Multi-scale Traffic Flow Modeling: A Renormalization Group Approach

Traffic flow modeling is typically performed at one of three different scales (microscopic, mesoscopic, or macroscopic), each with distinct modeling approaches. Recent works that attempt to merge models at different scales have yielded some success, but there still exists a need for a single modeling framework that can seamlessly model traffic flow across several spatiotemporal scales. The presented work utilizes a renormalization group (RG) theoretic approach, building upon our prior research on statistical mechanics-inspired traffic flow modeling. Specifically, we use an Ising model-inspired cellular automata model to represent traffic flow dynamics. RG transformations are applied to this model to obtain coarse-grained parameters (interaction and field coefficients) to simulate traffic at coarser spatiotemporal scales and different vehicular densities. We measure the accuracy of the coarse-grained traffic flow simulation using a pixel-based image correlation metric and find good correlation between the dynamics at different scales. Importantly, emergent traffic dynamics such as backward moving congestion waves are retained at coarser scales with this approach. The presented work has the potential to spur the development of a unified traffic flow modeling framework for transportation analysis across varied spatiotemporal scales, while retaining an analytical relationship between the model parameters at these scales.