Traffic flow modeling forms the foundation for all aspects of transportation from planning through design. Having an accurate and reliable model allows decision makers to select projects that provide the greatest public benefit. Traditionally the reliability of the model comes from the accuracy of initial conditions. The initial conditions provide a baseline upon which response action and forecast condition scenario models can be built. Existing traffic flow modeling methodologies may not provide desired fidelity in representing the requisite baseline condition. Traffic flow that is modeled for a slice of time may overstate or understate observed baseline traffic flow.
A variety of microscopic (microsimulation) and macroscopic modeling methodologies have shown great success in incorporating vehicular, infrastructure and driver interactions in a variety of applications. Popular commercial model platforms have offered continuous improvements that include behavioral and predictive deterministic analytical options. Advanced techniques based on the discrete cellular approach have also been useful in adding spatial-temporal traffic flow evolution based on combination of flow methods and driver unpredictability.
To counter potential initial condition traffic flow bias, a new methodology was developed that that utilizes a closed form solution of the traffic flow equation and is insensitive to the initial condition misspecification. This new generalized traffic flow methodology can be applied for any initial condition, and may be universally applied to any size network—corridor, sub-area, or region. Further, application of the new modeling approach was implemented in a spreadsheet vehicle that is open source and readily applicable to diverse modeling applications.
In this paper, the authors will examine traffic flow conservation fidelity using advanced self-similar techniques to solve a generalized set of continuity equations at different scales – macroscopic, microscopic and mesoscopic. Spreadsheet implementation of closed form solutions generalized to include merging/diverging and gridlock boundary conditions is applied to corridor analysis in Colorado Springs. Comparative analysis with commercial modeling tools is used to demonstrate the simplicity of the model and sensitivity to many practical situations.