Delay and Capacity Trade-offs for Wireless Ad Hoc Networks with Random Mobility

In this paper, we study the delay and capacity trade-offs for wireless ad hoc networks with random mobility. We consider some simple distributed scheduling and relaying protocols that are motivated by the 2-hop relaying protocol proposed by Grossglauser and Tse (2001). We consider a model in which the nodes are placed uniformly on a sphere, and move in accordance with an i.i.d. mobility model. We consider two i.i.d mobility models: Brownian mobility model and random way-point mobility model. We show that under a distributed Grossglauser-Tse 2-hop relaying protocol, the delay scales as Θ(Tp(n)n) for random way-point mobility model, and O(Tp(n) log 2 n) for Brownian mobility model, where Tp(n) is the transmission time of the packet. In the case, where only nearest neighbor transmissions are allowed, the delay is shown to scale as Ω(Tp(n) √ n), for all possible scheduling and relaying protocols. In the case of random way-point mobility model, we show that delay/capacity ≥ Θ(Tp(n)n) is a necessary trade-off. Two protocols which achieve the lower bound of Θ(Tp(n)n) are considered, and their relative performance in terms of delay/capacity trade-off is established. Our results indicate that significant improvement in the delay can be achieved by reducing the packet size, at high node speeds.