Scale-free resilience of real traffic jams

Spatiotemporal dynamics of traffic bottlenecks yields an early signal of heavy congestions

Heavy traffic jams are difficult to predict due to the complexity of traffic dynamics. Understanding the network dynamics of traffic bottlenecks can help avoid critical large traffic jams and improve overall traffic conditions. Here, we develop a method to forecast heavy congestions based on their early propagation stage. Our framework follows the network propagation and dissipation of the traffic jams originated from a bottleneck emergence, growth, and its recovery and disappearance. Based on large-scale urban traffic-speed data, we find that dissipation duration of jams follows approximately power-law distributions, and typically, traffic jams dissolve nearly twice slower than their growth. Importantly, we find that the growth speed, even at the first 15 minutes of a jam, is highly correlated with the maximal size of the jam. Our methodology can be applied in urban traffic control systems to forecast heavy traffic bottlenecks and prevent them before they propagate to large network congestions.

Empirical analysis of congestion spreading in Seoul traffic network

Understanding how local traffic congestion spreads in urban traffic networks is fundamental to solving congestion problems in cities. In this work, by analyzing the high-resolution data of traffic velocity in Seoul, we empirically investigate the spreading patterns and cluster formation of traffic congestion in a real-world urban traffic network. To do this, we propose a congestion identification method suitable for various types of interacting traffic flows in urban traffic networks. Our method reveals that congestion spreading in Seoul may be characterized by a treelike structure during the morning rush hour but a more persistent loop structure during the evening rush hour. Our findings suggest that diffusion and stacking processes of local congestion play a major role in the formation of urban traffic congestion.

Understanding congestion propagation by combining percolation theory with the macroscopic fundamental diagram

The science of cities aims to model urban phenomena as aggregate properties that are functions of a system's variables. Following this line of research, this study seeks to combine two well-known approaches in network and transportation science: (i) The macroscopic fundamental diagram (MFD), which examines the characteristics of urban traffic flow at the network level, including the relationship between flow, density, and speed. (ii) Percolation theory, which investigates the topological and dynamical aspects of complex networks, including traffic networks. Combining these two approaches, we find that the maximum number of congested clusters and the maximum MFD flow occur at the same moment, precluding network percolation (i.e. traffic collapse). These insights describe the transition of the average network flow from the uncongested phase to the congested phase in parallel with the percolation transition from sporadic congested links to a large, congested cluster of links. These results can help to better understand network resilience and the mechanisms behind the propagation of traffic congestion and the resulting traffic collapse.

Fragmentation of outage clusters during the recovery of power distribution grids

The understanding of recovery processes in power distribution grids is limited by the lack of realistic outage data, especially large-scale blackout datasets. By analyzing data from three electrical companies across the United States, we find that the recovery duration of an outage is connected with the downtime of its nearby outages and blackout intensity (defined as the peak number of outages during a blackout), but is independent of the number of customers affected. We present a cluster-based recovery framework to analytically characterize the dependence between outages, and interpret the dominant role blackout intensity plays in recovery. The recovery of blackouts is not random and has a universal pattern that is independent of the disruption cause, the post-disaster network structure, and the detailed repair strategy. Our study reveals that suppressing blackout intensity is a promising way to speed up restoration.

Neighborhood, built environment and resilience in transportation during the COVID-19 pandemic

COVID-19 has swept the world, and the unprecedented decline in transit ridership has been noticed. However, little attention has been paid to the resilience of the transportation system, particularly in medium-sized cities. Drawing upon a light rail ridership dataset in Salt Lake County from 2017 to 2021, we develop a novel method to measure the vulnerability and resilience of transit ridership using a Bayesian structure time series model. The results show that government policies have a more significant impact than the number of COVID-19 cases on transit ridership. Regarding the built environment, a highly compact urban design might reduce the building coverage ratio and makes transit stations more vulnerable and less resilient. Furthermore, the high rate of minorities is the primary reason for the drops in transit ridership. The findings are valuable for understanding the vulnerability and resilience of transit ridership to pandemics for better coping strategies in the future.

Identification, cost evaluation, and prioritization of urban traffic congestions and their origin

The increasing urbanization in the last decades results in significant growth in urban traffic congestion around the world. This leads to enormous time people spent on roads and thus significant money waste and air pollution. Here, we present a novel methodology for identification, cost evaluation, and thus, prioritization of congestion origins, i.e., their bottlenecks. The presented work is based on network analysis of the entire road network from a global point of view. We identify and prioritize traffic bottlenecks based on big data of traffic speed retrieved in near-real-time. Our approach highlights the bottlenecks that have the most significant effect on the global urban traffic flow. We follow the evolution of every traffic congestion in the entire urban network and rank all the congestions, based on the cost they cause (in Vehicle Hours units). We show that the macro-stability that represents the seeming regularity of traffic load both in time and space, overshadows the existence of meso-dynamics, where the bottlenecks that create these congestions usually do not reappear on different days or hours. Thus, our method enables to identify in near-real-time both recurrent and nonrecurrent congestions and their sources.

Quantifying the Resilience Performance of Airport Flight Operation to Severe Weather

The increased number of severe weather events caused by global warming in recent years is a major turbulence factor for airport operation and results in more irregular flights. Quantifying the system response status towards turbulence is critical, in order for airports to deal with severe weather. For this reason, we propose a resilience framework that is in compliance with resilience theory to evaluate airport flight operations. In this framework, the departure rate (DPR), normal weather baseline (NWB), and nonnegative general resilience (NGR) were defined and used. Meanwhile, the whole process is divided into five phases before and after disturbance, and the system capacities of susceptibility, absorption, adaptation, and recovery are assessed. In order to clarify the performance of the framework towards various severe weather conditions, an analysis was conducted at Beijing Capital Airport in China based on a dataset that includes both the meteorological terminal aviation weather report (METAR) and flight operations from January to July 2021. The results show that the newly proposed resilience framework can commendably reflect airport flight operation performance. The airport flight operation resilience characteristic is different with severe weather. Compared to sandstorms and snow, airport flight operation with stronger robustness was observed during thunderstorm events. The study also confirms that, as the weather warning level increases, the disruption time increases and response time decreases accordingly. The above results could assist researchers and policy makers in clearly understanding the real-world resilience of airport flight operation, in both theory and practice, and responding to emergent disruptive events effectively.

Effect of load-capacity heterogeneity on cascading overloads in networks

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.

Dynamical efficiency for multimodal time-varying transportation networks

Spatial systems that experience congestion can be modeled as weighted networks whose weights dynamically change over time with the redistribution of flows. This is particularly true for urban transportation networks. The aim of this work is to find appropriate network measures that are able to detect critical zones for traffic congestion and bottlenecks in a transportation system. We propose for both single and multi-layered networks a path-based measure, called dynamical efficiency, which computes the travel time differences under congested and free-flow conditions. The dynamical efficiency quantifies the reachability of a location embedded in the whole urban traffic condition, in lieu of a myopic description based on the average speed of single road segments. In this way, we are able to detect the formation of congestion seeds and visualize their evolution in time as well-defined clusters. Moreover, the extension to multilayer networks allows us to introduce a novel measure of centrality, which estimates the expected usage of inter-modal junctions between two different transportation means. Finally, we define the so-called dilemma factor in terms of number of alternatives that an interconnected transportation system offers to the travelers in exchange for a small increase in travel time. We find macroscopic relations between the percentage of extra-time, number of alternatives and level of congestion, useful to quantify the richness of trip choices that a city offers. As an illustrative example, we show how our methods work to study the real network of a megacity with probe traffic data.

Effects of mobility restrictions during COVID19 in Italy

To reduce the spread and the effect of the COVID-19 global pandemic, non-pharmaceutical interventions have been adopted on multiple occasions by governments. In particular lockdown policies, i.e., generalized mobility restrictions, have been employed to fight the first wave of the pandemic. We analyze data reflecting mobility levels over time in Italy before, during and after the national lockdown, in order to assess some direct and indirect effects. By applying methodologies based on percolation and network science approaches, we find that the typical network characteristics, while very revealing, do not tell the whole story. In particular, the Italian mobility network during lockdown has been damaged much more than node- and edge-level metrics indicate. Additionally, many of the main Provinces of Italy are affected by the lockdown in a surprisingly similar fashion, despite their geographical and economic dissimilarity. Based on our findings we offer an approach to estimate unavailable high-resolution economic dimensions, such as real time Province-level GDP, based on easily measurable mobility information.

Empirical evidence for a jamming transition in urban traffic

Understanding the mechanisms leading to the formation and the propagation of traffic jams in large cities is of crucial importance for urban planning and traffic management. Many studies have already considered the emergence of traffic jams from the point of view of phase transitions, but mostly in simple geometries such as highways for example or in the framework of percolation where an external parameter is driving the transition. More generally, empirical evidence and characterization for a congestion transition in complex road networks are scarce, and here, we use traffic measures for Paris (France) during the period 2014-2018 for testing the existence of a jamming transition at the urban level. In particular, we show that the correlation function of delays due to congestion is a power law (with exponent η ≈ 0.4) combined with an exponential cut-off ξ. This correlation length is shown to diverge during rush hours, pointing to a jamming transition in urban traffic. We also discuss the spatial structure of congestion and identify a core of congested links that participate in most traffic jams and whose structure is specific during rush hours. Finally, we show that the spatial structure of congestion is consistent with a reaction-diffusion picture proposed previously.

Study of Synergistic Effects in Complex Stochastic Systems

In this paper, a method for detecting synergistic effects of the interaction of elements in multi-element stochastic systems of separate redundancy, multi-server queuing, and statistical estimates of nonlinear recurrent relations parameters has been developed. The detected effects are quite strong and manifest themselves even with rough estimates. This allows studying them with mathematical methods of relatively low complexity and thereby expand the set of possible applications. These methods are based on special techniques of the structural analysis of multi-element stochastic models in combination with majorant asymptotic estimates of their performance indicators. They allow moving to more accurate and rather economical numerical calculations, as they indicate in which direction it is most convenient to perform these calculations.

Association between population distribution and urban GDP scaling

Urban scaling and Zipf’s law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.

Universal scaling laws of collective human flow patterns in urban regions

Detail observation of human locations became available recently by the development of information technology such as mobile phones with GPS (Global Positioning System). We analyzed temporal changes of global human flow patterns in urban regions based on mobile phones' GPS data in 9 large cities in Japan. By applying a new concept of drainage basins in analogous to river flow patterns, we discovered several universal scaling relations. These include, the number of moving people in a drainage basin of diameter L is proportional to [Formula: see text] in the morning rush hour, which is surprisingly different from reasonable intuition of proportionality to the 2 dimensional area, [Formula: see text]. We show that this unexpected 3 dimensional feature is related to the strong attraction of the city center to become a 3 dimensional structure due skyscrapers.

Emergence of Scale-Free Blackout Sizes in Power Grids

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.

mD-Resilience: A Multi-Dimensional Approach for Resilience-Based Performance Assessment in Urban Transportation

As demonstrated for extreme events, the resilience concept is used to evaluate the ability of a transportation system to resist and recover from disturbances. Motivated by the high cumulative impact of recurrent perturbations on transportation systems, we have investigated resilience quantification as a performance assessment method for high-probability low-impact (HPLI) disturbances such as traffic congestions. Resilience-based metrics are supplementary to conventional travel-time-based indices in literature. However, resilience is commonly quantified as a scalar variable despite its multi-dimensional nature. Accordingly, by hypothesizing increased information gain in performance assessment, we have investigated a multi-dimensional approach (mD-Resilience) for resilience quantification. Examining roadways’ resilience to recurrent congestions as a contributor to sustainable mobility, we proposed to measure resilience with several attributes that characterize the degradation stage, the recovery stage, and possible recovery paths. These attributes were integrated into a performance index by using Data Envelopment Analysis (DEA) as a non-parametric method. We demonstrated the increased information gain by quantifying the performance of major freeways in Los Angeles, California using Performance Measurement System (PeMS) data. The comparison of mD-Resilience approach with the method based on area under resilience curves showed its potential in distinguishing the severity of congestions. Furthermore, we showed that mD-Resilience also characterizes performance from the lens of delay and bottleneck severities.

A unified spatial multigraph analysis for public transport performance

Public transport performance not only directly depicts the convenience of a city's public transport, but also indirectly reflects urban dwellers' life quality and urban attractiveness. Understanding why some regions are easier to get around by public transport helps to build a green transport friendly city. This paper initiates a new perspective and method to investigate how public transport network's morphology contributes significantly to its performance. We investigate the significance of morphology from the perspective of graph classification - by extracting the typical local structures, called "motifs", from the multi-modal public transport multigraph. A motif is seen as a certain connectivity pattern of different transport modes at a local scale. Combinations of various motifs decide the output of graph classification, particularly, public transport performance. We invent an innovative method to extract motifs on complex spatial multigraphs. The proposed method is adaptable to unify complex factors into one simple form for swift coding, and depends less on observational data to handle data unavailability. In the study area of Beijing, we validate that the measure can infer varied public transport efficiencies and access equalities of different regions. Some typical areas with undeveloped or unevenly distributed public transport are further discussed.

Unraveling reaction-diffusion-like dynamics in urban congestion propagation: Insights from a large-scale road network

We study the dynamical process of congestion formation for large-scale urban networks by exploring a unique dataset of taxi movements in a megacity. We develop a dynamic model based on a reaction and a diffusion term that properly reproduces the cascade phenomena of traffic. The interaction of these two terms brings the values of the speeds on road network in self-organized patterns and it reveals an elegant physical law that reproduces the dynamics of congestion with very few parameters. The results presented show a promising match with an available real data set of link speeds estimated from more than 40 millions of GPS coordinates per day of about 20,000 taxis in Shenzhen, China.

Ordered Avalanches on the Bethe Lattice

We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to s−τ. When the avalanche mass is conserved (k=b), we get τ=1. For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent τ is found to depend on the model parameters; τ ≈ log(b)/log(k). The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength αmax in the bifractal spectrum is found to be 1/τ.