Contagion mean field model for transport in urban traffic networks

TL;DR

This work addresses how macroscopic congestion in urban traffic can emerge as an epidemic-type contagion process. It develops a mean-field network model at crossroads that maps density dynamics to a Susceptible-Infected-Susceptible (SIS) form, and with time-interval transport constraints extends to a Susceptible-Infected-Recovered (SIR) description; flux-conservation at intersections yields a Fundamental Diagram-like flow-density relationship, with a predictive critical density given by $\rho_c = 1 - \frac{\gamma}{\beta s_0} e^{\beta \rho_c}$. The authors validate the framework via Saltillo field data and the UTD19 sensor dataset, estimating parameters $\beta$ and $\gamma$ and showing that the model captures the FDT backbone and the SIR-like dynamics despite fluctuations. The results offer a principled basis for immunization-like traffic control strategies by tuning crossroad transmission and venting rates, and point to directions for incorporating network topology in larger-scale deployments.

Abstract

Theoretical arguments and empirical evidence for the emergence of macroscopic epidemic type behavior, in the form of Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) processes in urban traffic congestion from microscopic network flows is given. Moreover, it's shown that the emergence of SIS/SIR implies a relationship between traffic flow and density, which is consistent with observations of the so called \emph{Fundamental Diagram of Traffic} (FDT), which is a characteristic signature of vehicle movement phenomena that spans multiple scales. Our results put in more firm grounds recent findings that indicate that traffic congestion at the aggregate level can be modeled by simple contagion dynamics.

Figures (6)

• Figure 1: Schematic representation of the Fundamental Diagram of Traffic (FDT). The triangular shape illustrates the two distinct regimes: the free-flow phase (blue solid line) where flow increases linearly with density, and the congested phase (red dashed line) where interactions reduce flow as density approaches the jam density ($\rho_{jam}$). The peak represents the road capacity ($q_{max}$) at the critical density ($\rho_c$).
• Figure 2: Junctions level illustration of the contagion traffic flow model. In the mean field limit, the aggregation of inflow and outflow intersections like those in the Figure, give a coarse grained description equivalent to a Susceptible-Infected-Susceptible (SIS) contagion process under stationary flow conditions. If the total transport is constrained to occur in a given time interval, the mean field model is then equivalent to a Susceptible-Infected-Recovered (SIR) process.
• Figure 3: Fitting of the SIR mean field model to experimental data in the city of Saltillo, Mexico (see Subsection \ref{['saltillo']} for a thorough explanation).
• Figure 4: Experimental vehicle flow vs density data from the city of Saltillo, Mexico (black dotted lines) and the FDT function that results from the estimated SIR model (red dotted dashed lines).
• Figure 5: Traffic dynamics from a single detector of the Schimmelstrasse street in the Aussersihl district of Zurich, Switzerland, at Wednesday 28th October, 2015. Empirical data is shown in black while the fit of the local mean field contagion model to the data is shown in red.