Scaling laws for capacity and delay in wireless ad hoc networks with random mobility

We study the asymptotic throughput capacity and delay in mobile ad hoe networks following the 2-hop relaying algorithm proposed by Grossglauser and Tse (2001). We assume the nodes to be distributed uniformly on a sphere, and consider two canonical mobility models: the Brownian mobility model (BMM), and the random way-point mobility model (RWMM). We show that for an ad hoe network formed by n mobile nodes the delay scales as O(log(2)n/sigma(2)(n)) under the BMM, and e under the RWMM, where sigma(2)(n) is the variance parameter of the BMM, v(n) is the average speed of nodes under the RWMM, and r(n) is the communication radius of the nodes.