ADDENDUM Details of the Derivation of the Probability of Coverage for the Relaying Scheme (Section IV in the paper: "A Poisson Line Process based Framework for Determining the Needed RSU Density and Relaying Hops in Vehicular Networks'') (2006.11434v1)

Abstract: This paper develops a framework to study multi-hop relaying in a vehicular network consisting of vehicles and Road Side Units (RSUs), and the effect of this relaying on the network coverage and the communication delay. We use a stochastic geometry model that consists of a combination of Poisson Line Process (PLP) and 1D Poisson Point Process (PPP) to reliably characterize the vehicular network layout and the locations of the vehicles and the RSUs. Using this model, we analyze the effect of the different network parameters on the coverage provided by the RSUs to the vehicles. Then, we investigate how the uncovered vehicles can receive their intended packets by relaying them through multiple hops that form connected paths to the RSUs. We also analyze the delay introduced to packet delivery due to multi-hop relaying. Namely, we present results that illustrate the coverage gains achieved through multi-hop relaying and the delays induced. Such results could be used by network planners and operators to decide on the different configurations and operational parameters of the vehicular network to suit particular scenarios and objectives.