Asymptotic upper bound on the packet propagation speed in WANETs with directional antennas

The lack of understanding on the fundamental performance limits is a major obstacle stunting the application of wireless ad hoc networks (WANETs). The upper bound on the packet propagation speed, an important component of the performance limits, has recently attracted a lot of academic interest. While the metric has been investigated for several network scenarios, two important aspects remain unexplored. The first one is that the impact of local delay on packet propagation speed is largely neglected and the other one is that the packet propagation speed remains unknown when using directional antennas. In this paper, we consider a WANET, where opportunistic aloha with transmission probability p is adopted for packet delivery and each node equips a general directional antenna for data transmission. We first derive the coverage probability in the considered network and then proceed to analyze the asymptotic upper bound on the packet propagation speed. Simulation and numerical studies are also conducted to validate and illustrate the theoretical results. Our results show that there exists a threshold of transmission probability, independent of node density and antenna pattern, above which the upper bound is zero. Below the threshold, the upper bound is a positive constant; furthermore, using directional antenna can provide a performance improvement, which increases as the antenna directivity increase.