Distributional Convergence of Intermeeting Times under the Generalized Hybrid Random Walk Mobility Model

The performance of a mobile wireless network depends on the time-varying connectivity of the network as nodes move around. Hence, there has been a growing interest in the distribution of intermeeting times between two nodes in mobile wireless networks. We study the distribution of intermeeting times under the generalized Hybrid Random Walk mobility model. We show that when 1) the (conditional) probability that two nodes can communicate directly with each other given that they are in the same cell is small and 2) node's transitions in locations are independent over time, the distribution of intermeeting times can be well approximated using an exponential distribution. Moreover, the mean of intermeeting times can be estimated using the number of cells in the network and the aforementioned conditional probability of having a communication link when the two nodes are in the same cell. We also offer some insight behind the emergence of an exponential distribution, borrowing well-known results in existing literature on rare events.