Abstract-IEEE 802.11p and 1609 standards are currently under development to support Vehicle-to-Vehicle and Vehicleto-Infrastructure communications in vehicular networks. For infrastructure-based vehicular relay networks, access probability is an important measure which indicates how well an arbitrary vehicle can access the infrastructure, i.e. a base station (BS). On the other hand, connectivity probability, i.e. the probability that all the vehicles are connected to the infrastructure, indicates the service coverage performance of a vehicular relay network. In this paper, we develop an analytical model with a generic radio channel model to fully characterize the access probability and connectivity probability performance in a vehicular relay network considering both one-hop (direct access) and two-hop (via a relay) communications between a vehicle and the infrastructure. Specifically, we derive close-form equations for calculating these two probabilities. Our analytical results, validated by simulations, reveal the tradeoffs between key system parameters, such as inter-BS distance, vehicle density, transmission ranges of a BS and a vehicle, and their collective impact on access probability and connectivity probability under different communication channel models. These results and new knowledge about vehicular relay networks will enable network designers and operators to effectively improve network planning, deployment and resource management.Index Terms-Vehicular Ad Hoc Network (VANET), Wireless Access in Vehicular Environments (WAVE), IEEE 802.11p, IEEE 1609, access probability, connectivity, relay.

In this paper we investigate the critical node density required to ensure that an arbitrary node in a large-scale wireless multi-hop network is connected (via multi-hop path) to infinitely many other nodes with a positive probability. Specifically we consider a wireless multi-hop network where nodes are distributed in R d (d = 2, 3) following a homogeneous Poisson point process. The establishment of a direct connection between any two nodes is independent of connections between other pairs of nodes and its probability satisfies some intuitively reasonable conditions, viz. rotational and translational invariance, nonincreasing monotonicity, and integral boundedness. Under the above random connection model we first obtain analytically the upper and lower bounds for the critical density. Then we compare the new bounds with other existing bounds in the literature under the unit disk model and the log-normal model which are special cases of the random connection model. The comparison shows that our bounds are either close to or tighter than the known ones. To the best of our knowledge, this is the first result for the random connection model in both 2D and 3D networks. The result is of practical use for designing large-scale wireless multihop networks such as wireless sensor networks.

Abstract-Coverage is an important problem in wireless networks. Together with the access probability, which measures how well an arbitrary user can access a wireless network, in particular VANET, they are often used as major indicators of the quality of the network. In this paper, we investigate the coverage and access probability of the vehicular networks with roadside infrastructure, i.e. base stations. Specifically, we analyze the relation between these key parameters, i.e. the coverage range of base stations, coverage range of vehicles, vehicle density and distance between adjacent base stations, and how these parameters interact with each other to collectively determine the coverage and the access probability. We use the connectivity probability, the probability that all nodes in the network are connected to at least one base station within a designated number of hops, as a measure of the coverage. We derived close-form formulas for the connectivity probability and the access probability for a 1D vehicular network bounded by two adjacent base stations. The analytical results have been validated by simulations. The results in the paper can be used by network operators to design networks with specific service coverage guarantees.Index Terms-Vehicular Ad Hoc Network (VANET), Wireless Access in Vehicular Environments (WAVE), IEEE 802.11p, access probability, connectivity, relay.