3) additional insights on how fractal theory can be applied in traffic management strategies; and (4) summary of research findings and recommendations for more detailed research. Two fractal techniques, the fractal dimension and the Hurst exponent, were applied to detect the existence of fractal characteristics in traffic and crash data from Florida. Traffic volume, speed, and occupancy data obtained from 15-min and 1-hr detector data at two locations in Miami-Dade County were found to exhibit fractal characteristics. Furthermore, the speed trend revealed stronger fractal behavior compared to the volume and occupancy trends for the same time period. The existence of fractal characteristics in crash data was detected in both annual and daily frequency trends. However, the daily crash frequency trends exhibited greater extent of fractal behavior compared to the annual trends, mainly due to the existence of more random fluctuations. The fractal investigation of both annual and three-year average crash rates at ten randomly-selected signalized intersections revealed that the annual crash rate trend, in general, exhibited relatively more fractal characteristics than the three-year average trend. Future research could make use of the insights presented in this study to apply fractal theory in traffic management strategies such as managed lanes, ramp metering, crash analysis, and travel time reliability. Compared to traditional models, fractal theory is anticipated to yield more precise estimates of performance measures. Therefore, a potential future research is to apply fractal theory for predicting short-term traffic flow. Another promising avenue is to apply fractal theory to identify high-crash locations and to predict crash rate at specific locations. These approaches could potentially result in increased efficiency, mobility, and safety of the entire roadway network.
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