Analysis of Connectivity and Capacity in 1-D Vehicle-to-Vehicle Networks.

A vehicle-to-vehicle (V2V) network is one type of mobile ad hoc network. Due to mobility, the topology in a V2V network is time-varying, which complicates the analysis and evaluation of network performance. In this paper, we model the network as geometric elements of lines and points and analyze the connectivity and capacity of the network using geometric probability. Under the assumption that $n$ vehicles randomly arrive with a Poisson distribution, our analysis shows that the spatial distribution of vehicles within a given distance $D$ , is uniform and that the average number of vehicles to be fully connected is approximately $({1}/{a})( \\log {({1}/{a})} + \\log \\log {({1}/{a})} )$ for $a={R_{T}}/{D}$ , where $R_{T}$ is the maximum transmission range of a vehicle. When a random access scheme is adopted, only $({1}/{2})(1-e^{-2})n$ of links comprised of two adjacent nodes are simultaneously activated, on average, so the expected network capacity increases in a way linearly proportional to $({1}/{2})(1-e^{-2})$ as the number of vehicles increases. Through numerical studies and simulations, we verify the efficacy of our analytical results.