Multicast Capacity for VANETs With Directional Antenna and Delay Constraint Under Random Walk Mobility Model

In this paper, we investigate the multicast capacity for vehicular ad hoc networks with directional antennas and the end-to-end delay constraint. We consider a torus of unit area with $n$ vehicles (nodes), there are $n_{s}$ multicast sessions and each session contains one source vehicle which is associated with $p$ destinations. We study the 2D and 1D random walk mobility models with two different time scales, i.e., fast and slow mobility. Given a delay constraint $D$ and assuming that each vehicle is equipped with a directional antenna, we obtain the multicast capacity of the two mobility models with two different time scales in the order of magnitude, respectively. We then characterize the impact of the network parameters (i.e., the end-to-end delay constraint $D$ , the beamwidth of directional antenna $\theta$ , and the number of destinations $p$ in each session) on the multicast capacity. Moreover, we find that the unicast capacity can be considered as a special case of our multicast results when the beamwidth of directional antenna $\theta$ tends to $2\pi$ and the number of destinations $p$ tends to 1 in the sense of probability.