Modelling Traffic Congestion as a Spreading Phenomenon

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. This dissertation presents frameworks 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. Specifically, we model the spread of congestion in urban networks by adapting a classical epidemic model to include a propagation and dissipation mechanism dependent on time-varying travel demand and consistent with the fundamentals of network traffic flow theory. We describe the dynamics of congestion spread using two macroscopic new parameters (propagation rate β and recovery rate μ) embedded within a system of ordinary differential equations, similar to the well-known susceptible-infected-recovered (SIR) model. For simplicity, we initially assumed the topological distribution of road networks to be homogeneous. The proposed contagion-based dynamics are verified through empirical multi-city analysis. In addition to the simplistic homogeneous SIR approach, we also explored the significance of the degree of heterogeneity in urban street networks using both empirical and simulation-based traffic data. However, this approach inherently assumes an undirected network with uniform recovery rate compared to a road network, which usually displays directed flow and topological reliance on congestion recovery. Keeping in view of these constraints, we proposed a modification to the heterogeneous mean-field model to describe the spreading process of congestion in urban street networks. A practical application of the proposed model is also tested in this dissertation in the context of signal optimisation using cycle length as a controlling function. The experiments helped quantify the characteristic differences between two widely used traffic assignment models, i.e. Dynamic User Equilibrium (DUE) and Stochastic Route Choice (SRC). Comparison has been made at two levels: link-level flows and network-level congestion patterns. Furthermore, we explored an alternative approach for congestion dynamic modelling, namely the "Reaction-Diffusion (RD) model", with a similar concept as our proposed frameworks but at link-level. This model, with its complexity, requires higher computation time with detailed link-level information of congestion dynamics