Power Law and Exponential Decay of Intercontact Times between Mobile Devices

TLDR

Prior work shows that intercontact times between mobile devices follow a power‑law distribution up to about half a day, challenging the adequacy of common mobility models. The study investigates which properties govern performance metrics in opportunistic communications. The authors analyze intercontact time distributions and human mobility patterns, showing that return times to preferred locations may explain the observed power‑law to exponential transition. Empirical traces reveal a half‑day characteristic time after which intercontact times decay exponentially, a behavior also seen in simple mobility models, implying that the exponential tail—often overlooked—may make opportunistic forwarding less pessimistic than previously thought.

Abstract

We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of intercontact 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 power law finding was previously used to support the hypothesis that intercontact time has a power law tail, and that common mobility models are not adequate. However, we observe that the timescale 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 waypoint can exhibit the same dichotomy in the distribution of intercontact time as in 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 based on power law tails might be overly pessimistic.