Multicast capacity scaling for inhomogeneous mobile ad hoc networks

We study multicast capacity for a large-scale spatial inhomogeneous mobile network consisting of n ad hoc nodes. Under our mobility model, the stationary spatial distribution of a node is non-uniform; each node spends most of the time in a certain region, and rarely (or never) visits out of such region. To characterize the inhomogeneity of the mobility model, we define an activity exponent c and two clustering parameters (m(n),r(n)), where c 2 [0,1] measures the strength of node mobility, m(n) denotes the number of clusters, r(n) denotes the radius of the cluster. We classify the mobility into two cases according to the strength of mobility of each node, called strong and weak mobility, respectively. Two corresponding scheduling schemes and routing policies combined with the Manhattan multicast tree method are proposed. Suppose there are ns = H(n) multicast sessions. Each source has nd destinations which are selected randomly and independently. We show that under strong mobility case, the per-node multicast capacity is 1 ffiffiffiffi nd p !ðnÞ " # with !ðnÞ 1⁄4 n 1$" 2 ; under weak mobility case, when nd 1⁄4 O mðnÞ log mðnÞ " # , the multicast throughput is 1ffiffiffiffi nd p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mðnÞ n2 log mðnÞ q " # ; when nd 1⁄4 mðnÞ log mðnÞ " # , the multicast throughput is n $ % . Particularly, as a special case, i.e., by letting nd = 1, our results unify the previous unicast capacity bounds. ! 2012 Elsevier B.V. All rights reserved.