1Mobility Increases the Connectivity of Wireless Networks

Abstract—In this paper we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in k-hop clustered networks, and compare to existing results on non-clustered stationary networks. By introducing k-hop clustering, any packet from a cluster member can reach a cluster head within k hops, and thus the transmission delay is bounded as (1) for any finite k. We first characterize the critical transmission range for connectivity in mobile k-hop clustered networks where all nodes move under either the random walk mobility model with non-trivial velocity or the i.i.d. mobility model. By the term non-trivial velocity, we mean that the velocity of a node v is! r(n), where r(n) is the transmission range of the node. We then compare with the critical transmission range for stationary k-hop clustered networks. In addition, the critical number of neighbors is studied in a parallel manner for both stationary and mobile networks. We also study the transmission power versus delay trade-off and the average energy consumption per flow among different types of networks. We show that random walk mobility with non-trivial velocities increases connectivity in k-hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay trade-off. The decrease of energy consumption per flow is shown to be logn nd in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network. I