Multicast capacity for hybrid wireless networks

We study the multicast capacity of a random wireless network consisting of ordinary wireless nodes and base stations, known as a hybrid network. Assume that n ordinary wireless nodes are randomly deployed in a square region and all nodes have the uniform transmission range r and uniform interference range R > r. We further assume that each ordinary wireless node can transmit/receive at W bits/second over a common wireless channel. In addition, there are m additional base stations (neither source nodes nor receiver nodes) placed regularly in this square region and connected by a high-bandwidth wired network. For each ordinary node v, we randomly pick κ - 1 nodes from the other n - 1 ordinary nodes as the receivers of the multicast session rooted at node v. The aggregated multicast capacity is defined as the total data rate of all multicast sessions in this hybrid network. We derive asymptotic upper bounds and lower bounds on multicast capacity of the hybrid wireless networks. The total multicast capacity is O(√n/√log n · √m/κ · W) when κ = O(n/log n), κ = O(m), κ/√m → ∞ and m = o(α²/r²); the total multicast capacity is Θ (√n/√log n · w/√κ) when κ = O(n/log n), κ = Ω(m) and m/κ → 0. When κ = O(n/log n) and κ = O(√m), the upper bound for the minimum multicast capacity is at most O(r·n/α · √m · W/κ) and is Ω(W) respectively. When κ = Ω(n/log n), the multicast capacity is Θ(W).