Degenerate delay-capacity tradeoffs in ad-hoc networks with Brownian mobility

There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this correspondence, the fundamental tradeoff between the capacity and delay for a mobile ad hoc network under the Brownian motion model is studied. It is shown that the two-hop relaying scheme proposed by Grossglauser and Tse (2001), while capable of achieving a per-node throughput of Θ(1), incurs an expected packet delay of Ω(logn/σ_n²), where σ_n² is the variance parameter of the Brownian motion model. It is then shown that an attempt to reduce the delay beyond this value results in the throughput dropping to its value under static settings. In particular, it is shown that under a large class of scheduling and relaying schemes, if the mean packet delay is O(n^α/σ_n²), for any α<0, then the per-node throughput must be O(1/√n). This result is in sharp contrast to other results that have recently been reported in the literature.