An accurate and analytically tractable model for human inter-contact times

Abstract

We present an analytically tractable mathematical approach for accurately modeling the distribution of inter-contact times between mobile devices carried by users. The contribution of this paper is two-fold: (1) we show how to employ a Markov-modulated Poisson process (MMPP) for characterizing long-term dependencies in the mobility behavior, and (2) we propose to employ a graph-based clustering approach for taking into account different user groups with inhomogeneous mobility patterns. We illustrate the effectiveness of the proposed approach by considering two comprehensive real-world trace data sets. The presented quantitative results show that the proposed modeling approach closely approximates the dichotomy of the distribution of human inter-contact times into an exponential and power-law distribution observed in recent studies of real-world trace data. As the presented modeling approach for inter-contact times is both analytically tractable and captures long-term dependencies in the mobility behavior, it possesses clear advantages over methods previously introduced for analyzing the performance of opportunistic networking protocols.