Distributional Convergence of Inter-Meeting Times Under Generalized Hybrid Random Walk Mobility Model

Abstract

The performance of a mobile wireless network depends on the time-varying connectivity of the network as nodes move around. Therefore, there has been a growing interest in the distribution of inter-meeting times between two nodes in mobile wireless networks. We study the distribution of inter-meeting times under the (generalized) Hybrid Random Walk mobility model. We show that when the (conditional) probability that the two nodes can communicate directly with each other given that they are in the same cell is small, the distribution of inter-meeting times can be well approximated using an exponential distribution. In addition, the mean of the inter-meeting 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 show that such an approximation does not hold for the Random Walk mobility model.