On the Connectivity of Large-Scale Hybrid Wireless Networks

Abstract-Many real systems are hybrid networks which include infrastructure nodes in multi-hop wireless networks, such as sinks in sensor networks and mesh routers in mesh networks. However, we have very little understanding of network connectivity in such networks. Therefore, in this paper, we consider hybrid networks denoted by H(α, β) with ad hoc nodes and base stations and prove how base stations can improve the connectivity of ad hoc nodes in subcritical phase, that is, the ad hoc node density, λ_α is lower than the critical density λ_α^c. We first study the impact of density of base stations, λ_β on the connectivity, and find that with the existence of a positive density of base stations which have the same transmission range as ad hoc nodes, i.e., λ_β > 0, the number of connected ad hoc nodes is Θ(n) with probability nearly 1, where n is the number of ad hoc nodes. However, the size of connected ad hoc component scales linearly with λ_β with probability nearly 1 when λ_β is lower than c₁(λ_α). We then study the impact of transmission range of base stations, τ_β on the connectivity, and find the additional benefit of enlarging r_β to enhance the connectivity of ad hoc nodes.