On multicast throughput scaling of hybrid wireless networks with general node density

In this paper, we consider hybrid wireless networks with a general node density λ ∈ [1, n], where n ad hoc nodes are uniformly distributed and m   base stations (BSs) are regularly placed in a square region A(n,A)=1,A×1,A with A ∈ [1, n]. We focus on multicast sessions in which each ad hoc node as a user chooses randomly d ad hoc nodes as its destinations. Specifically, when d = 1 (or d = n − 1), a multicast session is essentially a unicast (or broadcast) session. We study the asymptotic multicast throughput for such a hybrid wireless network according to different cases in terms of m ∈ [1, n] and d ∈ [1, n], as n → ∞. To be specific, we design two types of multicast schemes, called hybrid scheme and BS-based scheme, respectively. For the hybrid scheme, there are two alternative routing backbones: sparse backbones and dense backbones  . Particularly, according to different regimes of the node density λ=nA, we derive the thresholds in terms of m and d. Depending on these thresholds, we determine which scheme is preferred for the better performance of network throughput.