Fundamental relationship between NodeDensity and delay in wireless ad hoc networks with unreliable links

We investigate the fundamental relationship between node density and transmission delay in large-scale wireless ad hoc networks with unreliable links from percolation perspective. Previous works[11][2][10] have already showed the relationship between transmission delay and distance from source to destination. However, it still remains as an open question how transmission delay varies in accordance with node density. Answering this question can provide guidance for determining the number of nodes to meet the delay requirement when designing ad hoc networks. In this paper, we study the impact of node density λ on the ratio of delay and distance, denoted by γ(λ). We analytically characterize the properties of γ(λ) as a function of λ. And then we present upper and lower bounds to γ(λ). Next, we take propagation delay into consideration and obtain further results on the upper and lower bounds of γ(λ). Finally, we make simulations to verify our theoretical analysis.