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 hoc networks following the 2-hop relaying algorithm proposed by Grossglauser and Tse (2001). We assume the nodes to be uniformly distributed 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 hoc network formed by n mobile nodes the delay scales as O (log²n/σ²(n)) under the BMM, and, Θ (1/r(n)v(n)) under the RWMM, where σ²(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.