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 and congestion dissipation rate . We describe the dynamics of congestion propagation and dissipation using these new parameters, , and , 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.Unlike individual link traffic shockwaves in a two-dimensional time-space diagram, which are categorized as forward or backward moving, network traffic jams evolve in multi directions over space. Therefore, we propose that a network's propagation and recovery can be characterized by two average rates, namely the congestion propagation rate and a congestion recovery rate , which together reflect the number of congested links in the network over time. These two macroscopic characteristics are critical in modeling congestion propagation and dissipation as a simple contagion process [21].Despite the complex human behavior-driven nature of traffic, we demonstrate that urban network traffic congestion follows a surprisingly similar spreading pattern as in other systems, including the spread of infectious disease in a population or diffusion of ideas in a social network, and can be described using a similar parsimonious theoretical network framework. Specifically, we model the spread of congestion in urban networks by adapting a classical epidemic model to include a propagation and recovery mechanism dependent on time-varying travel demand and consistent with fundamentals of network traffic flow theory. We illustrate the model to be a robust and predictive analytical model, and validate the framework using empirical and simulation-based numerical experiments.

Given the efficiency and equity concerns of a cordon toll, this paper proposes a few alternative distance-dependent area-based pricing models for a large-scale dynamic traffic network. We use the Network Fundamental Diagram (NFD) to monitor the network traffic state over time and consider different trip lengths in the toll calculation. The first model is a distance toll that is linearly related to the distance traveled within the cordon. The second model is an improved joint distance and time toll (JDTT) whereby users are charged jointly in proportion to the distance traveled and time spent within the cordon. The third model is a further improved joint distance and delay toll (JDDT) which replaces the time toll in the JDTT with a delay toll component. To solve the optimal toll level problem, we develop a simulation-based optimization (SBO) framework. Specifically, we propose a simultaneous approach and a sequential approach, respectively, based on the proportional-integral (PI) feedback controller to iteratively adjust the JDTT and JDDT, and use a calibrated large-scale simulation-based dynamic traffic assignment (DTA) model of Melbourne, Australia to evaluate the network performance under different pricing scenarios. While the framework is developed for static pricing, we show that it can be easily extended to solve time-dependent pricing by using multiple PI controllers. Results show that although the distance toll keeps the network from entering the congested regime of the NFD, it naturally drives users into the shortest paths within the cordon resulting in an uneven distribution of congestion. This is reflected by a large clockwise hysteresis loop in the NFD. In contrast, both the JDTT and JDDT reduce the size of the hysteresis loop while achieving the same control objective. We further conduct multiple simulation runs with different random seed numbers to demonstrate the effectiveness of different pricing models against simulation stochasticity. However, we postulate that the feedback control is not applicable with guaranteed convergence if the periphery of the cordon area becomes highly congested or gridlocked.

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Stories of mega-jams that last tens of hours or even days appear not only in fiction but also in reality. In this context, it is important to characterize the collapse of the network, defined as the transition from a characteristic travel time to orders of magnitude longer for the same distance traveled. In this multicity study, we unravel this complex phenomenon under various conditions of demand and translate it to the travel time of the individual drivers. First, we start with the current conditions, showing that there is a characteristic time τ that takes a representative group of commuters to arrive at their destinations once their maximum density has been reached. While this time differs from city to city, it can be explained by Γ, defined as the ratio of the vehicle miles traveled to the total vehicle distance the road network can support per hour. Modifying Γ can improve τ and directly inform planning and infrastructure interventions. In this study we focus on measuring the vulnerability of the system by increasing the volume of cars in the network, keeping the road capacity and the empirical spatial dynamics from origins to destinations unchanged. We identify three states of urban traffic, separated by two distinctive transitions. The first one describes the appearance of the first bottlenecks and the second one the collapse of the system. This collapse is marked by a given number of commuters in each city and it is formally characterized by a nonequilibrium phase transition.

This paper presents a bi-level optimization problem to estimate offline time-dependent origin–destination (time-dependent O-D) demand on the basis of link flows and historical O-D matrices. The upper-level problem aimed to minimize the summation of errors in both traffic counts and O-D demand. Conventionally, O-D flows are linearly mapped to link flows with the assignment matrix proportions obtained from the dynamic traffic assignment, which is typically formulated as the lower-level problem. However, the linear relationship may be invalid when congestion builds up in the network, and a nonlinear relation between O-D flows and link flows may result. The nonlinearity may lead to a converged solution that is far from the global optimum. An accurate solution should be able to relax the linear assumption and to consider the effect of other O-D flows on the links’ traffic volumes. In this study, a solution method that relied on the sensitivity of assignment proportions to O-D flows was proposed and applied; it required a number of further assignments. To overcome the extra computational requirement, a heuristic method to exclude the extra assignments and to improve the performance of the solution was proposed. The proposed algorithm was applied to multiple networks of varying sizes and congestion levels. The results demonstrated the efficiency of the proposed method for congested networks with less computation time.

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