Power law and exponential decay of inter contact times between mobile devices

TLDR

In many studies, inter‑contact time distributions follow a power law up to a characteristic time, beyond which they decay exponentially. The study investigates the fundamental properties that determine performance metrics for opportunistic communications. The authors analyze inter‑contact time distributions from diverse mobility traces and conduct extensive human‑mobility analyses, showing that return times to preferred locations explain the observed power‑law/exponential dichotomy. They find a characteristic half‑day time after which inter‑contact times decay exponentially, confirm that simple mobility models reproduce this dichotomy, and suggest that prior power‑law‑based forwarding performance estimates may be overly pessimistic.

Abstract

We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of inter-contact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the distribution decays exponentially. Up to this value, the distribution in many cases follows a power law, as shown in recent work. This powerlaw finding was previously used to support the hypothesis that inter-contact time has a power law tail, and that common mobility models are not adequate. However, we observe that the time scale of interest for opportunistic forwarding may be of the same order as the characteristic time, and thus the exponential tail is important. We further show that already simple models such as random walk and random way point can exhibit the same dichotomy in the distribution of inter-contact time ascin empirical traces. Finally, we perform an extensive analysis of several properties of human mobility patterns across several dimensions, and we present empirical evidence that the return time of a mobile device to its favorite location site may already explain the observed dichotomy. Our findings suggest that existing results on the performance of forwarding schemes basedon power-law tails might be overly pessimistic.