Crossing over the bounded domain: from exponential to power-law intermeeting time in mobile ad hoc networks

Intermeeting time between mobile nodes is one of the key metrics in a mobile ad hoc network (MANET) and central to the end-to-end delay of forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: The intermeeting time distribution, in fact, follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution of the intermeeting time and, thus, calls for further study on the power-law intermeeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the intermeeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the intermeeting time. We then discuss the relationship between the size of the boundary and the relevant timescale of the network scenario under consideration. Our results thus provide guidelines on the mobility modeling with power-law intermeeting time distribution, new protocols including packet-forwarding algorithms, as well as their performance analysis.