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 modelingapproaches. Recent works that attempt to merge models at different scales haveyielded some success, but there still exists a need for a single modelingframework that can seamlessly model traffic flow across several spatiotemporalscales. The presented work utilizes a renormalization group (RG) theoreticapproach, building upon our prior research on statistical mechanics-inspiredtraffic flow modeling. Specifically, we use an Ising model-inspired cellularautomata model to represent traffic flow dynamics. RG transformations areapplied to this model to obtain coarse-grained parameters (interaction andfield coefficients) to simulate traffic at coarser spatiotemporal scales anddifferent vehicular densities. We measure the accuracy of the coarse-grainedtraffic flow simulation using a pixel-based image correlation metric and findgood correlation between the dynamics at different scales. Importantly,emergent traffic dynamics such as backward moving congestion waves are retainedat coarser scales with this approach. The presented work has the potential tospur the development of a unified traffic flow modeling framework fortransportation analysis across varied spatiotemporal scales, while retaining ananalytical relationship between the model parameters at these scales.