Synthesis of the Advance in and Application of Fractal Characteristics of Traffic Flow
The Florida Department of Transportation is continuously looking for ways to improve traffic safety and mobility through the implementation of advanced traffic management strategies. Examples of such strategies include managed lanes, ramp metering, dynamic message signs or other motorist information systems, real-time signal timing/phasing changes, etc. The Department implements these strategies through the transportation management centers (TMCs), which function as nerve centers and provide monitoring and control capabilities for various Intelligent Transportation Systems (ITS). Florida’s TMCs use the SunGuide software to monitor and control ITS devices (cameras, vehicle detectors, dynamic message signs), manage incidents, and collect traffic flow data.
Successful implementation of advanced traffic management strategies requires the ability to estimate/predict traffic conditions. To date, the process of estimating the impact of various traffic management strategies on traffic flow has been largely based on existing traffic flow models, which view traffic either as a stochastic process or as a kinematic fluid. While these models have the advantages of requiring minimal amount of data and are relatively simple to use, they are based on non-linear differential equations that have been reported to be unsatisfactory for modeling some real-world traffic flow conditions.
Additionally, traditional traffic analysis methodologies which rely on sampling techniques inevitably introduce uncertainties in the analysis results. The continued use of sampling techniques, which were once justified by the high cost associated with collecting traffic flow data, is no longer necessary given that the Department now has unprecedented abilities to collect traffic flow data through vehicle detectors installed as part of ITS projects. Hence, the use of sampling techniques may be avoided by using other appropriate models that can analyze large and complex datasets, particularly those generated from vehicle detectors.
The wide coverage currently provided by vehicle detectors on both freeway and arterial networks provides unique opportunities to harness the data and provide predictive capabilities for anticipating traffic conditions and enhance system performance based on network-wide historic and real-time data. However, these abundant data have been, at best, underutilized. The SunGuide software currently used by TMCs does not have any capabilities to analyze and apply these large datasets for traffic predictions for decision supports.
A novel approach to capitalize on the wealth of traffic data and to explore new traffic flow analysis methods is clearly needed. Such a new approach may emanate from viewing transportation networks from a fractal perspective. A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.” The use of fractal dimension analysis is becoming widespread. Experts in fields such as medicine, physics, seismology, finance/economics, meteorology, and ecology are using fractal analysis to quantify various phenomena. For example, the finance industry uses the fractal applications to predict stock market movements. Previous research studies have determined the fractal nature of electrical networks and of other types of networks which may share similarities with transportation networks.
Traditional traffic analysis methods may not properly address the nature of traffic flow if the inherent traffic structure were fractal. The main advantage and strength of fractal analysis lies in its ability to find patterns in large and complex datasets; for instance those generated by vehicle detectors. Traffic flow is very dynamic and has been shown to exhibit fractal characteristics. As such, fractal analysis may potentially be a promising tool for improving traffic flow analysis methods. Several pioneering studies have shown evidences on the presence of a fractal nature in traffic flow and outlined the potential benefits of employing fractal theory in traffic-related applications. Examples of potential applications include incident detection and traffic volume/flow prediction.
The appeal to use fractal geometry to analyze traffic data is that it does not filter out the roughness nor neglects the fractal interdependencies in the way that basic statistical methods often do, nor does it round off the roughness in the way that curve fitting does. Fractal geometry could, therefore, be useful in situations where the nature of the 'roughness', the dynamics of the underlying data, or the variations in the data patterns are important. This is true for, among other things, the understanding of traffic crashes, arrival of vehicles at intersections, and the way in which traffic demand varies.
The purpose of this study is to develop a synthesis report on potential applications of fractal theory in traffic flow analysis. The study will identify those elements of traffic flow which exhibit fractal characteristics and how fractal theory can be applied to transportation network management. It is believed that fractal theory has the potential to play an important role in developing predictive models feeding decision support systems that would improve traffic management in terms of both recurring and non-recurring congestion. Accordingly, this research will be conducted with the end target of improving the modeling systems to better predict traffic behavior from an operations, safety, traffic engineering and transportation planning dimension.