Origin of the scaling law in human mobility: Hierarchy of traffic systems

Abstract

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which a random walker will generate a power-law travel displacement distribution with exponent -2. When considering the inhomogeneities of cities' locations and attractions, this model reproduces a power-law displacement distribution with an exponential cutoff, as well as a scaling behavior in the probability density of having traveled a certain distance at a certain time. Our results agree very well with the empirical observations reported in [D. Brockmann et al., Nature 439, 462 (2006)].PACS numbers: 89.75.Fb, 05.40.Fb, 89.75.Da Studies on the non-Poisson statistics of human behaviors have recently attracted much attention [1,2,3]. Besides the inter-event or waiting time distribution, the spatial movements of human also exhibit non-Poisson statistics. Brockmann et al. [4] investigated the bank note dispersal, as a proxy for human movements, and revealed indirectly a power-law distribution of human travel displacements. Gonzalez et al.[5] studied the human travel patterns by measuring the distance of mobile phone users' movements in different stations, and observed a similar scaling law. Actually, the mobility patterns of many animals also show power-law-like displacement distributions [6,7,8]. The ubiquity of such kind of distributions attracts scientists to dig into the underlying mechanism. Some interpretations, such as optimal search strategy [9, 10], olfactory-driven foraging [11] and deterministic walks [12], have already been raised for the power-law displacement distribution in animals mobility patterns, however, they are based on the prey processes and thus cannot be used to explain the observed scaling law in human trajectories, which is still an open problem. In this paper, we propose a model to mimic the human travel pattern, where the hierarchical organization of the real human traffic systems is taken into account. Our model can reproduce the power-law displacement distributions, as well as the scaling behavior in probability density of having traveled a certain distance at a certain time, agreeing very well with the empirical results reported in Ref. [4].Let's think about the real human traffic systems. Generally speaking, a district (e.g., a province or a state) usually has a core city, like its capital; around this core city, there are several big cities as the secondary centers (e.g., municipalities); then, each of these centers is rounded by some counties; and towns and villages will surround each of the counties. A hierarchical traffic system is built accordingly. Imaging people traveling from a town, a, subordinating to the central city, A, to another town b that is subordinated to the central city B. There is usually no direct way connecting a and b, and the typical route is a → A → B → b. This kind of hierarchical organization is not just inside a countr...

An empirical study on human mobility and its agent-based modeling

“…This simulation result is based on two ingredients of the model: the structure of the hierarchical purpose clusters and the individual preferential behavior. Indeed, the underlying geographical structure has a significant influence on the mode and/or distance of human travel; for instance, most people would probably like to travel the short distances to neighboring places by car whereas some people might prefer to travel long distances to far places by flying, and this argument has also been suggested by other studies [2,18]. On the other hand, the individual preferential behavior reflects Figure 11.…”

“…In this respect, we come up with another assumption: that the human preferential selection of available resources might also have a non-negligible influence on the mobility pattern. Our assumptions seem to be more similar to the hypotheses given by [2] and [18] than the others [3,19]. This paper thereby sets up two steps for verifying these assumptions.…”

“…This is a relatively partial approach since some people may prefer to choose the destination according to its priority. Han et al [18] proposed a hierarchical model based on a square lattice to examine human mobility. Their model considered the priority of choosing the next location and captured well the scaling law of human displacement, and importantly they attributed the scaling property to the hierarchical organization of the traffic system.…”

The scaling of human mobility by taxis is exponential

“…The authors also propose a new model to characterize human mobility patterns [20]. Han et al [21] demonstrate that the scaling law in human mobility could be explained by hierarchy of the traffic systems.…”

Power law and small world properties in a comparison of traffic city networks

“…Guimera et al [25] showed that the worldwide air traffic network was a scale-free and small world network. Wang et al [26] proposed a hierarchical geographical model to mimic a real traffic system, upon which a random walk generates a power-law-like travel displacement distribution with tunable exponent. Li and Cai [16] showed that the topological structure of the air traffic network of China (ANC) had two key characteristics of smallworld networks, a short average path-length and a high degree of clustering.…”