Multicast Capacity for Hybrid MANETs with Direction Antenna and Delay Constraint

We study the multicast throughput capacity for hybrid wireless mobile ad hoc networks (MANETs) with a directional antenna and delay constraint. The hybrid wireless network consists of a mobile ad hoc network with $n$ nodes and $m$ regularly placed base stations connected by high-bandwidth wired links. For the MANET, there are $n_s$ multicast sessions and each multicast session has one source which transmits identical informations to its associated $p$ destinations. Assuming that the mobile nodes adopt 2D-i.i.d. mobility model, we investigate the ad hoc mode multicast throughput capacity when each node is equipped with a directional antenna along with a tolerant delay $D$. That is, a source node transmits to its $p$ destinations only with the help of normal nodes within $D$consecutive time slots. Otherwise, the transmission will be switched to the infrastructure mode, where the base stations serve as relays. We find that the multicast throughput capacity of a hybrid wireless MANETs greatly depends on the delay constraints $D$, the number of base stations $m$, and the beamwidth of directional antenna $\theta$. We show that the multicast throughput capacity of the hybrid directional wireless network is $\Theta(\sqrt{\theta})+\Theta(\frac{m}{n_sp}W_2)$ bits/sec, if $D=\Omega(\frac{n_s}{(\log p)^2(\log(\theta n_sp))^2})$; $\Theta(\frac{m}{n_sp}W_2)$ bits/sec, if $D=O(\sqrt[3]{\frac{n_s}{(\log p)^2(\log(\theta n_sp))^2}})$; and $O((\log p)(\log(\theta n_sp))\sqrt{\frac{\theta D}{n_s}})+\Theta(\frac{m}{n_sp}W_2)$ bits/sec, otherwise. We analyze the impact of $D$, $m$ and $\theta$ on the multicast throughput capacity of the hybrid MANET. Finally, we derive lower bound of the muticast throughput using a similar raptor coding approach as in\cite{ZY10}.