1Node Density and Delay in Large-Scale Wireless Networks with Unreliable Links

Abstract—We study the delay performance in large-scale wire-less multi-hop networks with unreliable links from percolation perspective1. Previous works [12][3][11] have showed that the end-to-end delay scales linearly with the source-to-destination distance, and thus the delay performance can be characterized by the delay-distance ratio . However, the range of , which may be the most important parameter for delay, remains unknown. We expect that may depend heavily on the node density of a wireless multi-hop network. In this paper, we investigate the fundamental relationship between and . Obtaining the exact value of () is extremely hard, mainly because of the dynamically changing network topologies caused by the link unreliability. Instead, we provide both upper bound and lower bound to the delay-distance ratio (). Simulations are conducted to verify our theoretical analysis. Index Terms—Connectivity, Delay, Density I