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 k 2 [1,n], where n ad hoc nodes are uniformly distributed and m base stations (BSs) are regularly placed in a square region Aðn;AÞ 1⁄4 1; ffiffiffi A p h i $ 1; ffiffiffi A p h i with A 2 [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 2 [1,n] and d 2 [1,n], as n ?1. 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 k 1⁄4 n A, 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. ! 2011 Elsevier B.V. All rights reserved.