Source-linked AI summary
A simple contagion process describes spreading of traffic jams in urban networks
Meead Saberi, Mudabber Ashfaq, Homayoun Hamedmoghadam, Seyed Amir Hosseini, Ziyuan Gu, Sajjad Shafiei, Divya J. Nair, Vinayak Dixit, Lauren Gardner, S. Travis Waller, Marta C. González
TL;DR
Urban traffic models often depend on computationally intensive microscopic approaches, while network-level congestion spreading remains incompletely characterized. The paper adapts a simple contagion process and SIR-like ordinary differential equations using congestion propagation and recovery rates. Empirical and simulation-based analyses show that congestion propagation is a network spreading phenomenon and that buildup and recovery depend on the propagation-to-recovery rate ratio.
Problem
Existing urban traffic models can be computationally burdensome and highly parameterized, while congestion propagation and dissipation have not been characterized as a network spreading phenomenon.
Method
The paper models congested, free-flow, and recovered links with SIR-like ordinary differential equations governed by congestion propagation rate 𝛽 and recovery rate 𝜇.
Results
Empirical and simulation-based analyses show that congestion propagation is a spreading phenomenon and that network congestion buildup and recovery depend on the ratio of propagation to recovery rates.
Takeaways & Limitations
The contagion-based dynamics provide a framework to describe congestion propagation and dissipation and to model the fraction of congested links over time.
Takeaways & Limitations
Google empirical data cannot be made available because of contractual and privacy reasons.
Abstract
from arXiv · showhide
The spread of traffic jams in urban networks has long been viewed as a complex spatio-temporal phenomenon that often requires computationally intensive microscopic models for analysis purposes. In this study, we present a framework to describe the dynamics of congestion propagation and dissipation of traffic in cities using a simple contagion process, inspired by those used to model infectious disease spread in a population. We introduce two novel macroscopic characteristics of network traffic, namely congestion propagation rate \b{eta} and congestion dissipation rate μ. We describe the dynamics of congestion propagation and dissipation using these new parameters, \b{eta}, and μ, embedded within a system of ordinary differential equations, analogous to the well-known Susceptible-Infected-Recovered (SIR) model. The proposed contagion-based dynamics are verified through an empirical multi-city analysis, and can be used to monitor, predict and control the fraction of congested links in the network over time.
INTRODUCTION
Urban congestion is difficult to model with computationally intensive microscopic approaches, while network-level propagation and dissipation remain incompletely characterized. The paper proposes a simple contagion framework using macroscopic propagation and recovery rates to describe congestion across networks.
- Motivation: Traffic jams propagate over time and space, but existing city-traffic models often require high computational burden and extensive calibration.Limited transport infrastructure data further challenges modeling, although mobile sensors can provide continuous spatial data for real-time traffic-condition estimation.
- Research gap: Network-level congestion propagation and dissipation have not previously been characterized as a spreading phenomenon.Prior macroscopic approaches include percolation theory, but the proposed framing treats traffic as spreading and recovering throughout the network.
- Macroscopic characterization: Network traffic jams evolve in multiple spatial directions, motivating average congestion propagation rate 𝛽 and recovery rate 𝜇.Together, these rates represent the number of congested links over time in a simple contagion process.
- Proposed framework: The framework adapts an epidemic-style contagion model with propagation and recovery mechanisms dependent on time-varying travel demand.The model is presented as parsimonious, predictive, and evaluated using empirical and simulation-based numerical experiments.
RESULTS
The study applies a simple contagion framework to model congestion propagation and dissipation across urban networks, using macroscopic rates and empirical and simulated traffic data. Results show epidemic-like congestion dynamics, demand- and threshold-dependent rate relationships, and non-random spatial spreading.
- Empirical and simulation evaluation: Traffic conditions from six cities and Melbourne simulations are used to fit ODE dynamics and estimate congestion propagation and recovery rates.The framework models the fraction of congested links over time using traffic observations and calibrated dynamic traffic assignment data.
- Contagion model: The model represents congestion with free-flow, congested, and recovered link states, analogous to an SIR contagion process.The ODE system describes changes in congested, recovered, and free-flow link fractions through propagation and recovery rates.
- Threshold sensitivity: Smaller congestion thresholds better reflect congestion formation, whereas ρ=0.9 classifies nearly 15% of links as congested at simulation start.With ρ=0.1, congestion is nearly absent during the first simulation hour; larger thresholds identify congestion earlier.
- Propagation and dissipation: Congestion follows initial exponential growth and subsequent exponential recovery, while the physically meaningful quantity is the relative rate β/μ rather than either rate alone.Both β and μ decrease exponentially as ρ increases, but β/μ increases; the rates therefore require relative interpretation.
- Spatial spreading: Congested upstream clusters in simulations differ from a randomized null model, indicating non-random spatial spreading across the network.The analysis compares time-varying upstream cluster sizes between simulated congestion and independently randomized link thresholds.
- Demand dependence: Increasing demand raises the congested fraction and delays recovery, while β/μ varies jointly with demand and ρ.For smaller ρ values, the relationship between β/μ and demand is approximately linear.
DISCUSSION
The study finds that traffic-jam propagation and dissipation can be described as a simple contagion process, with network-scale dynamics governed by propagation and recovery rates. Demand and the ratio of these rates influence congestion growth and recovery.
- The proposed ordinary-differential-equation contagion model describes urban traffic-jam propagation and dissipation using congestion propagation and recovery rates.
- Congestion propagation is supported as a network spreading phenomenon in both empirical and simulation-based analyses.
- The propagation-to-recovery rate ratio influences congestion buildup and recovery duration, analogous to arrival and departure rates in a queuing system.
- Increasing travel demand raises the propagation-to-recovery rate ratio, producing larger traffic jams and longer recovery times that follow an exponential response.
METHODS
The methods combine calibrated Melbourne traffic simulation with Google speed observations from six cities. Congested links are identified from time-dependent speed data, model parameters are fitted by global pattern search, and simulation data support replication.
- The Melbourne traffic simulation uses a calibrated and validated mesoscopic dynamic traffic-assignment model for the 6–10 AM morning peak.Many demand and supply parameters require calibration before simulation outcomes are used.
- Google traffic data provide link-level speeds for Melbourne, Sydney, London, Paris, Chicago, and Montreal during city-specific morning-peak modeling periods.The data were collected on 27/06/2018, with speeds recorded at continuous intervals.
- The analysis uses 6:00–10:00 AM observations across cities, while each city’s modeling timeframe is selected from its congested-link profile.
- Model parameters are estimated by fitting modeled congested-link fractions to simulated data with derivative-free global pattern search minimizing RMSE.
- Simulation data and the dynamic traffic-assignment model are publicly available, but contractual and privacy restrictions prevent release of the empirical Google data.