arXiv subjects

Marc Barthelemy

Publications and source records attributed to Marc Barthelemy.

At least 55 records · Page 3Linked to original sources

arXiv2021

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 is 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 $η\approx 0.4$) combined with an exponential cut-off $ξ$. This correlation length $ξ$ 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.

physics.soc-ph↗

arXiv2021

From one-way streets to percolation on random mixed graphs

In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirical effect of one-way streets in about $140$ cities in the world. Their presence induces a detour that persists over a wide range of distances and characterized by a non-universal exponent. The effect of one-ways on the pattern of shortest paths is then twofold: they mitigate local traffic in certain areas but create bottlenecks elsewhere. This empirical study leads naturally to consider a mixed graph model of 2d regular lattices with both undirected links and a diluted variable fraction $p$ of randomly directed links which mimics the presence of one-ways in a street network. We study the size of the strongly connected component (SCC) versus $p$ and demonstrate the existence of a threshold $p_c$ above which the SCC size is zero. We show numerically that this transition is non-trivial for lattices with degree less than $4$ and provide some analytical argument. We compute numerically the critical exponents for this transition and confirm previous results showing that they define a new universality class different from both the directed and standard percolation. Finally, we show that the transition on real-world graphs can be understood with random perturbations of regular lattices. The impact of one-ways on the graph properties were already the subject of a few mathematical studies, and our results show that this problem has also interesting connections with percolation, a classical model in statistical physics.

cond-mat.stat-mech↗

arXiv2020

Access to mass rapid transit in OECD urban areas

As mitigating car traffic in cities has become paramount to abate climate change effects, fostering public transport in cities appears ever-more appealing. A key ingredient in that purpose is easy access to mass rapid transit (MRT) systems. So far, we have however few empirical estimates of the coverage of MRT in urban areas, computed as the share of people living in MRT catchment areas, say for instance within walking distance. In this work, we clarify a universal definition of such a metrics, the "People Near Transit (PNT)", and present measures of this quantity for 85 urban areas in OECD countries, the largest dataset of such a quantity so far. By suggesting a standardized protocol, we make our dataset sound and expandable to other countries and cities in the world, which grounds our work into solid basis for multiple reuses in transport, environmental or economic studies.

physics.soc-ph↗

arXiv2020

Scenarios for a post-COVID-19 world airline network

The airline industry was severely hit by the COVID-19 crisis with an average demand decrease of about $64\%$ (IATA, April 2020) which triggered already several bankruptcies of airline companies all over the world. While the robustness of the world airline network (WAN) was mostly studied as an homogeneous network, we introduce a new tool for analyzing the impact of a company failure: the `airline company network' where two airlines are connected if they share at least one route segment. Using this tool, we observe that the failure of companies well connected with others has the largest impact on the connectivity of the WAN. We then explore how the global demand reduction affects airlines differently, and provide an analysis of different scenarios if its stays low and does not come back to its pre-crisis level. Using traffic data from the Official Aviation Guide (OAG) and simple assumptions about customer's airline choice strategies, we find that the local effective demand can be much lower than the average one, especially for companies that are not monopolistic and share their segments with larger companies. Even if the average demand comes back to $60\%$ of the total capacity, we find that between $46\%$ and $59\%$ of the companies could experience a reduction of more than $50\%$ of their traffic, depending on the type of competitive advantage that drives customer's airline choice. These results highlight how the complex competitive structure of the WAN weakens its robustness when facing such a large crisis.

physics.soc-ph↗

arXiv2020

The effect of interurban movements on the spatial distribution of population in China

Understanding how interurban movements can modify the spatial distribution of the population is important for transport planning but is also a fundamental ingredient for epidemic modeling. We focus here on vacation trips (for all transportation modes) during the Chinese Lunar New Year and compare the results for 2019 with the ones for 2020 where travel bans were applied for mitigating the spread of a novel coronavirus (COVID-19). We first show that these travel flows are broadly distributed and display both large temporal and spatial fluctuations, making their modeling very difficult. When flows are larger, they appear to be more dispersed over a larger number of origins and destinations, creating de facto hubs that can spread an epidemic at a large scale. These movements quickly induce (in about a week) a very strong population concentration in a small set of cities. We characterize quantitatively the return to the initial distribution by defining a pendular ratio which allows us to show that this dynamics is very slow and even stopped for the 2020 Lunar New Year due to travel restrictions. Travel restrictions obviously limit the spread of the diseases between different cities, but have thus the counter-effect of keeping high concentration in a small set of cities, a priori favoring intra-city spread, unless individual contacts are strongly limited. These results shed some light on how interurban movements modify the national distribution of populations, a crucial ingredient for devising effective control strategies at a national level.

physics.soc-ph↗

arXiv2019

Revisiting the coupling between accessibility and population growth

The coupling between population growth and transport accessibility has been an elusive problem for more than 60 years now. Due to the lack of theoretical foundations, most of the studies that considered how the evolution of transportation networks impacts the population growth are based on regression analysis in order to identify relevant variables. The recent availability of large amounts of data allows us to envision the construction of new approaches for understanding this coupling between transport and population growth. Here, we use a detailed dataset for about 36000 municipalities in France from 1968 until now. In the case of large urban areas such as Paris, we show that growth rate statistical variations decay in time and display a trend towards homogeneization where local aspects are less relevant. We also show that growth rate differences due to accessibility are very small and can mostly be observed for cities that experienced very large accessibility variations. This suggests that the relevant variable for explaining growth rate variations is not the accessibility but its temporal variation. We propose a model that integrates the stochastic internal variation of the municipalitie's population and an inter-urban migration term that we show to be proportional to the accessibility variation and has a limited time duration. This model provides a simple theoretical framework that allows to go beyond econometric studies and sheds a new light on the impact of transportation modes on city growth.

physics.soc-ph↗

arXiv2019

The shape of shortest paths in random spatial networks

In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^χ$, while the transversal fluctuations, known as wandering, grow as $L^ξ$. We find that when weighting edges directly with their Euclidean span in various spatial network models, we have two distinct classes defined by different exponents $ξ=3/5$ and $χ= 1/5$, or $ξ=7/10$ and $χ= 2/5$, depending only on coarse details of the specific connectivity laws used. Also, the travel time fluctuations are Gaussian, rather than Tracy-Widom, which is rarely seen in first passage models. The first class contains proximity graphs such as the hard and soft random geometric graph, and the $k$-nearest neighbour random geometric graphs, where via Monte Carlo simulations we find $ξ=0.60\pm 0.01$ and $χ= 0.20\pm 0.01$, showing a theoretical minimal wandering. The second class contains graphs based on excluded regions such as $β$-skeletons and the Delaunay triangulation and are characterised by the values $ξ=0.70\pm 0.01$ and $χ= 0.40\pm 0.01$, with a nearly theoretically maximal wandering exponent. We also show numerically that the KPZ relation $χ= 2ξ-1$ is satisfied for all these models. These results shed some light on the Euclidean first passage process, but also raise some theoretical questions about the scaling laws and the derivation of the exponent values, and also whether a model can be constructed with maximal wandering, or non-Gaussian travel fluctuations, while embedded in space.

cond-mat.stat-mech↗

arXiv2019

Tomography of scaling

Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^β$ with a nontrivial value of the exponent $β$, usually determined by regression methods. The presence of noise can make it difficult to conclude about the existence of a non-linear behavior with $β\neq 1$ and we propose here to circumvent fitting problems by investigating how two different systems of sizes $P_1$ and $P_2$ are related to each other. This leads us to define a local scaling exponent $β_{\mathrm{loc}}$ that we study versus the ratio $P_2/P_1$ and provides some sort of `tomography scan' of scaling across different values of the size ratio, allowing us to assess the relevance of nonlinearity in the system and to identify an effective exponent that minimizes the error for predicting the value of $Y$. We illustrate this method on various real-world datasets for cities and show that our method reinforces in some cases the standard analysis, but is also able to provide new insights in inconclusive cases and to detect problems in the scaling form such as the absence of a single scaling exponent or the presence of threshold effects.

physics.soc-ph↗

arXiv2019

Critical factors for mitigating car traffic in cities

Car traffic in urban systems has been studied intensely in past decades but models are either limited to a specific aspect of traffic or applied to a specific region. Despite the importance and urgency of the problem we have a poor theoretical understanding of the parameters controlling urban car use and congestion. Here, we combine economical and transport ingredients into a statistical physics approach and propose a generic model that predicts for different cities the share of car drivers, the $CO_2$ emitted by cars and the average commuting time. We confirm these analytical predictions on 25 major urban areas in the world, and our results suggest that urban density is not the most relevant variable controlling car-related quantities but rather are the city's area size and the density of public transport. Mitigating the traffic (and its effect such as $CO_2$ emissions) can then be obtained by reducing the urbanized area size or, more realistically, by improving either the public transport density or its access. In particular, increasing the population density is a good idea only if it also increases the fraction of individuals having access to public transport.

physics.soc-ph↗

arXiv2019

Modeling cities

Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines such as quantitative geography, spatial economics, geomatics and urbanism, and more recently physics. (Statistical) Physics plays a major role by bringing tools and concepts able to bridge theory and empirical results, and we will illustrate this on some fundamental aspects of cities: the growth of their surface area and their population, their spatial organization, and the spatial distribution of activities. We will present state-of-the-art results and models but also open problems for which we still have a partial understanding and where physics approaches could be particularly helpful. We will end this short review with a discussion about the possibility of constructing a science of cities.

physics.soc-ph↗

arXiv2019

The statistical physics of Cities

Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the structure and evolution of cities is therefore critical because policy makers need robust theories and new paradigms for mitigating these problems. Fortunately, the increased data available about urban systems opens the possibility of constructing a quantitative 'science of cities', with the aim of identifying and modelling essential phenomena. Statistical physics plays a major role in this effort by bringing tools and concepts able to bridge theory and empirical results. This article illustrates this point by focusing on fundamental objects in cities: the distribution of the urban population; segregation phenomena and spin-like models; the polycentric transition of the activity organization; energy considerations about mobility and models inspired by gravity and radiation concepts; CO2 emitted by transport; and finally, scaling that describes how various socio-economical and infrastructures evolve when cities grow.

physics.soc-ph↗

arXiv2019

The optimal geometry of transportation networks

Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the optimal network changes as $L$ increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the optimal networks. As a second variant we consider the optimal network that minimizes the average travel time to a central destination, and discuss both analytically and numerically some simple shapes such as the star network, the ring or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as $L$ increases, resources go preferentially to radial branches and that there is a sharp transition at a value $L_c$ where a loop appears.

physics.soc-ph↗

arXiv2019

Efficiency and shrinking in evolving networks

Characterizing the spatio-temporal evolution of networks is a central topic in many disciplines. While network expansion has been studied thoroughly, less is known about how empirical networks behave when shrinking. For transportation networks, this is especially relevant on account of their connection with the socio-economical substrate, and we focus here on the evolution of the French railway network from its birth in 1840 to 2000, in relation to the country's demographic dynamics. The network evolved in parallel with technology (e.g., faster trains) and under strong constraints, such as preserving a good population coverage and balancing cost and efficiency. We show that the shrinking phase that started in 1930 decreased the total length of the network while preserving efficiency and population coverage: efficiency and robustness remain remarkably constant while the total length of the network shrinks by $50\%$ between 1930 and 2000, and the total travel time and time-diameter decreased by more than $75\%$ during the same period. Moreover, shrinking the network did not affect the overall accessibility, with an average travel time that decreases steadily since its formation. This evolution leads naturally to an increase of transportation multimodality (such as a massive use of cars) and shows the importance of considering together transportation modes acting at different spatial scales. More generally, our results suggest that shrinking is not necessarily associated with a decay in performance and functions, but can be beneficial in terms of design goals and can be part of the natural evolution of an adaptive network.

physics.soc-ph↗

arXiv2018

Transitions in spatial networks

Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the Erdos-Renyi graph, and spatial networks display a large variety of behaviors. We will discuss here some (mostly recent) results about topological transitions, `localization' transitions seen in the shortest paths pattern, and also about the effect of congestion and fluctuations on the structure of optimal networks. The importance of spatial networks in real-world applications makes these transitions very relevant and this review is meant as a step towards a deeper understanding of the effect of space on network structures.

cond-mat.stat-mech↗

arXiv2018

Towards a classification of planar maps

Planar graphs and their spatial embedding -- planar maps -- are used in many different fields due to their ubiquity in the real world (leaf veins in biology, street patterns in urban studies, etc.) and are also fundamental objects in mathematics and combinatorics. These graphs have been well described in the literature, but we do not have so far a clear way to cluster them in different families. A typology of planar maps would be very useful and would allow to monitor their changes, to compare them with each other, or to correlate their structure with other properties. Using an algorithm which merges recursively the smallest areas in the graph with the largest ones, we plot the Gini coefficient of areas of cells and obtain a profile associated to each network. We test the relevance of these `Gini profiles' on simulated networks and on real street networks of Barcelona (Spain), New York City (USA), Tokyo (Japan), and discuss their main properties. We also apply this method to the case of Paris (France) at different dates which allows us to follow the structural changes of this system. Finally, we discuss the important ingredient of spatial heterogeneity of real-world planar graphs and test some ideas on Manhattan and Tokyo. Our results show that the Gini profile encodes various informations about the structure of the corresponding planar map and represents a good candidate for constructing relevant classes of these objects.

cond-mat.stat-mech↗

arXiv2018

From the betweenness centrality in street networks to structural invariants in random planar graphs

We demonstrate that the distribution of betweenness centrality (BC), a global structural metric based on network flow, is an invariant quantity in most planar graphs. We confirm this invariance through an empirical analysis of street networks from 97 of the most populous cities worldwide, at scales significantly larger than previous studies. We also find that the BC distribution is robust to major alterations in the network, including significant changes to its topology and edge weight structure, indicating that the only relevant factors shaping the distribution are the number of nodes and edges as well as the constraint of planarity. Through simulations of random planar graph models and analytical calculations on Cayley trees, this invariance is demonstrated to be a consequence of a bimodal regime consisting of an underlying tree structure for high BC nodes, and a low BC regime arising from the presence of loops providing local path alternatives. Furthermore, the high BC nodes display a non-trivial spatial dependence, with increasing spatial correlation as a function of the number of edges, leading them to cluster around the barycenter at large densities. Our results suggest that the spatial distribution of the BC is a more accurate discriminator when comparing patterns across cities. Moreover, the BC being a static predictor of congestion in planar graphs, the observed invariance and spatial dependence has practical implications for infrastructural and biological networks. In particular, for the case of street networks, as long as planarity is conserved, bottlenecks continue to persist, and the effect of planned interventions to alleviate structural congestion will be limited primarily to load redistribution, a feature confirmed by analyzing 200 years of data for central Paris.

physics.soc-ph↗

arXiv2018

The spatial organization of the population density in cities

Although the average population density of a city is an extremely simple indicator, it is often used as a determinant factor for describing various aspects of urban phenomena. On the other hand, a plethora of different measures that aim at characterizing the urban form have been introduced in the literature, often with the risk of redundancy. Here, we argue that two measures are enough to capture a wealth of different forms of the population density. First, fluctuations of the local density can be very important and we should distinguish almost homogeneous cities from highly heterogeneous ones. This is easily characterized by an indicator such as the Gini coefficient $G$, or equivalently by the relative standard deviation or the entropy. The second important dimension is the spatial organization of the heterogeneities in population density and we propose a dispersion index $η$ that characterizes the degree of localization of highly populated areas. We argue that these two dimensions are enough to characterize the spatial organization of cities, and we discuss this approach using a dataset of about $4,500$ cities belonging to the $10$ largest urban areas in France, for which we have high resolution data. Representing cities in the plane $(G,η)$ allows us to construct families of cities. On average, compactness increases with heterogeneity, and we find four large categories of cities (with population $>10,000$ inhabitants): (i) first, homogeneous and dispersed cities with small density fluctuations, (ii) very heterogeneous cities with a compact organization of large densities areas. The last two groups comprise heterogeneous cities with (iii) a monocentric organization or (iv) a more delocalized, polycentric structure. Integrating these two parameters in econometric analysis could improve our understanding of the impact of urban form on various socio-economical aspects.

physics.soc-ph↗

arXiv2018

From global scaling to the dynamics of individual cities

Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of urban datasets displays apparent nonlinear behaviors whose statistical validity and meaning were recently the focus of many debates. We discuss here another aspect which is the implication of such scaling forms on individual cities and how they can be used for predicting the behavior of a city when its population changes. We illustrate this discussion on the case of delay due to traffic congestion with a dataset for 101 US cities in the range 1982-2014. We show that the scaling form obtained by agglomerating all the available data for different cities and for different years displays indeed a nonlinear behavior, but which appears to be unrelated to the dynamics of individual cities when their population grow. In other words, the congestion induced delay in a given city does not depend on its population only, but also on its previous history. This strong path-dependency prohibits the existence of a simple scaling form valid for all cities and shows that we cannot always agglomerate the data for many different systems. More generally, these results also challenge the use of transversal data for understanding longitudinal series for cities.

physics.soc-ph↗