Demystifying Levy Walk Patterns in Human Walks

This paper reports that bursty hot spot sizes are a key factor in causing the heavy-tail distribution of flights in human walks. A heavy-tailed distribution of flights is a signature feature of Levy walks. The data analysis based on GPS traces of human walks reveals that the sizes of a few extremely large hot spots are dominating the mean size of hot spots and they cause the bursty (i.e., long-range dependent) dispersion of visit points where people make a stop. Bursty visit points cause the characteristic distance among visit points to have a heavy-tail distribution. On top of bursty visit points, humans perform a distance-optimizing algorithm to plan their trips much like a heuristic to the traveling salesman problem. These factors in combination make human walks to have a heavy-tailed flight distribution. The above findings enable the construction of a simple human mobility model that taking as input the degree of burstiness in visit point dispersion, can naturally emulate hot spots as well as a heavy-tail flight distribution, both known to be important in measuring the realistic performance of mobile networks.