Modification of the gravity model and application to the metropolitan Seoul subway system

Spatiotemporal behaviors of the ridership of a public transportation system during an epidemic outbreak: case of MERS in Seoul

During May and June 2015, an outbreak of the Middle East respiratory syndrome (MERS) occurred in Korea, which raised the fear of contagion throughout society and suppressed the use of public transportation systems. Exploring daily ridership data of the Seoul bus transportation system, along with the number of infected patients and search volume in web portals, we observe that ridership decreased abruptly while attention was heavily focused online. Then this temporal reduction recovered exponentially with a characteristic time of 3 weeks when newly confirmed cases began to decrease. We also find with the data of ranked keywords of web portals that areas with severely reduced ridership tended to cluster and spatiotemporal variations of such clusters were highly associated with general hospitals where MERS patients were treated. On the other hand, the spatial reduction in ridership relaxed algebraically with the distance from a general hospital while the outbreak was severe. We further probe the influence of the epidemic outbreak in the framework of linear response theory, which relates the responses to the epidemic outbreak ("perturbation") with correlations in the absence of the perturbation. Indeed, the spatial correlation function of the ridership changes is observed to follow a power law, sharing the same exponent as the spatial relaxation of the response function. This new theoretical approach offers a useful tool for understanding responses of public transportation system to epidemic or accidental disasters.

Gravity model in dockless bike-sharing systems within cities

Due to previous technical challenges with the collection of data on riding behaviors, there have only been a few studies focusing on patterns and regularities of biking traffic, which are crucial to understand to help achieve a greener and more sustainable future urban development. Recently, with the booming of the sharing economy, and the development of the Internet of Things (IoT) and mobile payment technology, dockless bike-sharing systems that record information for every trip provide us with a unique opportunity to study the patterns of biking traffic within cities. We first reveal a spatial scaling relation between the cumulative volume of riding activities and the corresponding distance to the city center, and a power law distribution on the volume of biking flows between fine-grained locations in both Beijing and Shanghai. We validate the effectiveness of the general gravity model on predicting biking traffic at fine spatial resolutions, where population-related parameters are less than unity, indicating that smaller populations are relatively more important per capita in generating biking traffic. We then further study the impacts of spatial scale on the gravity model and reveal that the distance-related parameter grows in a similar way as population-related parameters when the spatial scale of the locations increases. In addition, the flow patterns of some special locations (sources and sinks) that cannot be fully explained by the gravity model are studied.

Hub-Periphery Hierarchy in Bus Transportation Networks: Gini Coefficients and the Seoul Bus System

Bus transportation networks are characteristically different from other mass transportation systems such as airline or subway networks, and thus the usual approach may not work properly. In this paper, to analyze the bus transportation network, we employ the Gini coefficient, which measures the disparity of weights of bus stops. Applied to the Seoul bus system specifically, the Gini coefficient allows us to classify nodes in the bus network into two distinct types: hub and peripheral nodes. We elucidate the structural properties of the two types in the years 2011 and 2013, and probe the evolution of each type over the two years. It is revealed that the hub type evolves according to the controlled growth process while the peripheral one, displaying a number of new constructions as well as sudden closings of bus stops, is not described by growth dynamics. The Gini coefficient thus provides a key mathematical criterion of decomposing the transportation network into a growing one and the other. It would also help policymakers to deal with the complexity of urban mobility and make more sustainable city planning.

A universal opportunity model for human mobility

Predicting human mobility between locations has practical applications in transportation science, spatial economics, sociology and many other fields. For more than 100 years, many human mobility prediction models have been proposed, among which the gravity model analogous to Newton's law of gravitation is widely used. Another classical model is the intervening opportunity (IO) model, which indicates that an individual selecting a destination is related to both the destination's opportunities and the intervening opportunities between the origin and the destination. The IO model established from the perspective of individual selection behavior has recently triggered the establishment of many new IO class models. Although these IO class models can achieve accurate prediction at specific spatiotemporal scales, an IO class model that can describe an individual's destination selection behavior at different spatiotemporal scales is still lacking. Here, we develop a universal opportunity model that considers two human behavioral tendencies: one is the exploratory tendency, and the other is the cautious tendency. Our model establishes a new framework in IO class models and covers the classical radiation model and opportunity priority selection model. Furthermore, we use various mobility data to demonstrate our model's predictive ability. The results show that our model can better predict human mobility than previous IO class models. Moreover, this model can help us better understand the underlying mechanism of the individual's destination selection behavior in different types of human mobility.

Equivalence and its invalidation between non-Markovian and Markovian spreading dynamics on complex networks

Epidemic spreading processes in the real world depend on human behaviors and, consequently, are typically non-Markovian in that the key events underlying the spreading dynamics cannot be described as a Poisson random process and the corresponding event time is not exponentially distributed. In contrast to Markovian type of spreading dynamics for which mathematical theories have been well developed, we lack a comprehensive framework to analyze and fully understand non-Markovian spreading processes. Here we develop a mean-field theory to address this challenge, and demonstrate that the theory enables accurate prediction of both the transient phase and the steady states of non-Markovian susceptible-infected-susceptible spreading dynamics on synthetic and empirical networks. We further find that the existence of equivalence between non-Markovian and Markovian spreading depends on a specific edge activation mechanism. In particular, when temporal correlations are absent on active edges, the equivalence can be expected; otherwise, an exact equivalence no longer holds.

Gravity model explained by the radiation model on a population landscape

Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.

Why do people move? Enhancing human mobility prediction using local functions based on public records and SNS data

The quality of life for people in urban regions can be improved by predicting urban human mobility and adjusting urban planning accordingly. In this study, we compared several possible variables to verify whether a gravity model (a human mobility prediction model borrowed from Newtonian mechanics) worked as well in inner-city regions as it did in intra-city regions. We reviewed the resident population, the number of employees, and the number of SNS posts as variables for generating mass values for an urban traffic gravity model. We also compared the straight-line distance, travel distance, and the impact of time as possible distance values. We defined the functions of urban regions on the basis of public records and SNS data to reflect the diverse social factors in urban regions. In this process, we conducted a dimension reduction method for the public record data and used a machine learning-based clustering algorithm for the SNS data. In doing so, we found that functional distance could be defined as the Euclidean distance between social function vectors in urban regions. Finally, we examined whether the functional distance was a variable that had a significant impact on urban human mobility.

Universal model of individual and population mobility on diverse spatial scales

Studies of human mobility in the past decade revealed a number of general scaling laws. However, to reproduce the scaling behaviors quantitatively at both the individual and population levels simultaneously remains to be an outstanding problem. Moreover, recent evidence suggests that spatial scales have a significant effect on human mobility, raising the need for formulating a universal model suited for human mobility at different levels and spatial scales. Here we develop a general model by combining memory effect and population-induced competition to enable accurate prediction of human mobility based on population distribution only. A variety of individual and collective mobility patterns such as scaling behaviors and trajectory motifs are accurately predicted for different countries and cities of diverse spatial scales. Our model establishes a universal underlying mechanism capable of explaining a variety of human mobility behaviors, and has significant applications for understanding many dynamical processes associated with human mobility.

Relating Land Use and Human Intra-City Mobility

Understanding human mobility patterns—how people move in their everyday lives—is an interdisciplinary research field. It is a question with roots back to the 19th century that has been dramatically revitalized with the recent increase in data availability. Models of human mobility often take the population distribution as a starting point. Another, sometimes more accurate, data source is land-use maps. In this paper, we discuss how the intra-city movement patterns, and consequently population distribution, can be predicted from such data sources. As a link between land use and mobility, we show that the purposes of people's trips are strongly correlated with the land use of the trip's origin and destination. We calibrate, validate and discuss our model using survey data.

Universal predictability of mobility patterns in cities

Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without any adjustable parameters to capture the underlying driving force accounting for human mobility patterns at the city scale. We use various mobility data collected from a number of cities with different characteristics to demonstrate the predictive power of our model. We find that insofar as the spatial distribution of population is available, our model offers universal prediction of mobility patterns in good agreement with real observations, including distance distribution, destination travel constraints and flux. By contrast, the models that succeed in modelling mobility patterns in countries are not applicable in cities, which suggests that there is a diversity of human mobility at different spatial scales. Our model has potential applications in many fields relevant to mobility behaviour in cities, without relying on previous mobility measurements.

Explaining the power-law distribution of human mobility through transportation modality decomposition

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.

Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

Statistical mechanics of multiedge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Unraveling the origin of exponential law in intra-urban human mobility

The vast majority of travel takes place within cities. Recently, new data has become available which allows for the discovery of urban mobility patterns which differ from established results about long distance travel. Specifically, the latest evidence increasingly points to exponential trip length distributions, contrary to the scaling laws observed on larger scales. In this paper, in order to explore the origin of the exponential law, we propose a new model which can predict individual flows in urban areas better. Based on the model, we explain the exponential law of intra-urban mobility as a result of the exponential decrease in average population density in urban areas. Indeed, both empirical and analytical results indicate that the trip length and the population density share the same exponential decaying rate.