Researchers find that human walks resemble levy walk patterns

An empirical study revealed that human walks resemble statistical movement patterns known as Levy walk, yielding atypical supper-diffusive mobility.

Article  |  Spring 2014

Researchers in KAIST and North Carolina State University have reported that human walk patterns contain statistically similar features observed in a stochastic model known as Levy walk. These features include heavy-tail flight distributions and, consequently, a super-diffusive nature of mobility. A flight is defined as the longest straight-line trip of a human from one location to another without a directional change or pause. The study was based on 226 daily GPS traces collected from over 100 volunteers in five different outdoor sites: two university campuses (KAIST and North Carolina State University), one metropolitan area (New York City), one theme park (Disney World), and one state fair.

Commonly-used mobility models in many scientific and engineering disciplines include random walk models such as Brownian motion and Markovian mobility. These models are simple enough to be theoretically tractable and, at the same time, to be emulated in a scalable manner. However, no empirical evidence has been found so far to prove the accuracy of such models in representing human walk patterns. In physics, Brownian motion is used to characterize the diffusion of tiny particles. Einstein first showed that the probability of such a particle being at distance r from the initial position after time t follows a Gaussian distribution, and consequently, the mean squared displacement, which is a measure of the average displacement of a given object from the origin, is proportional to t. This mobility is said to have normal diffusion. Many objects in the physical world undergo normal diffusion. For example, when sugar dissolves in a cup of still water, sugar particles undergo normal diffusion.

Physicists have found that there are other objects in the physical world whose mobility cannot be characterized by normal diffusion. Levy walks are one of the random walk models that describe such atypical mobility undergoing super-diffusion, as their mean square displacement increases super-linearly with respect to time t. Typically, turbulent flows are super-diffusive. For example, when sugar dissolves in a cup of stirred water, it undergoes super-diffusion. The super-diffusive nature of Levy walks results from the heavy-tail distribution of their constituent flights. Intuitively, Levy walks consist of many short flights and occasionally long flights. See an illustrated comparison of Brownian motion and Levy walk motion in Figures (a) and (b).

The research team made up of members from KAIST and North Carolina State University also demystified the Levy walk nature of human walking patterns. They showed that the heavy-tail flight patterns are in fact caused by the power-law dispersion of waypoints, which are typical in cities and towns.

This new finding on human mobility provides insight for research in a variety of fields, ranging from urban planning to mobile networking to epidemic disease outbreaks.

“On the Levy-Walk Nature of Human Mobility” was published in the June 2011 issue of IEEE/ACM Transaction on Networking.

by Professor Song Chong (Department of Electrical Engineering)